A predicate is vague if its extension lacks sharp boundaries, if there are "borderline" cases, cases where it's unclear whether the predicate applies. Vagueness is a pervasive feature of natural language, but it has proven resistant to satisfying theoretical delineation. For any attempt to characterize the semantics and logic of vague terms (that is, any attempt to characterize what they mean and what reasoning involving them is valid) must yield a compelling solution to the Sorites Paradox. Here's a version of the paradox using the vague term 'bald': Someone with no hairs is bald. But one hair can't make the difference between being bald and not being bald. (That is, for any number n, if someone with n hairs is bald, so is someone with n+1 hairs.) So, someone with 1,000,000 hairs is bald. It's clear that something has gone badly wrong here, but it turns out not to be so easy to say just what.

This talk will provide an "invitation" to vagueness by critically surveying the most important approaches to the subject currently being pursued, including many-valued semantics (an example of which is "fuzzy logic"), supervaluationist semantics, epistemicism, and contextualist accounts.