Vagueness and Logic

The plan of this survey is to discuss the sort of model-theory that is suggested (or demanded) by the main, rival accounts of vagueness, and to thereby delineate the logic of each. I will try to indicate, in each case, what the logic would be if the account in question were correct. Since the main logical problem facing vagueness is the sorites paradox, the present survey assesses what each account has to say about typical sorites arguments. Nihilistic and epistemicist accounts do not demand any change in the model theory. Supervaluationist and some contextualist accounts require the introduction of partial interpretations and sharpenings. Subvaluationist and some inconsistency accounts are dual to this, and also make use of partial interpretations and sharpenings. The model theories for some many-valued accounts are also sketched, including a boolean valued account that sanctions classical logic. The resolution of higher-order vagueness is also briefly treated.