This thesis deals with three interconnected questions: What does it mean to say that an expression is vague? Could there be 'higher-order' vagueness? And could there be a correct theory of the meaning of vague terms?
I argue that a traditional answer to the first question - that if an expression is vague, it has borderline cases and does not draw any knowable sharp boundaries - is incorrect. If this answer were correct, vague terms would exhibit higher-order vagueness. But I demonstrate a number of problems with this implication. I then put forward an alternative characterisation of vagueness: roughly, if a term is vague, speakers will fail to reach a certain kind of consensus on how that term is to be applied.
In answering the second question, I discuss some paradoxes that seem to emerge from the existence of higher-order vagueness. These paradoxes present a serious threat to the possibility of making sense of higher-order vagueness. I show that one such paradox can be generated using fewer resources than has previously been suggested, and so that this threat is greater than it may have seemed. I then argue that an attempt to avoid these paradoxes, Bobzien's 'columnar' theory of higher-order vagueness, fails to provide a plausible, or consistent, picture of higher-order vagueness.
Finally, I make use of my alternative characterisation of vagueness to argue that there is no correct semantics for vague terms. I discuss some ways in which theorists about vagueness could make sense of this, reflecting on the aims that we might have when approaching logic and semantics in the first place.
