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Abstract
The phenomenon of first-order vagueness is characterized by predicates that lead to borderline utterances that seem to violate bivalence. A closely related phenomenon is higher-order vagueness. That is, it might be unclear whether a case is a borderline case of baldness.
In Chapter 1, I introduce the phenomenon of vagueness.
In Chapter 2, I show that Timothy Williamson's two reductio proofs that purport to show that all our utterances must have precise (and unknowable) boundaries fail. I argue that one can coherently deny bivalence by recognizing that the proper characterization of bivalence involves the use of two distinct extensions of classical negation.
In Chapter 3, I argue that supervaluationism is not a viable theory. My main argument is that the supervaluationist's claim that we can sharpen our truth-valueless utterances so that they can be classified as either true or false leads, contrary to the supervaluationists claim of a sparse ontology, to semantic extravagance: there will be a multiplicity of sharp expressions for every vague utterance.
In Chapter 4, I argue that nihilism can be resisted by showing that the problem of the many has nothing to do with the sorites paradox but with reference.
In Chapter 5, I argue for the novel view that ontological vagueness should be understood as vague unity relations.
In Chapter 6, I argue that our use of vague utterances are sufficiently illuminated by the practice of assigning grades. This gives us evidence for my anti-bivalentist position without involving any ignorance. I defuse the sorites paradox (and higher-order vagueness), explain the semantics of my third truth-value, b, and explain why we are attracted to sorites reasoning in virtue of subjunctive, not indicative conditionals.
