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Vagueness is the study of concepts that admit borderline cases: the property of being bald is vague because there are people who are neither definitely bald, nor definitely not bald. The epistemology of vagueness concerns the sorts of attitudes we ought to have towards propositions we know to be borderline. Is it possible to discover whether a borderline bald man is bald? Could two people with access to the same facts reasonably disagree about whether he is bald? Does it matter, when making practical decisions, whether he is bald? By drawing on such considerations, Andrew Bacon develops a novel theory of vagueness in which vagueness is fundamentally a property of propositions, and is explicated in terms of its role in thought. On this theory, language plays little role in explaining the central puzzles of vagueness. Part I of the book outlines some of the central questions regarding the logic and epistemology of vagueness, and criticizes some extant approaches to them. Part II concerns issues in the epistemology of vagueness, touching on the ramifications of vague thoughts on the study of evidence, ignorance, desire, probability theory, and decision theory. By examining the effects of vague information on one's beliefs about the precise, a positive theory of vagueness is proposed. Part III concerns the logic of vagueness, including the interaction between vagueness and modality, vague identity, and the paradoxes of higher-order vagueness. Bacon suggests that some familiar philosophical notions -- including the concept of a fundamental proposition, a possible world and a precisification -- need to be revised.