Abstract
The borderlineness operator can be given a relatively straightforward semantics in terms of the theory of precisifications. Without the assumption that vagueness can be analysed in terms of borderlineness, this machinery does not generalize particularly well to a semantics for vagueness. This chapter provides a novel semantics for vagueness in terms of symmetries: automorphisms on the set of propositions that preserve rational credences and values. It shows how the theory of propositional vagueness developed in Chapters 6, 8, and 10 can be unified under an analysis of vagueness in terms of symmetries. It then demonstrates that it is possible to define vagueness explicitly in terms of its role in thought.
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