Vagueness is related to the existence of borderline cases, and its incidence permeates both science and metaphysics.
Theories and accounts of vagueness try to find a solution to the problem of how to treat predicates such as “is bald” or “moves in a straight line”, both in natural language and in scientific theories. Is vagueness an epistemological problem? Is all vagueness linguistic? Could there be intrinsically vague objects? What logical tools may help in formalizing and resolving the paradoxes of vagueness? Is vagueness equally unavoidable in the scientific language?
Discussion of vagueness may equally arise in the context of the philosophy of mathematics, where the term ‘indeterminacy’ is often preferred. Are our mathematical terms determinate? How can we guarantee that arithmetic is determinate? Could set theory be indeterminate, in light of independence results? Is the Continuum Hypothesis a case of indeterminacy in mathematics? Moreover, the problem of indeterminacy spans quantum mechanics as well, presented, for instance, in the form of the so-called measurement problem. How can we make sense of quantum indeterminacy? Does contemporary physics provide a complete, deterministic picture of physical reality?