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date: 26 June 2019

Abstract and Keywords

The principle that every statement is bivalent (i.e. either true or false) has been a bone of philosophical contention for centuries, for an apparently powerful argument for it (due to Aristotle) sits alongside apparently convincing counterexamples to it. This chapter analyzes Aristotle’s argument, then, in the light of this analysis, examines three sorts of problem case for bivalence. Future contingents, it is contended, are bivalent. Certain statements of higher set theory, by contrast, are not. Pace the intuitionists, though, this is not because excluded middle does not apply to such statements, but because they are not determinate. Vague statements too are not bivalent, in this case because the law of proof by cases does not apply. The chapter goes on to show how this opens the way to a solution to the ancient paradox of the heap (or Sorites) that draws on quantum logic.

Keywords: bivalence, future contingents, Continuum Hypothesis, Georg Kreisel, vagueness, quantum logic, paradox of the heap, Sorites paradox

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