Intuitionism and the Sorites Paradox

This chapter revisits and further develops all the principle themes and concepts of the preceding chapters. Epistemicism about vagueness postulates a realm of distinctions drawn by basic vague concepts that transcend our capacity to know them. Its treatment of their subject matter is thus broadly comparable to the Platonist philosophy of mathematics. An intuitionist philosophy of vagueness, as do many philosophies of the semantics and metaphysics of vague expressions, finds this idea merely superstitious and rejects it. The vagueness-intuitionist, however, credits the epistemicist with a crucial insight: that vagueness is indeed a cognitive, rather than a semantic, phenomenon—something that is not a consequence of some kind of indeterminacy, or open-endedness in the semantics of vague expressions but rather resides in our brute inability to bring, for example, yellow and orange right up against one another, so to speak, so as to mark a sharp and stable boundary. A solution to the Sorites paradox is developed that is consonant with this basic idea but, by motivating a background logic that observes (broadly) intuitionistic restrictions on the proof theory for negation, allows us to treat the paradoxical reasoning as a simple reductio of its major premise, without the unwelcome implication, sustained by classical logic, of sharp cut-offs.