- In the classical conception, it is no accident that a concept draws sharp boundaries. Concepts are used in classification, classification is the assignment of things to classes, and classes are sharp: for any class and any object, there is a definite fact of the matter whether or not the latter belongs to the former. A concept must have sharp boundaries because there are no such things as unsharp boundaries: the extension of a concept is like a geometrical area and there is no such thing as an unsharp area. In applying a concept in a simple sentence, we select a single possible state of affairs and exclude all others, and this presupposes a sharp demarcation between states of affairs, and thus between things which fall under a concept and things which do not.
- The classical conception finds vagueness a problem: at best an aberration, at worst (as Frege is reputed to have believed) an impossibility and therefore an illusion. Those who argue that vague predicates are incoherent are, conditionally, right: vague predicates are incoherent if the classical conception is correct. So we must either turn our backs upon vague predicates, or else upon the classical conception. My preference is for the latter. In this paper I show how the concessive classicist - one who would try to find a place for vagueness within the classical landscape - is forced to misunderstand vagueness; and I gesture towards a non-classical way of looking at concepts and classification, a way upon which vagueness is the norm, and sharpness an artefact.
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