Vagueness Through Definitions

At the basis of categorization theory stands the difference between sharp and vague concepts. Sharp concepts are those for which categorial membership is an all-or-nothing matter: a given object falls or does not fall under a sharp concept, and no intermediate state is conceivable. For vague concepts, on the contrary, intermediate states are possible, and categorial membership becomes a matter of degree. This definition of vagueness as opposed to sharpness conceals the fact that this notion is by no means a uniform one, and that different types of vagueness coexist. The treatment of vague concepts therefore depends of the type of vagueness these concepts instantiate. In this paper, we restrict our attention to the family of concepts that are learnt and known through a list of defining features. Partial membership to the corresponding category then results from partial membership relative to its defining features. In this elementary type of vagueness, we show that the categorization process is fully accounted for by the construction of a membership order among the objects at hand, which, naturally defined for simple concepts, can be easily extended to compound concepts, thus providing an interesting solution to the problem of compositionality.