The Problem of the Many: Supervaluation, Rough Sets and Faultless Disagreement

In the paper I make three comments concerning the existing solutions to the problem of the many: supervaluationism, fuzzy sets and Lewis’s combined solution consisting of supervaluation and almost-identity. First, I try to defend supervaluationism from the charge that the precisifications it postulates are not admissible, because they do not preserve penumbral connections and clear cases. I argue that two types of vagueness should be distinguished and that the requirements that are imposed on precisifications postulated in one case do not apply in the other case. Next, concerning the solution advocating fuzzy sets I suggest that rough sets rather than fuzzy sets might be regarded as a good way of looking at composite objects. And finally, I point out to a surprising consequence of Lewis’s combined solution. Namely, in my view Lewis’s solution leads to the acceptance of faultless disagreements concerning the number of objects of the same type.