Supernumeration: Vagueness and Numbers
There is a notable discrepancy between philosophers and practitioners on approaches to vagueness. Philosophers almost all reject fuzzy logic and a majority accept some form of supervaluational theory. Practitioners analysing real data, on the other hand, use fuzzy logic, because computer algorithms exist for it despite its theoretical shortcomings. These two communities should not remain separate. This chapter argues that the solution is to put supervaluation and numbers together. After reviewing the principal and well-known defects of fuzzy logic, it shows how to use numerical values in conjunction with a supervaluational approach to vagueness. The two principal working ideas are degrees of candidature (of objects and predicates) and expected truth-value. The chapter presents an outline of the theory, which combines vagueness of predicates and vagueness of objects, and discusses its pros and cons, considering the obvious principal objections: that the theory is complex, that there is arbitrariness in the selection of numbers, and that penumbral connections must be accounted for. The chapter contends that all these objections can be answered.
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