Comments on Fuzzy Logic and Higher-Order Vagueness by Nicholas J.J. Smith

Smith’s article Fuzzy logic and higher-order vagueness [12] presents a solution to the problem of artificial precision, encountered in the degree-theoretical semantics of vagueness. The solution is based on fuzzy plurivaluationism, which has been discussed in more detail in Smith’s book [11]. Within the degree-theoretical framework, fuzzy plurivaluationism is certainly the appropriate treatment of vague propositions: it has often been implicitly used by formal fuzzy logicians, too—namely, in their modeling of vague concepts by means of formal theories over fuzzy logic (see, e.g., [6, 7]). Such theories have (usually infinite) classes of models, which directly correspond to Smith’s fuzzy plurivaluations. I therefore very much welcome that thanks to Smith, the multi-model fuzzy semantics of vague predicates has been explicitly spelt out in philosophical terms and discussed in the context of the philosophy of vagueness. For the most part, Smith’s article [12] and book [11] only deal with fuzzy (plurivaluationistic) semantics of vague predicates, putting aside its logical aspects.1 Nevertheless, as I try to argue in this Comment, the logical facet of fuzzy plurivaluationism is quite relevant, and it supplements the fuzzy plurivaluationistic picture in important respects. In particular, it can play a rôle in the justification of fuzzy plurivaluationistic semantics, as well as in ascertaining an appropriate characterization of vagueness.