Fuzziness as Multiplicity

Fuzziness is considered to be inherent to all empirical discourse, & its bearing on the notion of truth for empirical statements is examined. The domain of the interpretation of natural languages contains entities for which some predicates are not well defined. Can a model theoretic version of logical semantics be applied in such cases? The proposed solution interprets fuzzy predicates as classes of sets that would interpret the given predicate if it was not fuzzy. Fuzziness is interpreted as multiplicity. For a given predicate p, let P+ be the set of all positive instances of p, & let P- be the set of all negative instances of p, & P the set of all borderline cases. Then the interpretation of p is defined as the class of all sets that include P+ & exclude P-: note that this interpretation is defined in a nonconstructivist way. The interpretation of language L is no longer a structure, but a class of structures M. A notion of approximate truth is defined: a sentence (S) is approximately true if & only if s is true in some structure in M. A. Orianne