Fuzziness in classical two-valued logic

Classical two-valued logic has been thought to be inadequate as a logic of fuzzy predicates, because the interpretation of a predicate in classical two-valued logic is just a set of objects, and a set is a precise mathematical entity with nothing fuzzy about it. The aim of this paper is to show that fuzziness may, after all, be successfully modelled in classical two-valued logic via (i) the introduction of a notion of weak negation, where natural language occurrences of `not´ are not necessarily translated into logic as `~´, and (ii) giving fuzzy predicates recursively enumerable but not recursive interpretations. The model developed is computer-implementable and well-motivated