ABSTRACT
In ‘Vagueness and Alternative Logic’, Hilary Putnam puts forward a suggestion for a formal treatment of the logic of vagueness. His leading thought, although not presented in the context of exactly the foregoing perspective on the problem, is in effect that the equivalence of with is not intuitionistically valid. Consequently the unrestricted validity of Double Negation Elimination for statements containing vague expressions is indeed in doubt, and Putnam’s proposal has point to that extent. Although Putnam’s proposal is unsatisfactory, its failure is instructive: if the denial of principles like is considered to follow from the vagueness of the relevant expressions, endorses reductio ad absurdum and the classical handling of the quantifiers and conjunction can prevent the derivation of Sorites paradoxes. From one point of view, it may seem that Sorites Paradoxes are a consequence of the very nature of vagueness. The central tenet of relevant logic is that the mere lack of a counterexample does not guarantee an entailment.
