Hairier than Putnam Thought

This chapter is a short note, co-written with Stephen Read, reacting to Hilary Putnam’s observation in his ‘Vagueness and Alternative Logic’ that intuitionistic logic would block the transition from the negation of the usual universally quantified conditional form of major premise for a Sorites to the assertion of a sharp boundary to the target predicate in the series concerned, and would thus allow the paradox to be reconceived as a straightforward reductio of its major premise. It is pointed out that a Sorites need not employ that form of major premise but can instead proceed, in intuitionistic logic, from the negation of the existential claim that the series in question contains a sharp boundary and that, while an intuitionistically suspect double negation elimination step would still be needed to enforce the unpalatable conclusion that the predicate in question indeed has a sharp boundary, nothing like the semantic motivation that the Intuitionists have favoured in mathematics for a restriction on double negation elimination can be operative in this context.