Quine on Quantification

Karen Green (University of Melbourne, Monash University)

It has been said of Frege that he ‘introduced and brilliantly exploited second-order variables ranging over concepts’ so that contemporary higher order logic ‘is a good model’ of his logicist system. Quine has been a fierce critic of second-order logic and has consistently advocated restricting quantification to first-order variables. Second-order variables are commonly taken to range over concepts, properties, relations, or functions and from early in his career, Quine deemed these to be ‘abstract entities’ of dubious scientific value. In this paper I ask, do Quine’s objections to second-order quantification engage with Frege? I argue that they do not. Quine fails to differentiate, within the notion of meaning, Fregean concepts–– which are not objects––from objects, the referents of singular terms. Nor does he recognise the difference between the concept/object distinction and that between the sense of an expression and what is indicated by it. He has in his sights Carnapian ‘intensions,’ which confusedly merge Frege’s concept/object and sense/indication (reference) distinctions. Because he does not engage with Frege’s actual semantics, Quine’s objections to Frege’s second-order quantifiers fail. Moreover, it is argued, once looked at in a Fregean light, Quine’s account of quantification turns out to be seriously confused.