Identity and quantification

It is a philosophical commonplace that quantification involves, invokes, or presupposes, the relation of identity. There seem to be two major sources for this belief: (1) the conviction that identity is implicated in the phenomenon of bound variable recurrence within the scope of a quantifier; (2) memories of Quine’s insistence that quantification requires absolute identity for the values of variables. With respect to (1), I show that the only extant argument for a dependence of variable recurrence on identity, due to John Hawthorne, fails. I further show that the function of variable recurrence is not subsumed under that of identity, so that a dependence of the former on the latter, if any, would have to be of a rather indirect nature. With respect to (2), I argue that the relevant passage in Quine fails to establish a connection between quantification and the identity relation, and indeed wasn’t intended by Quine to do so.