Abstract

I defend an alternative reading of §56 of Frege's Grundlagen, one that rescues Frege from Dummett's charge that this section is the weakest in the whole book. On my reading, Frege is not presenting arguments against the adjectival strategy. Rather, Frege presents the definitions in §55 in order to convince his reader that numbers must be objects. In §56 Frege suggests that these definitions contain two shortcomings that adequate definitions of numbers must overcome. And these short-comings, he argues, can only be avoided if numbers are objects. Further, I have argued that my alternative reading defuses three of Dummett's four criticisms of §56, consequently challenging Dummett's claim that this section should be stigmatized as the weakest in the whole book. Nevertheless, I am inclined to agree with Dummett that the adjectival strategy is more robust than Frege suggests. Frege's arguments seem far from conclusive. Thus, it may be that the adjectival strategy can provide us with definitions that can do everything we can expect from adequate definitions of numbers.