Abstract objects as constituents of external reality: A defense of the fregean account against Dummett’s objections

Abstract

In his Foundations of Arithmetic (1980) Gottlob Frege sets out to give an account of the existence of some types of abstract objects by means of justifying ascription of reference to singular terms purporting to refer to these objects. To this end he employs his Context Principle (CP), which states that “it is only in the context of a sentence that a word has any meaning” (§62, p. 73; §60, p. 71). Michael Dummett contends that Frege’s CP and his realism are in conflict, and hence that the account of reference given by means of CP makes it implausible to think of the references of names for abstract objects as external objects, i.e. as constituents of reality. In this study, an attempt is made to respond to Dummett’s three objections to Frege’s account, by pointing out the similarities between the assumptions lying behind Dummett’s criticisms and those of the nominalist view in regard to the existence of abstract objects. It is concluded that Dummett’s assumptions suffer from similar criticisms directed by Frege to the nominalist view, and that the Fregean account has the answers to Dummett’s objections.