The Evolution of Chihara's Anti-Nominalistic Nominalism

Regarding the Existence of Mathematical Objects

Abstract

Charles Chihara argues that many scholars in the philosophy of mathematics have adopted a false assumption, the Fregean Assumption, that mathematical theorems are propositions about the actual world. Chihara, who does not believe in the existence of abstract objects but does believe in abstract notions such as satisfiability in a structure, contends that mathematical theorems are rather only true in the sense that they are satisfied by appropriate kinds of structures. Chihara's thesis is presented and analyzed particularly in the context of Set Theory.