Conceptual realism versus Quine on classes and higher-order logic (Q1187230)

This paper attempts to refute Quine's analysis of set theory and 2nd- order logic, arguing that Quine fundamentally confuses \textit{sets} (defined by their membership), and \textit{classes} (defined as the extensions of concepts). It is argued that because of this failure to distinguish between membership and predication, Quine confuses set theory with 2nd-order predicate logics. Most of this paper is devoted to developing a 2nd-order logic appropriate to express `conceptual realism'. The logic contains not only predicate variables, but also nominalised predicates as singular terms, on a par with individual variables. In this way the distinction between membership and predication is examined, and a very detailed comparison with Quine's views is presented, especially the system and arguments of \textit{W. Quine}'s 1940 book ``Mathematical logic''. There is also discussion of `referential' and `substitutional' theories of predication. Finally the paper ends with a discussion of the ontology. Quine's Platonism, founded on an impredicative theory of classes, is contrasted with a `holistic conceptual realism' according to which abstract objects are `evolutionary products of language and culture' explicated as `the truth conditions of concepts'.