Meinongian type theory and its applications

Abstract

In this paper I propose a fundamental modification of standard type theory, produce a new kind of type theoretic language, and couch in this language a comprehensive theory of abstract individuals and abstract properties and relations of every type. I then suggest how to employ the theory to solve the four following philosophical problems: (A) the identification and ontological status of Frege's Senses; (B) the deviant behavior of terms in propositional attitude contexts; (C) the non-identity of necessarily equivalent propositions, and (D) the “paradox” of analysis. We can roughly describe these solutions as follows: (A) the senses of English names and descriptions which denote individuals will be modelled as abstract individuals; the senses of English relation denoting expressions of a given type will be modelled as abstract relations of that type. (B) Inside de dicto attitude contexts, these English expressions denote (the abstract objects which serve as) their senses. (C) Relations and propositions will not be identified with their extensions, nor with functions or sets of any kind. They will be taken as primitive, and precise “being” and identity conditions will be proposed consistent with the view that necessarily equivalent relations and propositions may be distinct. (D) With the modelling described in (A), the expressions “being a brother” and “being a male sibling” may both denote the same property, though (the abstract properties which serve as) their senses may differ. Just as Frege predicts, “being a brother just is being a male sibling” is an informative identity statement because the terms flanking the identity sign have the same denotation, though distinct senses.