The Typed Theory of Abstract Objects

Abstract

The typed version of our theory commits us not only to abstract objects, but also to abstract properties, abstract relations, abstract properties of properties, abstract properties of relations, etc. We can use these entities to model impossible relations, like the symmetrical, non-symmetrical relation, and fictional relations, like simultaneity.1 However, the primary motivation for developing the typed theory is to account for the data concerning the propositional attitudes and to model the fictional relations of mathematics.