Conceptualism, Ramified Logic, and Nominalized Predicates

Abstract

Conceptualism differs from intuitionism in being a theory about the construction of concepts and not about the construction of proofs. Constructive conceptualism is similar to nominalism in excluding an impredicative comprehension principle, but differs from nominalism in the kind of ramified predicative logic each validates. Ramified constructive conceptualism leads in a natural way to holistic conceptualism, and, unlike nominalism, both can extended to a type of realism in which some nominalized predicates denote abstract objects. Intermediate positions of conceptual realism are distinguished regarding which concepts can be projected to have abstract objects corresponding to their nominalizations.