A Concepturalist Second-Order Logical System with Ramified Lambda Operators

Abstract

We develop a second order logical system with ramified lambda operators, having ramified conceptualism as its philosophical background. Such a system is shown to relatively consistent. Finally, we construct a non-standard second order semantics and prove a completeness theorem with respect to a uotion oí validity, provided by the semantics, and certain extensions oí the second order system.