Frege's argument-function model for predication and his theory of quantification are among the few really new ideas introduced into philosophy since the time of the Greeks. His critique of the traditional account of predication and his invention of the quantifier-variable notation for expressing generality revolutionized both logic and ontology.¹ Before discussing the ontological implications of his new interpretation of the logical structure of the world, it will be helpful to clarify the relationship between his argument-function model and his account of quantification, and to consider some of the paradoxes engendered by his extensional logic.