The first of three fundamental principles Frege enunciates at the beginning of The Foundations of Arithmetic bids us "always to separate sharply the psychological from the logical, the subjective from the objective."¹ As commonly understood, this principle represents little more than Frege's insistence on the distinction between mind-independent objects and mind-dependent states, and so expresses his rejection of subjective idealism. Such an ontological construal of the objectivesubjective distinction in its turn supports a very common reading of Frege according to whch he is the archetypical metaphysical platonist. The mind-independent existence of things is for Frege a presupposition of the representational operation of language: it explains how our statements are determinately true or false apart from our ability to make or understand them. On this reading, Frege's novelty lies in his theory of language, a theory that offers an impressively general and precise account as to how the truth-value of a sentence is determined by the reference of its well formed parts. Frege is thus canonized the father of formal semantics. Furthermore, application of this theory to particular stretches of discourse enables us to uncover the ontological presuppositions of the discourse. Frege, in The Foundations of Arithmetic, provides the paradigm for phlosophical application of formal semantics in arguing that the objective truth of the statements of pure and applied arithmetic requires the mind-independent existence of numbers.