Frege is celebrated as an arch-Platonist and an arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments, and our thought; that there is a “third realm” containing nonphysical objects that are not ideas. In this chapter it is argued that, to sustain the view that Frege means these renowned claims as statements of metaphysical doctrines, it is necessary to reject most of his claims about the unsaturatedness of functions. It is widely believed that these claims should be rejected, since they give rise to apparently insuperable problems. In this chapter, however, it is argued that the problems result, not from Frege’s claims about unsaturatedness but, rather, the view that they are meant to form part of a metaphysical theory. Properly understood, Frege has no problem with the concept horse.