In this article, I argue that, in showing inconsistency of beliefs, Socratic elenchus is showing incompatibility of the desires those beliefs express. This thesis explains Socrates’ claim that, in refuting Callicles, he is also restraining his desires. The beliefs in question are about the best kind of life to lead; such beliefs express the second order desire to lead a life in which certain sorts of first order desires are satisfied. Socrates’ elenchus shows that Callicles is caught between two incompatible (...) second order desires: a desire to lead of life of enormous pleasure and a desire to lead a life in which his love of honor is satisfied. Socrates does not succeed with Callicles because the way out of this dilemma depends on a type of desire not found in the moral psychology of the Gorgias, i.e., a desire whose satisfaction is pleasure unmixed with pain, described in Republic 583c-585e and Philebus 50e-52b. (shrink)