So I owe you an analysis of Socrates's refutations of Cephalus and Polemarchus in Book I. Now if I were the type to put noble things to paltry use, as someone with no sensibility might use a heartfelt letter as scratch paper, I might say that justice, not being identical with paying one's debts, does not require me to do so — and that I could prove it. Because I, Sam-I-am that I am, being clever as clever as clever can be and having read Plato's Republic know Socrates's argument against Cephalus's definition of justice by heart.
And I could very well stoop to that, because I do think very much of how clever I am. But above all I want to show you that Socrates would not do so, that his form of refutation is completely different from this kind of artful dodge that "takes refuge in words." A Platonic dialectician is not a debater. He does not refute to hide from the obvious, nor to display his wit, nor even simply to prove a point (as one does for whom refutation just means proving the contradictory of the position to be refuted). He refutes as one who, knowing that he does not know, pursues wisdom.
But what do these high-sounding words actually mean? How do we see this knowledge and this pursuit in the refutations of Cephalus and Polemarchus — particularly as they may seem to us to be far from artless, and that they may seem to disclose Socrates as a teacher rather than a learner? This question sets the task of an analysis of these refutations, and with it, this analysis begins. In other words, the first step in understanding Socratic refutation is the refutation of the way in which Socratic refutation appears.