Readers who are introduced to philosophical analysis by reading the early Platonic dialogues may be puzzled to find that Plato, in his middle and late periods, largely abandons the style of analysis characteristic of early Plato, namely, the ‘Socratic elenchus’. This paper undertakes to solve the puzzle. In contrast to what is popularly called ‘the Socratic method’, the elenchus requires that Socrates, the lead investigator, not have a satisfactory answer to his ‘What is F-ness?’ question. Here is the bind. Part of what motivates the elenctic inquiry is the natural assumption that one cannot identify F-things unless one has a satisfactory analysis of what it is to be F. But to test the adequacy of suggested analyses of F-ness one needs to be able to identify counterexamples. Together these two points present us with a ‘catch-22’, which is something the ‘paradox of inquiry’ in the Meno brings out. In the Theaetetus Plato makes clear that, although the elenchus, including Socratic ignorance, can refute philosophical theses arrived at by other means, it cannot, by itself, give birth to viable philosophical theses. Its legitimate role is therefore only propaedeutic.