I address the problem of how Socrates can claim his elenchus, or refutation, establishes the falsehood of his interlocutor's initial claim, when all it seems to do is show that the initial claim is inconsistent with other beliefs that the interlocutor expresses in the argument. ;To address this problem, I first uncover its fundamentals, including its central issue and main assumptions. This is an epistemological problem, the central issue of which is how Socrates thinks he and the interlocutor are justified (...) in thinking that the auxiliary premises in his elenctic arguments are true. If they have the requisite justification for the auxiliary premises, then they have the requisite justification that the interlocutor's initial claim is false. Second, I argue that the main assumptions of the problem are justified and thereby argue that there is a legitimate problem that needs to be solved. Third, I argue that this problem has not been adequately solved. Fourth, I argue for my own original solution. ;My solution is that in cases within the scope of the problem, Socrates and the interlocutor agree to the auxiliary premises under two important conditions: they both aim to acquire truth and avoid error,1 and they both say what they really think. When they agree under these conditions, Socrates thinks they secure from each other corroborative agreement: they both check with each other that their judgements about that to which they agree have objectivity. Socrates' fundamental epistemic intuition is that agreement under these conditions amounts to something regarding justification for that upon which they agree; we can't expect to make any philosophical progress at all unless we thought that our agreements under these conditions stood for something. ;This solves the problem because Socrates and the interlocutor disagree about the initial claim, but they have corroborative agreement to the auxiliary premises, which gives both Socrates and the interlocutor the requisite justification for them. Since the auxiliary premises imply the negation of the initial claim, both Socrates and the interlocutor can justifiably think that the elenctic argument establishes the falsehood of the initial claim. ;1This condition is similar to one proposed by Keith Lehrer , 130), as are other insights that provided inspiration for the solution presented here. (shrink)