elementary quantification theory See FORMAL. LOGI. elenchus, a cross-examination or refutation. Typically in Plato’s early dialogues, Socrates has a conversation with someone who claims to have some sort of knowledge, and Socrates refutes this claim by showing the interlocutor that what he thinks he knows is inconsistent with his other opinions. This refutation is called an elenchus. It is not entirely negative, for awareness of his own ignorance is supposed to spur the interlocutor to further inquiry, and the concepts and assumptions employed in the refutations serve as the basis for positive Platonic treatments of the same topic. In contrast, sophistic elenchi are merely eristic: they aim simply at the refutation of an opponent by any means. Thus, Aristotle calls fallacies that only appear to be refutations ‘sophistical elenchi.’ See also SOCRATES. E.C.H.