 There are three closely related concepts needed to understand sophistical refutations. By a deduction (a  syllogism[3])  Aristotle meant an argument which satisfies three conditions: it “is based on certain statements made in such a way as necessarily to cause the assertion of things other than those statements and as a result of those statements” (SR 1 165a1–2). Thus an argument may fail to be a syllogism in three different ways. The premises may fail to necessitate the conclusion, the conclusion may be the same as one of the premises, and the conclusion may not be caused by (grounded in) the premises. The concept of a proof underlying Sophistical Refutations is similar to what is demanded of demonstrative knowledge in Posterior Analytics (I ii 71b20), viz., that the premises must be “true, primary, immediate, better known than, prior to, and causative of the conclusion,” except that the first three conditions do not apply to deductions in which the premises are obtained through questioning. A refutation, Aristotle says, is “a proof of the contradictory” (SR 6, 168a37)—a proof of the proposition which is the contradictory of the thesis maintained by the answerer. In a context of someone, S, maintaining a thesis, T, a dialectical refutation will consist in asking questions of S, and then taking S’s answers and using them as the premises of a proof via a deduction of not-T: this will be a refutation of T relative to the answerer (SR 8 170a13). The concept of contradiction can be found in Categories: it is those contraries which are related such that “one opposite needs must be true, while the other must always be false” (13b2–3). A refutation will be sophistical if either the proof is only an apparent proof or the contradiction is only an apparent contradiction. Either way, according to Aristotle, there is a fallacy. Hence, the opening of his treatise: “Let us now treat of sophistical refutations, that is, arguments which appear to be refutations but are really fallacies and not refutations” (SR 1 164a20).