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In  De Sophisticis Elenchis  4–5 Aristotle argues that there are thirteen modes of apparent refutation. However in Chapter 6 he claims to prove that all thirteen may be reduced (ἀναλῦσαι, 168a19-20) to one of these, viz., ‘ignorance of the definition of refutation’ (IE). The reduction proof raises a number of problems whose resolution has eluded commentators. I argue that the key to their solution is noting Aristotle’s subtle distinction between the cause of a refutation being ungenuine and the cause of its appearance of being genuine. The appearance of refutation in IE is produced by a missing question which disguises the refutation’s defect. That IE involves such an elliptical performance on the part of the questioner is confirmed by certain passages in Plato’s  Euthydemus  and  Theaetetus  wherein  ignoratio elenchi  in its original mode is on display. Since Aristotle takes a missing question to operate in all apparent refutation, the thesis of reduction entails that the other twelve heterogeneous modes of sophism must be solved on the model of IE. So understood the reduction proof ensures that a solution to apparent refutation will be fully explanatory: since the spur to an answerer’s dialectically appropriate objection to a sophism is its missing question, his objection will explain both the source of the appearance of refutation as well as its defect.

Aristotle on Ignorance of the Definition of Refutation