According to what a refutation is and which are the aims of sophists Aristotle in Sophistical Refutations says: First we must consider the aims of those who strive and contend in disputations. These are five in number: refutation, fallacy, paradox, solecism, and the fifth element is to make their opponent prate. And that is, to compel him to say the same thing again and again.
Or it is to give the impression that they attain each of the above but not in fact. For before anything else they mostly choose to refute, secondly, to show that their interlocutor is committing a fallacy, thirdly, to lead him into paradox, and fourthly, to make him commit a solecism. That is to say, to make the respondent, from the argument, use a verbal abuse. And the last case is to make him repeat himself.
For a syllogism is said of a refutation additionally, since if a refutation is possible it follows that a syllogism is possible too. but not vice versa if a syllogism then a refutation. And a syllogism is possible even if there is no contradictory statement with its proportions being affirmative, but no refutation is possible when all proportions are affirmative. One of the proportions must be negative and the other affirmative. For every refutation takes the contrary to the conclusion along with the other conceded proportion and leads to an absurdity through a syllogism.
For example, let the following syllogism: All men are rational. Every rational being is an animal. Therefore, man is an animal. Assuming now the contrary to the conclusion which says that no man is an animal, and granted that every rational being is an animal, we conclude that no man is a rational being — which is an absurdity.
Bibliography: Aristotle, On Sophistical Refutations (165b.12 to 165b.22) Translation: George Kotsalis