Ignoratio elenchi, also known as irrelevant conclusion, is the informal fallacy of presenting an argument that may or may not be logically valid, but fails nonetheless to address the issue in question.
Ignoratio elenchi falls into the broad class of relevance fallacies. It is one of the fallacies identified by Aristotle in his Organon. In a broader sense he asserted that all fallacies are a form of ignoratio elenchi.
Ignoratio Elenchi, according to Aristotle, is a fallacy which arises from “ignorance of the nature of refutation.” In order to refute an assertion, Aristotle says we must prove it's contradictory; the proof, consequently, of a proposition which stood in any other relation than that to the original, would be an ignoratio elenchi… Since Aristotle, the scope of the fallacy has been extended to include all cases of proving the wrong point… “I am required to prove a certain conclusion; I prove, not that, but one which is likely to be mistaken for it; in that lies the fallacy… For instance, instead of proving that ‘this person has committed an atrocious fraud,’ you prove that ‘this fraud he is accused of is atrocious;’” … The nature of the fallacy, then, consists in substituting for a certain issue another which is more or less closely related to it, and arguing the substituted issue. The fallacy does not take into account whether the arguments do or do not really support the substituted issue, it only calls attention to the fact that they do not constitute a proof of the original one… It is a particularly prevalent and subtle fallacy and it assumes a great variety of forms. But whenever it occurs and whatever form it takes, it is brought about by an assumption that leads the person guilty of it to substitute for a definite subject of inquiry another which is in close relation with it. —Arthur Ernest Davies, "Fallacies" in A Text-Book of LogicThe phrase ignoratio elenchi is Latin meaning "ignorance of refutation". Here elenchi is the genitive singular of the Latin noun elenchus, which is from the Greek ἔλεγχος elenchos, meaning an argument of disproof or refutation. The translation in English of the Latin expression has varied a fair bit. Hamblin proposed "misconception of refutation" or "ignorance of refutation" as a literal translation, Oesterle preferred "ignoring the issue", Irving Copi, Christopher Tindale and others used "irrelevant conclusion".
An example might be a situation where A and B are debating whether the law permits A to do something. If A attempts to support his position with an argument that the law ought to allow him to do the thing in question, then he is guilty of ignoratio elenchi. Dr Johnson's unique "refutation" of Bishop Berkeley's immaterialism, his claim that matter did not actually exist but only seemed to exist, has been described as Ignoratio elenchi: during a conversation with Boswell, Johnson powerfully kicked a nearby stone and proclaimed of Berkeley's theory, "I refute it thus!"
A related concept is that of the red herring, which is a deliberate attempt to divert a process of enquiry by changing the subject. Ignoratio elenchi is sometimes confused with straw man argument. For example, it has been described as "attacking what the other fellow never said" by Peter Jay in an article in a 1996 article in New Statesman.