An irrelevant conclusion, also known as ignoratio elenchi (Latin for ''ignoring refutation'') or missing the point, is the informal fallacy of presenting an argument that may or may not be logically valid and sound, but (whose conclusion) fails to address the issue in question. It falls into the broad class of relevance fallacies.
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 Logic
● Example 1: A and B are debating as to whether criticizing indirectly has any merit in general.
A attempts to support their position with an argument that politics ought not to be criticized on social media because the message is not directly being heard by the head of state; this would make them guilty of ignoratio elenchi, as people such as B may be criticizing politics because they have a strong message for their peers, or because they wish to bring attention to political matters, rather than ever intending that their views would be directly read by the president.
● Example 2: A and B are debating about the law.
B missed the point. The question was not if the law should allow, but if it does or not.
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!" (See also argumentum ad lapidem.)
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.
The phrase ignoratio elenchi is from Latin 'an ignoring of a refutation'. Here elenchi is the genitive singular of the Latin noun elenchus, which is from Ancient Greek ἔλεγχος (elenchos) 'an argument of disproof or refutation'. The translation in English of the Latin expression has varied somewhat. Hamblin proposed "misconception of refutation" or "ignorance of refutation" as a literal translation, John Arthur Oesterle preferred "ignoring the issue", and  Irving Copi, Christopher Tindale and others used "irrelevant conclusion".
- Bishop Whately, cited by John Stuart Mill: A System of Logic. London Colchester 1959 (first: 1843), pp. 542.
- Patrick J. Hurley (2011). A Concise Introduction to Logic. Cengage Learning. pp. 131–133. ISBN 978-0-8400-3417-5.
- Aristotle (1878). The Organon, or Logical treatises, of Aristotle. 2. Octavius Freire Owen (translation). Covent Garden: George Bell and Sons. pp. 548–553.
- "Ignoratio Elenchi". Introduction to Logic. 24 September 2009.
- Davies, Arthur Ernest (1915). A Text-Book of Logic. R. G. Adams and company. pp. 569–576. LCCN 15027713.
- H. W. Fowler, A Dictionary of Modern English Usage. Entry for ignoratio elenchi.
- Bate 1977, p. 316 harvnb error: no target: CITEREFBate1977 (help)
- Bagnall, Nicholas. Books: Paperbacks, The Sunday Telegraph 3 March 1996
- Boswell 1986, p. 122 harvnb error: no target: CITEREFBoswell1986 (help)
- Liddell–Scott–Jones. A Greek-English Lexicon.
- Charles Leonard Hamblin (1970). Fallacies. Methuen & Co. Ltd. p. 31.
- Christopher W. Tindale (2007). Fallacies and Argument Appraisal. Cambridge University Press. p. 34. ISBN 978-0-521-84208-2.
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