Ignoratio elenchi (also known as irrelevant conclusion) is the logical fallacy of presenting an argument that may in itself be valid, but which proves or supports a different proposition than the one it is purporting to prove or support. "Ignoratio elenchi" can be roughly translated by ignoring the issue; "elenchi" is from the Greek ελεγχος, meaning an argument of disproof or refutation.
Aristotle believed that an ignoratio elenchi is a mistake made by a questioner while attempting to refute a respondent's argument. He called it an ignorance of what makes for a refutation.
Red herrings
When this logical fallacy is used in an attempt to intentionally confuse or distract someone else, it is known as a "red herring". This phrase is thought to have originated from the use of smoked herring fish to distract dogs following a scent trail. The herring's strong smell could obscure the real trail and lay a false one.
Defense Lawyer: "Tax fraud is not much of a crime, and it is unfair for my client to be subjected to this lengthy and stressful trial over such a minor offense." (This is irrelevant, the lawyer's job is to prove innocence.)
There is a lot of violence in America's inner-cities. You should therefore support an increase to welfare funding. (One can agree with either of these statements without agreeing to the other. There is no proof one is relevant to the other.)
Baseball player Mark McGwire just retired. Clearly, he deserves to be in the Hall of Fame. After all, he's such a nice guy, and he gives a lot of money to all sorts of charities. (Charisma and charity are not qualifications for induction into the Hall of Fame, therefore they do not support the conclusion.)
The premier's tax policies may be popular, but I suspect he had an affair and is paying the woman to keep quiet. The media should investigate that! (This is an example of a red herring, as the speaker attempts to distract from tax policy with the unrelated matter of the alleged affair.)
The name of this fallacy comes from the sport of fox hunting in which a dried, smoked herring, which is red in color, is dragged across the trail of the fox to throw the hounds off the scent.
Thus, a "redherring" argument is one which distracts the audience from the issue in question through the introduction of some irrelevancy.
Of course, fallacies of ambiguity involve irrelevance, in that the premisses are logically irrelevant to the conclusion, but this fact is disguised by ambiguous language.
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