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 "red herring" argument is one which distracts the audience from the issue in question through the introduction of some irrelevancy. This frequently occurs during debates when there is an at least implicit topic, yet it is easy to lose track of it. By extension, it applies to any argument in which the premisses are logically irrelevant to the conclusion.
This is the most general fallacy of irrelevance. Any argument in which the premisses are logically unrelated to the conclusion commits this fallacy.
This fallacy is often known by the Latin name "ignoratio elenchi", or "ignorance of refutation". The ignorance involved is either ignorance of the conclusion to be refutedeven deliberately ignoring itor ignorance of what constitutes a refutation, so that the attempt misses the mark. This explanation goes back to Aristotle's On Sophistical Refutations, the focus of which is fallacious refutations in debate. As with all of Aristotle's original fallacies, its application has widened to all arguments.
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. However, Aristotle classifies Ignoratio Elenchi as language-independent, though he does say:
One might, with some violence, bring this fallacy into the group of fallacies dependent on language as well.
But this would make Ignoratio Elenchi so wide that just about every fallacywith the exception of Begging the Questionwould be a subfallacy of it. This is too wide to be useful, so I will follow Aristotle in restricting it to non-linguistic fallacies, excluding those disguised by ambiguity or vagueness.
Logical relevance is itself a vague and ambiguous notion. It is ambiguous in that different types of reasoning involve distinct types of relevance. It is vague in that there is little agreement among logicians about even deductive relevance, with logicians divided into different camps, so-called "relevance" logicians arguing for a more restrictive notion of logical relevance than so-called "classical" logicians.
Another ambiguity of the term "relevance" is that logical relevance can be confused with psychological relevance. The fact that two ideas are logically related may be one reason why one makes you think of the other, but there are other reasons, and the stream of consciousness often includes associations between ideas that are not at all logically related. Moreover, not all logical relations are obvious, so that a logical relationship may not cause a psychological relationship at all.
Because it is the most general fallacy of irrelevance, most fallacious arguments will be identified as some more specific type of irrelevancy.