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 irrelevancy, in that the premisses are logically irrelevant to the conclusion, but this fact is disguised by ambiguous language. One might, with some violence, bring this fallacy into the group of fallacies dependent on language as well. This is too wide to be useful, so we 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. 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. Aristotle, On Sophistical Refutations S. Morris Engel, Analyzing Informal Fallacies , Prentice-Hall, 1980.