Book excerpt: It is a longstanding if not altogether coherent tradition of logic and rhetorical studies that an argument can be incorrect or fallacious in virtue of some proposition in it being “irrelevant”. This monograph clarifies that tradition. Non-classical propositional calculi, including relevance logics and relatedness logics, are juxtaposed against conversational criticisms of irrelevance in natural argumentation, e.g. in parliamentary debates. The object is to see if there is a reasonable way of evaluating criticisms like “That’s beside the point!” or “That’s irrelevant!”.