Explanation

Fallacies of relevance are attempts to prove a conclusion by offering considerations that simply don’t bear on its truth. In order to prove that a conclusion is true, one must offer evidence that supports it. Arguments that commit fallacies of relevance don’t do this; the considerations that they offer in support of their conclusion are irrelevant to determining whether that conclusion is true. The considerations offered by such are usually psychologically powerful, however, even if they don’t have any evidential value.

Examples

Many of the familiar informal fallacies are fallacies of relevance, for example:

Personal attacks (arguments ad hominem) attempt to discredit a point of view by discrediting the person that holds it. The character of the person that holds a view, though, entails nothing about the truth of that view. Such arguments therefore commit a fallacy of relevance.

Appeals to consequences attempt to persuade someone to accept a position based either on the good consequences of their accepting it or on the bad consequences of their not accepting it. There is no guarantee, though, that the position that has the best consequences is true. Again, then, such arguments commit a fallacy of relevance.