No Requirement of Relevance

Classic logic defines entailment to hold between a premise (or set of premises) and a conclusion if and only if their logical form guarantees that either the premise (or at least one element of the set of premises) is false, or the conclusion is true. The definition obliges the logician to recognize certain degenerate entailments. A premise (or set of premises) that is contradictory in the sense that its logical form guarantees that it is false (or that at least one element of the set of is false) entails any conclusion: ex falso quodlibet. And a conclusion that is tautologous in the sense that its logical form guarantees that it is true is entailed by any premise (or set of premises): ex quolibet verum. The commitment of classical logic to these principles has frequently been attacked by indignant critics who denounce the degenerate cases of entailment as "paradoxes".