to say that, if everybody drinks, then anyone can be the witness for the validity of the theorem. And if someone does not drink, then that particular non-drinking individual can be the witness to the theorem's validity. Explanation of paradoxicality The paradox is ultimately based on the principle of formal logic that the statement is true whenever A is false, i.e., any statement follows from a false statement (ex falso quodlibet). What is important to the paradox is that the conditional in classical (and intuitionistic) logic is the material conditional. It has the property that is true only if B is true or if A is false (in classical logic, but not intuitionistic logic, this is also a sufficient condition). So as it was applied here, the statement "if they are drinking, everyone is drinking" was taken to be correct in one case, if everyone was drinking, and in the other case, if they were not drinking—even though their drinking may not have had anything to do with anyone else's drinking. History and variations Smullyan in his 1978 book attributes the naming of "The Drinking Principle" to his graduate students. He also discusses variants (obtained by replacing D with other, more dramatic predicates): "there is a woman on earth such that if she becomes sterile, the whole human race will die out." Smullyan writes that this formulation emerged from a conversation he had with philosopher John Bacon. A "dual" version of the Principle: "there is at least one person such that if anybody drinks, then he does." As "Smullyan's ‘Drinkers’ principle" or just "Drinkers' principle" it appears in H.P. Barendregt's "The quest for correctness" (1996), accompanied by some machine proofs. Since then it has made regular appearance as an example in publications about automated reasoning; it is sometimes used to contrast the expressiveness of proof assistants. Non-empty domain In the setting with empty domains allowed, the drinker paradox must be formulated as follows: A set P satisfies if and only if it is non-empty. Or in words: If and only if there is someone in the pub, there is someone in the pub such that, if they are drinking, then everyone in the pub is drinking. See also List of paradoxes Reification (linguistics) Temporal logic Relevance logic References Predicate logic Logical paradoxes