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Drinker paradox - mklabgr - 07-25-2026
Drinker paradox
Summary
The Drinker Paradox is a famous result in classical predicate logic that appears paradoxical because it conflicts with everyday intuition, even though it is logically valid. It states that in every non-empty pub, there exists a person such that if that person is drinking, then everyone in the pub is drinking. The statement seems strange because people often interpret "if...then" as implying causation, whereas formal logic treats it as material implication.
The proof relies on two simple cases: either everyone in the pub is drinking, in which case any person satisfies the statement, or at least one person is not drinking, and choosing that non-drinker makes the implication automatically true because a conditional with a false premise is considered true.
Thus, the paradox is not about drinking behaviour but about the precise meaning of logical implication. Popularized by mathematician Raymond Smullyan, it has become a classic example in mathematical logic, automated theorem proving, and the study of formal reasoning, illustrating the important distinction between natural language and the rigorous semantics of classical logic.
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