Slides for a seminar I gave at Swansea University and the University of Padua.
Update
A paper on this topic has since been written (posted here).
Abstract
Informally, the drinker paradox may be stated as “in every non-empty pub there is a person such that if that person is drinking, everybody in the pub is drinking”. The dual of the drinker paradox is a formulation of Hilbert’s epsilon operator for the existential quantifier. Both are theorems of classical logic, but non-constructive. They are independent of each other, and of the law of excluded middle, but each is sufficient to derive the limited principle of omniscience for binary sequences, and thus is analytically powerful. Kripke semantics can be used to classify the strength of these statements over intuitionistic and minimal logic.