# The Barber Paradox Revisited: Why We Need Set Theory

Here we consider simple variations of the famous Barber Paradox (3 versions) and demonstrate the need for set theory in a very simple and direct way. We will prove using set theory that the fabled village barber can actually shave those and only those men in that village who do not shave themselves *if and only if* that barber is *not* a man in the village. This would seem to be impossible to prove using only first-order predicate logic.

Last updated Feb. 10, 2017

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