This is a variant on what is normally framed as the paradox of the village barber who shaves all men who do not shave themselves. The paradox has historically been used as an argument for the incompleteness of set theory. One of the more interesting treatments of this paradox, regarded by some as a definitive solution, can be found in an essay by Wilfred van Orman Quine called "The Ways of Paradox." He resolves it by stating that there can be no such barber (or mayor). This is not just a trivial solution because it challenges the correspondence theory of meaning by pointing out that there are sentences that are intelligible without corresponding to some external state of affairs, and thus eliminating the need for recasting according to Russell's theory of description.