Paradoxically…
Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves. Under this scenario, we can ask the following question: Does the barber shave himself?
From Epimenides’ Paradox to the Omnipotence Paradox, more fun-with-logic at “Brain Twisting Paradoxes.”
As we return to first principles, we might wish a carefully-reasoned Joyeux Anniversaire to Félix-Édouard-Justin-Émile Borel, a mathematician and pioneer of measure theory and its application to probability theory; he was born in Saint-Affrique on this date in 1871. Borel is perhaps best remembered by (if not for) his thought experiment demonstrating that a monkey hitting keys at random on a typewriter keyboard will– with absolute certainty– eventually type every book in the Bibliothèque Nationale (or, as oft repeated, every play in the works of Shakespeare, or…)– that is, the infinite monkey theorem.
Borel (image source)