Russell's Paradox. Around the turn of the century, analytic philosopher extraordinaire Bertrand Russell identified a serious problem with this idea, known as Russell's Paradox.

This is called the arrow paradox, and it's another of Zeno's arguments against motion.The issue here is that in a single instant of time, zero seconds pass, and so zero motion happens. Zeno argued ...

There is a classic logic problem known as the Barber paradox (itself a variant of Russell’s paradox): in a town where the barber shaves every man who doesn’t shave himself, who shaves the barber?