I recently heard about Zeno's paradoxes, one of which involves the rather contrarian idea that the initiation of locomotion should be impossible; this is called the dichotomy paradox.

The best explanation of this paradox is given by Chad Orzel at Uncertain Principles:

[The dichotomy paradox argues] that motion ought to be impossible, because to cover any given distance requires you to first move half the distance, then half the remaining distance, then half again, and so on ad infinitum. Each of those distances should require a finite time to move, and there are infinitely many steps, so you should never get anywhere."

The solution, as it where, lies in the fact that space and time are not infinitely divisible. They are both quantal, and thank goodness for that!

Every time I consider ancient philosophy, I'm impressed. These people had so little to go on (no Newton, no calculus, no thermodynamics, no understanding of bacteria, or chemistry...), yet they came up with absolutely brilliant insights that have taken until the 20th century to be completely resolved. They may have been wrong (Zeno's reductio ad absurdum logic lead him to believe that motion was an illusion, rather than proving continuous space was an illusion), but many ancient philosophers were absolutely brilliant in their original ways of thinking.

What do philosophy students do now after college? As far as I know, most of them go to law school.