Zeno of Elea constructed several arguments that result in absurdity. They are paradoxical, contradicting, and just plain-strange. Oh, and did I mention that they are logically consistent, too?
One such paradox, perhaps the most well-known, is called the Achilles Paradox. Achilles was thought to be the fastest runner in Ancient Greece, and as such he should have no problem running down a tortoise, right? Zeno thinks not, and has a really good argument for why not.
Zeno of Elea
Alright, imagine Achilles and the tortoise, and let’s refer to the tortoise as Tom, because, well, a tortoise that races Achilles should probably have a name. Okay, so it is Achilles and Tom the tortoise at the starting line for this historical race. Since Achilles is the fastest man in Greece, he decides that it would only be fair to give Tom a head start.
Tom starts his crawl while Achilles poses and flexes for the crowd! What a showman! After a few moments Achilles takes off after Tom. According to Zeno, Achilles will never catch up to Tom because there is an infinite number of points between Achilles and Tom. Therefore Achilles can never reach Tom, because he cannot traverse an infinite number of points!