Zeno's Paradoxes

Some philosophical puzzles that are devised by Zeno of Elea to support Parmenides' doctrine that "all is one" and that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.

The Paradoxes of motion

Achilles and the tortoise
"You can never catch up."

"In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead." (Aristotle Physics VI:9, 239b15)

The dichotomy paradox
"You cannot even start."

"That which is in locomotion must arrive at the half-way stage before it arrives at the goal." (Aristotle Physics VI:9, 239b10)

The arrow paradox
"You cannot even move."

"If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." (Aristotle Physics VI:9, 239b5)

From Wikpedia