Zeno of Elea

Zeno of Elea is best known for his paradoxes, which were intended to support the doctrine of Parmenides (on the indivisibility of being and the impossibility of motion) and deny the doctrine of Pythagoras.

Almost nothing is known of his life. Aristotle called him the discoverer of dialectics. He was also one of the characters in Plato's dialogue Parmenides.

Zeno's Paradoxes:

1) The race between Achilles and the tortoise

Achillês stands at point A and the tortoise in front of him at point B. Achilles is faster, but by the time he reaches point B, the tortoise is already at point C. By the time Achilles is at point C, the tortoise is already at point D. The distances between the points keep decreasing, but according to Zeno, Achilles never catches up to the tortoise.

2) The flying arrow

A flying arrow observed at any moment of its motion is at one point at which it is de facto at rest. However, if it is at rest at any instant of its flight, this means that it is also at rest in time, which means that it is not moving.

In addition to these arguments, he made many (up to 40) others. His paradoxes are still an argument between philosophers and mathematicians today. Newton and Leibniz tried to refute them with their discovery of differential and integral calculus.