# Who is Zenon (Xenon) of Elea?

June 25, 2021Zeno of Elea (according to XeAristotle, Zeno of Elea (approximately 490-430) is the inventor of the dialectic in the sense of the doctrine of fallen developments.

Zeno supported Parmenides’s doctrine that the One is the only real being, by trying to show that it is unthinkable to assume multiplicity and motion, and that such a thought would lead to contradictions. He did this with his notorious arguments against multitude and movement.

According to one of the proofs showing that there cannot be a multiplicity, if objects are a multiplicity, they are both infinitely small and infinitely large. Because if we divide the existing and think that the parts we divide are no longer indivisible points, they become nothing without size; If we put them together, we still cannot achieve a positive magnitude; nothing gains anything in size by the addition of something without greatness to it. If we think of these parts as extended – they take up space in space – then an infinite greatness will occur when many of them come together. According to a second proof, if Objects are many, they are both finite and infinite in number.

They are finite in number, because the more they are, the more they will be, they cannot be more or less. Objects are also infinite in number, because they limit each other in length, thus separating themselves from other objects; these other objects themselves are also bounded by nearby objects, and so on. In a third proof, when Zenon says “everything is in space”, he says that space must also exist in a space, and that space, in which space is included, must also exist in a space, and this goes on to infinity. We learn from Aristotle the proofs that Zeno put forward against the reality of the movement. The best known among these is the evidence of the race between Achilles and the tortoise.

In this race, Achilles will never be able to catch up with the tortoise that set out just before him, because in the time it takes to run the distance between the original turtle and himself, the tortoise will have advanced a little, albeit a little. Achilles would have to run this gap as well, but meanwhile the tortoise had made some progress, albeit a little; this goes on to infinity. We can see the essence of this proof better in another proof “You never reach the end of a running track”, because you have to leave half of the track behind first, which goes on to infinity.

How can an infinite number of spaces be crossed in a finite time Another proof is “The flying arrow is at rest” because this arrow will always be at a certain point; to be at a certain point also means to stop; but if it stops at each moment of the movement, the arrow also stops all along its path. This last proof is also based on the relativity of motion. If a given set of points passes by two series, one at rest and the other running in opposite directions, it will have crossed both a large and a small distance in the same time, that is, this series will have passed several different distances in the same time. they will have velocities, given that we measure its motion with that of a stationary or advancing array.

These sharp antinomias of Zeno, of course, only to show that if we think of Being as a multiplicity and movement, we fall into contradictions, so that Being can only be “one” and motionless.

Also please see:

– Zenon, Elea School and Zenon Paradoxes

Prepared by: Sociologist Ömer YILDIRIM

Source: Omer YILDIRIM’s Personal Lecture Notes. Atatürk University Sociology Department 1st Year “Introduction to Philosophy” and 2nd, 3rd, 4th Grade “History of Philosophy” Lecture Notes (Ömer YILDIRIM); Open Education Philosophy Textbook, History of Philosophy; prof. Macit Gokberk; Who is Remzi Kitabevinon?