Zeno of Elea

Zeno was from Elea, a Greek city-state in Southern Italy. He was born about 490 BCE. He was a pupil of Parmenides. Zeno came up with about 40 arguments in support of Parmenides's belief that there is no change. Supposedly there are only 8 that have survived.

  1. The arrow: Imagine an arrow flying through the air. At any given moment the arrow is where it is and isn't anywhere else, so that if at any given movement the arrow is where it is then it is stationary, so if at any given moment the arrow is stationary, then at no moment is it moving.
  2. Achilles and the Tortoise: Achilles starts a race with a tortoise, but the tortoise has a head start. So Achilles, though he is moving at a constant rate that is faster than the tortoise's constant rate, must first reach the point where the tortoise started the race. But by the time Achilles will reach the point where the tortoise started the race the tortoise will have moved forward a bit, so then Achilles must reach this new point that the tortoise is at, but by the time Achilles reaches this new point the tortoise has moved up again, ad infinitum. Therefore, the faster never overtakes the slower. It is a reductio ad absurdum, assuming movement you arrive at a contradiction, therefore your initial assumption is wrong, suggesting that the possibility of movement is wrong.
  3. To get from point A to point B one must first reach the midpoint (point C) between point A and point B. But in order to reach point C one must first reach the midpoint (point D) between C and A. But in order to reach the point D one must reach the midpoint between D and A, ad infinitum. So in order to reach any point, one must first reach some other point, so then at no time can anyone ever reach any point.
  4. If more things than one exist, it is necessary for them to be as many as they are, and neither more nor fewer. But if they are as many as they are, they will be limited. If more things than one exist, the things which exist are limitless. For there are always others between the things which exist, and again others between them. And in this way the things which exist are limitless. So if more things than one exist, those same things must both be limited and unlimited.
  5. There is either an indivisible One or everything divided into a plurality. If there is a plurality it will be divisible every where alike and so will be infinitely divisible everywhere. But if it divides into an infinite number of minimal parts these will possess no size for each member is one and is the same as itself, and when these parts are added or subtracted to another thing, it will neither get larger or smaller, so they are clearly so small as to have no size at all. But in removing the parts of a thing there will never be a last part to remove, there will always be another part behind it, so its size is so large that it is limitless. Therefore, if there exist more things than one, then those things must be so small as not to have a size and so large that they are limitless.
  6. If places exists then everything which exists must be located in a place. But then places must be located in a place, and these places in a place, ad infinitum. Therefore, places do not exist.

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