Ideas of Zeno (Elea), by Theme

[Greek, c.490 - 430 BCE, Born at Elea, in Italy. Handsome young companion of Parmenides, based in Elea.]

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5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
The fast runner must always reach the point from which the slower runner started
     Full Idea: Zeno's so-called 'Achilles' claims that the slowest runner will never be caught by the fastest runner, because the one behind has first to reach the point from which the one in front started, and so the slower one is bound always to be in front.
     From: report of Zeno (Elea) (fragments/reports [c.450 BCE]) by Aristotle - Physics 239b14
     A reaction: The point is that the slower runner will always have moved on when the faster runner catches up with the starting point. We must understand how humble the early Greeks felt when they confronted arguments like this. It was like a divine revelation.
We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible
     Full Idea: Although it is impossible to make contact in a finite time with things that are infinite in quantity, it is possible to do so with things that are infinitely divisible, since the time itself is also infinite in this way.
     From: comment on Zeno (Elea) (fragments/reports [c.450 BCE], A25) by Aristotle - Physics 233a21
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does?
     Full Idea: Zeno is wrong in arguing that the tiniest fragment of millet makes a sound; there is no reason why the fragment should be able to move in any amount of time the air which the whole bushel moved as it fell.
     From: comment on Zeno (Elea) (fragments/reports [c.450 BCE], A29) by Aristotle - Physics 250a16
5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
Zeno's arrow paradox depends on the assumption that time is composed of nows
     Full Idea: Zeno's third argument claims that a moving arrow is still. Here the conclusion depends on assuming that time is composed of nows; if this assumption is not granted, the argument fails.
     From: comment on Zeno (Elea) (fragments/reports [c.450 BCE], A27?) by Aristotle - Physics 239b5
26. Natural Theory / A. Speculations on Nature / 1. Nature
If there are many things they must have a finite number, but there must be endless things between them
     Full Idea: It things are many, they can't be more or less than they are, so they must be finite, but also there must be endless things between each thing, so they must be infinite.
     From: Zeno (Elea) (fragments/reports [c.450 BCE], B3), quoted by Simplicius - On Aristotle's 'Physics' 140.29
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
That which moves, moves neither in the place in which it is, nor in that in which it is not
     Full Idea: That which moves, moves neither in the place in which it is, nor in that in which it is not.
     From: Zeno (Elea) (fragments/reports [c.450 BCE], B4), quoted by (who?) - where?
27. Natural Reality / C. Space / 5. Relational Space
If everything is in a place, what is the place in? Place doesn't exist
     Full Idea: If there is a place it will be in something, because everything that exists is in something. But what is in something is in a place. Therefore the place will be in a place, and so on ad infinitum. Therefore, there is no such thing as place.
     From: report of Zeno (Elea) (fragments/reports [c.450 BCE], B3) by Simplicius - On Aristotle's 'Physics' 9.562.3