Combining Philosophers

Ideas for Archimedes, Zeno (Elea) and A.R. Lacey

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4 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox

1507	We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea]
	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

5109	The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle]
	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.

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')

1512	Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea]
	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

1508	Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea]
	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