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Three Millennia of Greek Literature

A History of Greek Philosophy / THE ELEATICS / ZENO


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The arguments of Zeno may therefore be regarded as strictly arguments in kind; quibbles if you please, but in answer to quibbles. The secret of his method was what Aristotle calls Dichotomy—that is, he put side by side two contradictory propositions with respect to any particular supposed real thing in experience, and then proceeded to show that both these contradictories alike imply what is inconceivable. Thus “a thing must consist either of a finite number of parts or an infinite number.” Assume the number of parts to be finite. Between them there must either be something or nothing. If there is something between them, then the whole consists of more parts than it consists of. If there is nothing between them, then they are not separated, therefore they are not parts; therefore the whole has no parts at all; therefore it is nothing. If, on the other hand, the number of parts is infinite, then, the same kind of argument being applied, the magnitude of the whole is by infinite successive positing of intervening parts shown to be infinite; therefore this one thing, being infinitely large, is everything.

Take, again, any supposed fact, as that an arrow moves. An arrow cannot move except in space. It cannot move in space without being in space. At any moment of its supposed motion it must be in a particular space. Being in that space, it must at the time during which it is in it be at rest. But the total time of its supposed motion is made up of the moments composing that time, and to each of these moments the same argument applies; therefore either the arrow never was anywhere, or it always was at rest.

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