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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.
Or, again, take objects moving at unequal rates, as Achilles and a tortoise. Let the tortoise have a start of any given length, then Achilles, however {45} much he excel in speed, will never overtake the tortoise. For, while Achilles has passed over the originally intervening space, the tortoise will have passed over a certain space, and when Achilles has passed over this second space the tortoise will have again passed over some space, and so on ad infinitum; therefore in an infinite time there must always be a space, though infinitely diminishing, between the tortoise and Achilles, i.e. the tortoise must always be at least a little in front.
These will be sufficient to show the kind of arguments employed by Zeno. In themselves they are of no utility, and Zeno never pretended that they had any. But as against those who denied that existence as such was a datum independent of experience, something different from a mere sum of isolated things, his arguments were not only effective, but substantial. The whole modern sensational or experiential school, who derive our 'abstract ideas,' as they are called, from 'phenomena' or 'sensation,' manifest the same impatience of any analysis of what they mean by phenomena or sensation, as no doubt Zeno's opponents manifested of his analyses. As in criticising the one, modern critics are ready with their answer that Zeno's quibbles are simply "a play of words on the well-known properties of infinities," so they are quick to tell us that sensation is an "affection of the sentient organism"; ignoring in {46} the first case the prior question where the idea of infinity came from, and in the second, where the idea of a sentient organism came from.
Indirectly, as we shall see, Zeno had a great effect on subsequent philosophies by the development of a process of ingenious verbal distinction, which in the hands of so-called sophists and others became a weapon of considerable, if temporary, power.
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IV. MELISSUS.—The fourth and last of the Eleatic philosophers was Melissus, a native of Samos. His date may be fixed as about 440 B.C. He took an active part in the politics of his native country, and on one occasion was commander of the Samian fleet in a victorious engagement with the Athenians, when Samos was being besieged by Pericles. He belongs to the Eleatic school in respect of doctrine and method, but we have no evidence of his ever having resided at Elea, nor any reference to his connection with the philosophers there, except the statement that he was a pupil of Parmenides. He developed very fully what is technically called in the science of Logic [110] the Dilemma. Thus, for example, he begins his treatise On Existence or On Nature thus: "If nothing exists, then there is nothing for us to talk about. But if there is such a thing as existence it must either come into being or be ever-existing. If it come into being, it must come from the existing or the non-existing. Now that anything which exists, {47} above all, that which is absolutely existent, should come from what is not, is impossible. Nor can it come from that which is. For then it would be already, and would not come into being. That which exists, therefore, comes not into being; it must therefore be ever-existing."
[111]
By similar treatment of other conceivable alternatives he proceeds to show that as the existent had no beginning so it can have no ending in time. From this, by a curious transition which Aristotle quotes as an example of loose reasoning, he concludes that the existent can have no limit in space [112] either. As being thus unlimited it must be one, therefore immovable (there being nothing else into which it can move or change), and therefore always self-identical in extent and character. It cannot, therefore, have any body, for body has parts and is not therefore one.
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