To Parmenides the universe is not infinite, for, according the Greek artistic conception, what is infinite is imperfect.

Melissus (440) of Samos. Not only a philosopher but a soldier a stateman opposed to the lonic cosmogonies the eleatic doctrine of the world's eternity. Melissus was a materialist. If becoming be impossible, it is useless and absurd to inquire how the universe came to be. Being is infinite in duration and also in space. This last circumstance marks Melissus as a materialist and separates his Philosophy from that of Parmenides, and from that of most Greek systems whose reasoning is that to be infinite is to lack finiteness, consequently to be imperfect. It is an artistic conception. To them the universe is finite and has the form of a perfect sphere.

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Zeno, disciple of Parmenides, controversialist of the eleatics, is the inventor of the reductio ad absurdum, father of sophistry and dialectics.

The One alone can be conceived; extension, size, movement space cannot be.

1. Suppose a grandeur (limited) exists, it must necessarily be infinitely great and infinitely little.

Infinitely great, because, being divisible ad infinitum, it is composed of an infinite number of parts;

Infinitely little, because unextended parts, though multiplied ad infinitum, cannot make an extension, a grandeur.

2. Movement cannot be conceived.

a) Because the line which separates points of departure and of arrival is composed of points, and, since the point is unextended, of an infinite number of points.

Therefore even the smallest distance is infinite and the point of arrival cannot be reached.

b) Suppose rapid Achilles as near as you wish to the slow tortoise; he will never catch it up: because, to overtake it, he would have first to cover half the space however small that separates him; and before that half of this half and so on ad infinitum. The infinite divisibility of the line is to him an unsurmontable obstacle.

c) It is believed that the arrow flies; it does not: for to attain its end it must cover a series of points in space. It must successively occupy these different points.

But to occupy at a given moment any point in space, is to halt: the arrow does not move; its movement is but appearance.

3. But if movement exist, it can but exist in space.

Now, if space be real it must be found somewhere, i.e. in another space, and this one in another and so on ad infinitum.

Movement is therefore impossible: we cannot admit it to be real without affirming, in absurdity.

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Gorgias, of Leontium (...) brought the eleatic principle to its last consequences: nihilism. In his treatise (...) he goes beyond Zeno and demolishes being itself.

Argument: Nothing exists. If anything exists, it must be eternal (Parmenides). What is eternal is infinite; infinite Being is neither in time nor in space, which would limit it «tour à tour». It is nowhere, and what is nowhere does not exist. If (what is impossible) anything existed, we could not know it. And if we could know it we could not communicate this knowledge to others.

Gorgias’ indiscretion gives rise to the desire of Heraclitus. «Being is nothing (becoming) is all.»

Being of Parm[enides] and Zenon is but an abstraction eternal and immutable without positive attributes.