Early Greek Philosophy & Other Essays Collected Works, Volume Two · Friedrich Wilhelm Nietzsche
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The other idea, of greater import than that of the "Existent," and likewise invented already by Parmenides, although not yet so clearly applied as by his disciple Zeno is the idea of the Infinite. Nothing Infinite can exist; for from such an assumption the contradictory idea of a perfect Infinitude would result. Since now our actuality, our existing world everywhere shows the character of that perfect Infinitude, our world signifies in its nature a contradiction against logic and therewith also against reality and is deception, lie, fantasma. Zeno especially applied the method of indirect proof; he said for example, "There can be no motion from one place to another; for if there were such a motion, then an Infinitude would be given as perfect, this however is an impossibility." Achilles cannot catch up the tortoise which has a small start in a race, for in order to reach only the point from which the tortoise began, he would have had to run through innumerable, infinitely many spaces, viz., first half of that space, then the fourth, then the sixteenth, and so on _ad infinitum._ If he does in fact overtake the tortoise then this is an illogical phenomenon, and therefore at any rate not a truth, not a reality, not real "Being," but only a delusion.
For it is never possible to finish the infinite. Another popular expression of this doctrine is the flying and yet resting arrow. At any instant of its flight it has a position; in this position it rests. Now would the sum of the infinite positions of rest be identical with motion? Would now the Resting, infinitely often repeated, be Motion, therefore its own opposite? The Infinite is here used as the _aqua fortis_ of reality, through it the latter is dissolved. If however the Ideas are fixed, eternal and entitative--and for Parmenides "Being" and Thinking coincide--if therefore the Infinite can never be perfect, if Rest can never become Motion, then in fact the arrow has not flown at all; it never left its place and resting position; no moment of time has passed. Or expressed in another way: in this so-called yet only alleged Actuality there exists neither time, nor space, nor motion. Finally the arrow itself is only an illusion; for it originates out of the Plurality, out of the phantasmagoria of the "Non-One" produced by the senses. Suppose the arrow had a "Being," then it would be immovable, timeless, increate, rigid and eternal--an impossible conception! Supposing that Motion was truly real, then there would be no rest, therefore no position for the arrow, therefore no space--an impossible conception!
Supposing that time were real, then it could not be of an infinite divisibility; the time which the arrow needed, would have to consist of a limited number of time-moments, each of these moments would have to be an _Atomon_--an impossible conception! All our conceptions, as soon as their empirically-given content, drawn out of this concrete world, is taken as a _Veritas æterna,_ lead to contradictions. If there is absolute motion, then there is no space; if there is absolute space then there is no motion; if there is absolute "Being," then there is no Plurality; if there is an absolute Plurality, then there is no Unity. It should at least become clear to _us_ how little we touch the heart of things or untie the knot of reality with such ideas, whereas Parmenides and Zeno inversely hold fast to the truth and omnivalidity of ideas and condemn the perceptible world as the opposite of the true and omnivalid ideas, as an objectivation of the illogical and contradictory.
With all their proofs they start from the wholly undemonstrable, yea improbable assumption that in that apprehensive faculty we possess the decisive, highest criterion of "Being" and "Not-Being," _i.e.,_ of objective reality and its opposite; those ideas are not to prove themselves true, to correct themselves by Actuality, as they are after all really derived from it, but on the contrary they are to measure and to judge Actuality, and in case of a contradiction with logic, even to condemn. In order to concede to them this judicial competence Parmenides had to ascribe to them the same "Being," which alone he allowed in general as _the_ "Being"; Thinking and that one increate perfect ball of the "Existent" were now no longer to be conceived as two different kinds of "Being," since there was not permitted a duality of "Being." Thus the over-risky flash of fancy had become necessary to declare Thinking and "Being" identical. No form of perceptibility, no symbol, no simile could possibly be of any help here; the fancy was wholly inconceivable, but it was necessary, yea in the lack of every possibility of illustration it celebrated the highest triumph over the world and the claims of the senses. Thinking and that clod-like, ball-shaped, through-and-through dead-massive, and rigid-immovable "Being," must, according to the Parmenidean imperative, dissolve into one another and be the same in every respect, to the horror of fantasy. What does it matter that this identity contradicts the senses! This contradiction is just the guarantee that such an identity is not borrowed from the senses.
Text from Project Gutenberg, public domain in the United States.