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