# Zeno

(209a23) If space itself is an existent, it will be somewhere. Zeno's difficulty demands an explanation; for if everything that exists has a place, place too will have a place, and so on ad infinitum

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(210b22) Zeno's problem- that if place is something it must be in something- is not difficult to solve. There is nothing to prevent the first place from being in something else- not indeed in that as in a place, but as health is in the hot as a state of it or as the hot is in body as an affection. So we escape the infinite regress

(233a21) Zeno's argument makes a false assumption in asserting that it is impossible for a thing to pass over or severally to come in contact with infinite things in a finite time. For there are two ways in which length and time and generally anything continuous are called infinite: they are called so either in respect of divisibility or in respect of their extremities. So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility for in this sense the time itself is also infinite; and so we find that the time occupied by the passage over the infinite is not a finite but an infinite time, and the contact with the infinities is made by means of Moments not finite but infinite in number. The passage over the infinite, then, cannot occupy a finite time, and the passage over the finite cannot occupy an infinite time: if the time is infinite the magnitude must be infinite also, and if the magnitude is infinite, so also is the time

(239b10) Zeno's reasoning is fallacious when he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always in a now, the flying arrow is therefore motionless. This is false; for time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles

(250a20) Hence Zeno's reasoning is false when he argues that there is no part of the millet that does not make a sound; for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself; for no part even exists otherwise than potentially in the whole

(968a19) Zeno's argument proves that there must be partless magnitudes. For it is impossible to touch an Infinite number of things in a finite time, touching them one by one; and the moving body must reach the half-way point before it reaches the end; and there is always a half-way point in any non-partless thing. But even if the body, which is moving along the line, does touch the infinity of points in a finite time; and if the quicker the movement of the moving body, the greater the stretch which it traverses in an equal time; and if the movement of thought is quickest of all movements: it follows that thought too will come successively into contact with an infinity of objects in a finite time. And since thought's coming into contact with objects one-by-one is counting, it is possible to count infinitely many objects in a finite time. But since this is impossible, there must be such a thing as an indivisible line

Against the view that a finite stretch of space of time consists of a finite number of points and instants, Zeno's arguments are perfectly valid(okew174)

Zeno's arguments, in some form, have afforded grounds for almost all the theories of space and time and infinity which have been constructed from his day to our own(okew183)

Zeno's paradoxes, if they can be made initially puzzling, become less so when time is looked upon as space-like. Seeing time in the image of space helps us appreciate infinitely many periods of time can just as well add up to a finite period as can a finite distance be divided into infinitely many component distances(wo172)