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Originally published in 1936, this book presents the ancient Greek text of the paraphrases and quotations of Zeno's philosophical arguments, together with a facing-page English translation and editorial commentary. Detailed notes are incorporated throughout and a bibliography is also included. This book will be of value to anyone with an interest in Zeno and ancient philosophy.
- Sales Rank: #2340024 in Books
- Published on: 2015-02-12
- Released on: 2015-02-12
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .31" w x 5.51" l, .39 pounds
- Binding: Paperback
- 132 pages
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"Zeno, in support of his master, tried to prove that what is, is of necessity one and unmoved" (p. 13; Philoponus, 80.23)
By Viktor Blasjo
This is a useful collection of the fragments from the classical sources pertaining to Zeno.
Zeno most famously argued that motion is impossible. His "dichotomy" argument is perhaps most famous of all:
"An object in motion must move through a certain distance; but since every distance is infinitely divisible the moving object must first traverse half the distance through which it is moving, and then the whole distance; but before it traverses the whole of the half distance, it must traverse half of the half, and again the half of this half. If then these halves are infinite in number, because it is always possible to halve any given length, and if it is impossible to traverse an infinite number of positions in a finite time ... [then] therefore it is impossible to traverse any magnitude in a finite time." (p. 45; Simplicius 1013.4)
There is also the "Achilles" form of the argument:
"The argument is called the Achilles because of the introduction into it of Achilles, who, the argument says, cannot possibly overtake the tortoise he is pursuing. For the overtaker must, before he overtakes the pursued, first come to the point from which the pursued started. But during the time taken by the pursuer to reach this point, the pursued always advances a certain distance; even if this distance is less than that covered by the pursuer, because the pursued is the slower of the two, yet none the less it does advance, for it is not at rest. And again during the time which the pursuer takes to clever this distance which the pursued has advanced, the pursued again covers a certain distance ... And so, during every period of time in which the pursuer is covering the distance which the pursued ... has already advanced, the pursued advances a yet further distance; for even though this distance decreases at each step, yet, since the pursued is also definitely in motion, it does advance some positive distance. And so ... we arrive at the conclusion that not only will Hector never be overcome by Achilles, but not even the tortoise." (p. 51; Simplicius 1014.9)
This seems to be basically a literary elaboration of the dichotomy argument which adds little in terms of substance. However, unlike the dichotomy, it does not assume an absolute notion of distance, so it could be seen as an improvement on the former insofar as it strikes equally agains purely relativistic notions of motion.
A very different argument is the "arrow" argument:
"If everything is either at rest or in motion, but nothing is in motion when it occupies a space equal to itself, and what is in flight is always at any given instant occupying a space qual to itself, then the flying arrow is motionless." (p. 53; Aristotle Physics Z 9. 239b)
The precise meaning of this argument is not very clear, but one possible interpretation is this: if time is made up of instants and if the arrow is at any given instant occupying a fixed place, then how can it move? Analogously one might argue: if a line segment is made up of points, and a point has no length, how can the line segment have a length?
Finally, there is the "stadium" argument:
"The fourth [of Zeno's arguments against motion] is the one about the two rows of equal bodies which move past each other in a stadium with equal velocities in opposite directions ... This, [Zeno] thinks, involves the conclusion that half a given time is equal to its double [i.e. the whole time]." (p. 55; Aristotle Physics Z. 9. 239b)
For if the speed of the first row is measured relative to the fixed stadium, and the speed of the second row relative to the first, then it will appear that the second row is moving twice as fast.
Aristotle's attempt to refute this argument seems to me very naive. For he argues that "the fallacy lies in assuming that a body takes an equal time to pass with equal velocity a body that is in motion and a body that is at rest, an assumption which is false." But how do we tell whether an object is in motion or not? Zeno has just demonstrated that this is not such an easy problem, since it is not enough to compare it to some arbitrary reference point. Thus the burden of proof falls upon Zeno's opponents to specify a criterion for deciding which points are to be admitted as "true" reference points. Who is to say that the stadium itself is "really" at rest, for example? Even Aristotle is not allowed to settle such questions by simple decree.
It seems that Zeno struck upon his arguments regarding motion by a rather strange path. Evidently he was a follower of Parmenides and wanted to defend the latter's thesis that "what is, is one", though we have no indication of what Zeno's rationale may have been for adopting this stance in the first place, other than personal influence. Beside the motion arguments, the other fragments preserved from Zeno concern more explicit defenses of the Parmenidean thesis. These arguments are of incomparably lower quality than the motion arguments, so they are of very little interest in themselves. However, they are based on the infinite divisibility of the continuum, and thus they are in a sense very similar to the motion arguments. It seems quite plausible that Zeno started out fooling around with divisibility in this context, and only then discovered, as a kind of side effect, the much more compelling force of these kinds of arguments in the context of motion.
A sample of Zeno's more explicitly Parmenidean divisibility arguments is the following:
"[Zeno; cf. p. 22] had another argument which he thought to prove by means of dichotomy that what is, is one only, and accordingly without parts and indivisible. For, he argues, if it were divisible, then suppose the process of dichotomy to have taken place: then either there will be left certain ultimate magnitudes, which are minima and indivisible, but infinite in number, and so the whole will be made up of minima but an infinite number of them; or else it will vanish and be divided away to nothing, and so be made up of parts that are nothing. Both of which conclusions are absurd." (p. 13; Simplicius, 139.27)
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