Zeno of Elea - philosophy, książki, Philosphy
[ Pobierz całość w formacie PDF ]Zeno of Elea
Arthur Fairbanks, ed. and trans.
The First Philosophers of Greece
London: K. Paul, Trench, Trubner, 1898
Page 112-119.
Fairbanks's Introduction
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Zeno of Elea, son of Teleutagoras, was born early in the-fifth
century B.C. He was the pupil of Parmenides, and his relations with him
were so intimate that Plato calls him Parmenides's son (Soph. 241 D).
Strabo (vi. 1, 1) applies to him as well as to his master the name
Pythagorean, and gives him the credit of advancing the cause of law and
order in Elea. Several writers say that he taught in Athens for a while. There
are numerous accounts of his capture as party to a conspiracy; these
accounts differ widely from each other, and the only point of agreement
between them has reference to his determination in shielding his fellow
conspirators. We find reference to one book which he wrote in prose (Plato,
Parm. 127 c), each section of which showed the absurdity of some element
in the popular belief.
Literature: Lohse, Halis 1794; Gerling, de Zenosin Paralogismis, Marburg
1825; Wellmann, Zenos Beweise, G.-Pr. Frkf. a. O. 1870; Raab, D.
Zenonische Beweise, Schweinf. 1880; Schneider, Philol. xxxv. 1876;
Tannery, Rev. Philos. Oct. 1885; Dunan, Les arguments de Zenon, Paris
1884; Brochard, Les arguments de Zenon, Paris 1888; Frontera, Etude sur les
arguments de Zenon, Paris 1891
Simplicius's account of Zeno's arguments,
including the translation of the Fragments
30 r 138, 30. For Eudemos says in his Physics, 'Then does not this exist, and
is there any one ? This was the problem. He reports Zeno as saying that if
any one explains to him the one, what it is, he can tell him what things are.
But he is puzzled, it seems, because each of the senses declares that there
are many things, both absolutely, and as the result of division, but no one
establishes the mathematical point. He thinks that what is not increased by
receiving additions, or decreased as parts are taken away, is not one of the
things that are.' It was natural that Zeno, who, as if for the sake of exercise,
argued both sides of a case (so that he is called double-tongued), should
utter such statements raising difficulties about the one; but in his book
which has many arguments in regard to each point, he shows that a man
who affirms multiplicity naturally falls into contradictions. Among these
arguments is one by which he shows that if there are many things, these are
both small and great - great enough to be infinite in size, and small enough
to be nothing in size. By this he shows that what has neither greatness nor
thickness nor bulk could not even be. (Fr. 1)9 'For if, he says, anything were
added to another being, it could not make it any greater; for since greatness
does not exist, it is impossible to increase the greatness of a thing by adding
to it. So that which is added would be nothing. If when something is taken
away that which is left is no less, and if it becomes no greater by receiving
additions, evidently that which has been added or taken away is nothing.'
These things Zeno says, not denying the one, but holding that each thing
has the greatness of
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many and infinite things, since there is
always something before that which is apprehended, by reason of its infinite
divisibility; and this he proves by first showing that nothing has any
greatness because each thing of the many is identical with itself and is one.
Ibid
. 30 v 140, 27. And why is it necessary to say that there is a multiplicity
of things when it is set, forth in Zeno's own book? For again in showing
that, if there is a multiplicity of things, the same things are both finite and
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infinite, Zeno writes as follows, to use his own words: (Fr. 2) 'If there is a
multiplicity of things; it is necessary that these should be just as many as
exist, and not more nor fewer. If there are just as many as there are, then the
number would be finite. If there is a multiplicity at all, the number is
infinite, for there are always others between any two, and yet others
between each pair of these. So the number of things is infinite.' So by the
process of division he shows that their number is infinite. And as to
magnitude, he begins, with this same argument. For first showing that (Fr.
3) 'if being did not have magnitude, it would not exist at all,' he goes on, 'if
anything exists, it is necessary that each thing should have some magnitude
and thickness, and that one part of it should be separated from another. The
same argument applies to the thing that precedes this. That also will have
magnitude and will have something before it. The same may be said of each
thing once for all, for there will be no such thing as last, nor will one thing
differ from another. So if there is a multiplicity of things, it is necessary that
these should be great and small--small enough not to have any magnitude,
and great enough to be infinite.'
Ibid.
130 v 562,.3. Zeno's argument seems to deny that place exists, putting
the question as follows: (Fr. 4)
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'If there is such a thing as place,
it will be in something, for all being is in something, and that which is in
something is in some place. Then this place will be in a place, and so on
indefinitely. Accordingly there is no such thing as place.'
Ibid.
131 r 563, 17. Eudemos' account of Zeno's opinion runs as follows:
'Zeno's problem seems to come to the same thing. For it is natural that all
being should be somewhere, and if there is a place for things, where would
this place be? In some other place, and that in another, and so on
indefinitely.'
Ibid.
236 v. Zeno's argument that when anything is in a space equal to
itself, it is either in motion or at rest, and that nothing is moved in the
present moment, and that the moving body is always in a space equal to
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itself at each present moment, may, I think, be put in a syllogism as follows:
The arrow which is moving forward is at every present moment in a space
equal to itself, accordingly it is in a space equal to itself in all time; but that
which is in a space equal to itself in the present moment is not in motion.
Accordingly it is in a state of rest, since it is not moved in the present
moment, and that which is not moving is at rest, since everything is either
in motion or at rest. So the arrow which is moving forward is at rest while it
is moving forward, in every moment of its motion.
237 r. The Achilles argument is so named because Achilles is named in it as
the example, and the argument shows that if he pursued a tortoise it would
be impossible for him to overtake it. 255 r, Aristotle accordingly solves the
problem of Zeno the Eleatic, which he propounded to Protagoras the
Sophist.11 Tell me, Protagoras, said he, does one grain of millet make a
noise when it falls, or does the
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ten-thousandth part of a grain?
On receiving the answer that it does not, he went on: Does a measure of
millet grains make a noise when it falls, or not? He answered, it does make a
noise. Well, said Zeno, does not the statement about the measure of millet
apply to the one grain and the ten-thousandth part of a grain? He assented,
and Zeno continued, Are not the statements as to the noise the same in
regard to each? For as are the things that make a noise, so are the noises.
Since this is the case, if the measure of millet makes a noise, the one grain
and the ten-thousandth part of a grain make a noise.
Zeno's arguments as described by Aristotle
Phys
. iv. 1; 209 a 23. Zeno's problem demands some consideration; if all
being is in some place, evidently there must be a place of this place, and so
on indefinitely. 3; 210 b 22. It is not difficult to solve Zeno's problem, that
if place is anything, it will be in some place; there is no reason why the first
place should not be in something else, not however as in that place, but just
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as health exists in warm beings as a state while warmth exists in matter as a
property of it. So it is not necessary to assume an indefinite series of places.
vi. 2; 233 a 21. (Time and space are continuous . . . the divisions of time
and space are the same.) Accordingly Zeno's argument is erroneous, that it
is not possible to traverse infinite spaces, or to come in contact with infinite
spaces successively in a finite time. Both space and time can be called
infinite in two ways, either absolutely as a continuous whole, or by division
into the smallest parts. With infinites in point of quantity, it is not possible
for anything to come in contact in a finite time, but it is possible in the case
of the infinites
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reached by division, for time itself is infinite from
this standpoint. So the result is that it traverses the infinite in an infinite,
not a finite time, and that infinites, not finites, come in contact with
infinites.
vi. 9 ; 239 b 5. And Zeno's reasoning is fallacious. For if, he says, everything
is at rest [or in motion] when it is in a space equal to itself, and the moving
body is always in the present moment then the moving arrow is still. This is
false for time is not composed of present moments that are indivisible, nor
indeed is any other quantity. Zeno presents four arguments concerning
motion which involve puzzles to be solved, and the first of these shows that
motion does not exist because the moving body must go half the distance
before it goes the whole distance; of this we have spoken before (Phys. viii.
8; 263 a 5). And the second is called the Achilles argument; it is this: The
slow runner will never be overtaken by the swiftest, for it is necessary that
the pursuer should first reach the point from which the pursued started, so
that necessarily the slower is always somewhat in advance. This argument is
the same as the preceding, the only difference being that the distance is not
divided each time into halves. . . . His opinion is false that the one in
advance is not overtaken; he is not indeed overtaken while he is in advance;
but nevertheless he is overtaken, if you will grant that he passes through the
limited space. These are the first two arguments, and the third is the one
that has been alluded to, that the arrow in its flight is stationary. This
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