THE YOUNGER ELEATICS
[Sidenote: Relation to predecessors.]
154. The systems we have just been studying were all fundamentally
pluralist, and they were so because Parmenides had shown that, if we
take a corporeal monism seriously, we must ascribe to reality a number
of predicates which are inconsistent with our experience of a world
which everywhere displays multiplicity, motion, and change (§ 97). The
four “roots” of Empedokles and the innumerable “seeds” of Anaxagoras
were both of them conscious attempts to solve the problem which
Parmenides had raised (§§ 106, 127). There is no evidence, indeed, that
the Pythagoreans were directly influenced by Parmenides, but it has been
shown (§ 147) how the later form of their system was based on the theory
of Empedokles. Now it was just this prevailing pluralism that Zeno
criticised from the Eleatic standpoint; and his arguments were
especially directed against Pythagoreanism. Melissos, too, criticises
Pythagoreanism; but he tries to find a common ground with his
adversaries by maintaining the old Ionian thesis that reality is
infinite.
I. ZENO OF ELEA
[Sidenote: Life.]
155. According to Apollodoros,[851] Zeno flourished in Ol. LXXIX.
(464-460 B.C.). This date is arrived at by making him forty years
younger than his master Parmenides. We have seen already (§ 84) that the
meeting of Parmenides and Zeno with the young Sokrates cannot well have
occurred before 449 B.C., and Plato tells us that Zeno was at that time
“nearly forty years old.”[852] He must, then, have been born about 489
B.C., some twenty-five years after Parmenides. He was the son of
Teleutagoras, and the statement of Apollodoros that he had been adopted
by Parmenides is only a misunderstanding of an expression of Plato’s
_Sophist_.[853] He was, Plato further tells us,[854] tall and of a
graceful appearance.
Footnote 851:
Diog. ix. 29 (R. P. 130 a). Apollodoros is not expressly referred to
for Zeno’s date; but, as he is quoted for his father’s name (ix. 25;
R. P. 130), there can be no doubt that he is also the source of the
_floruit_.
Footnote 852:
Plato, _Parm._ 127 b (R. P. 111 d). The visit of Zeno to Athens is
confirmed by Plut. _Per._ 4 (R. P. 130 e), where we are told that
Perikles “heard” him as well as Anaxagoras. It is also alluded to in
_Alc._ I. 119 a, where we are told that Pythodoros, son of Isolochos,
and Kallias, son of Kalliades, each paid him 100 minae for
instruction.
Footnote 853:
Plato, _Soph._ 241 d (R. P. 130 a).
Footnote 854:
Plato, _Parm._, _loc. cit._
Like Parmenides and most other early philosophers, Zeno seems to have
played a part in the politics of his native city. Strabo ascribes to him
some share of the credit for the good government of Elea, and says that
he was a Pythagorean.[855] This statement can easily be explained.
Parmenides, we have seen, was originally a Pythagorean, and the school
of Elea was no doubt popularly regarded as a mere branch of the larger
society. We hear also that Zeno conspired against a tyrant, whose name
is differently given, and the story of his courage under torture is
often repeated, though with varying details.[856]
Footnote 855:
Strabo, vi. p. 252 (R. P. 111 c).
Footnote 856:
Diog. ix. 26, 27, and the other passages referred to in R. P. 130 c.
[Sidenote: Writings.]
156. Diogenes speaks of Zeno’s “books,” and Souidas gives some titles
which probably come from the Alexandrian librarians through Hesychios of
Miletos.[857] In the _Parmenides_, Plato makes Zeno say that the work by
which he is best known was written in his youth and published against
his will.[858] As he is supposed to be forty years old at the time of
the dialogue, this must mean that the book was written before 460 B.C.
(§ 84), and it is very possible that he wrote others after it. The most
remarkable title which has come down to us is that of the
_Interpretation of Empedokles_. It is not to be supposed, of course,
that Zeno wrote a commentary on the Poem of Empedokles; but, as Diels
has pointed out,[859] it is quite credible that he should have written
an attack on it, which was afterwards called by that name. If he wrote a
work against the “philosophers,” that must mean the Pythagoreans, who,
as we have seen, made use of the term in a sense of their own.[860] The
_Disputations_ and the _Treatise on Nature_ may, or may not, be the same
as the book described in Plato’s _Parmenides_.
Footnote 857:
Diog. ix. 26 (R. P. 130); Suidas _s.v._ (R. P. 130 d).
Footnote 858:
Plato, _Parm._ 128 d 6 (R. P. 130 d).
Footnote 859:
_Berl. Sitzb._, 1884, p. 359.
Footnote 860:
See above, p. 321, _n._ 740. It hardly seems likely that a later
writer would make Zeno argue πρὸς τοὺς φιλοσόφους, and the title given
to the book at Alexandria must be based on something contained in it.
It is not likely that Zeno wrote dialogues, though certain references in
Aristotle have been supposed to imply this. In the _Physics_[861] we
hear of an argument of Zeno’s, that any part of a heap of millet makes a
sound, and Simplicius illustrates this by quoting a passage from a
dialogue between Zeno and Protagoras.[862] If our chronology is right,
there is nothing impossible in the idea that the two men may have met;
but it is most unlikely that Zeno should have made himself a personage
in a dialogue of his own. That was a later fashion. In another place
Aristotle refers to a passage where “the answerer and Zeno the
questioner” occurred,[863] a reference which is most easily to be
understood in the same way. Alkidamas seems to have written a dialogue
in which Gorgias figured,[864] and the exposition of Zeno’s arguments in
dialogue form must always have been a tempting exercise. It appears also
that Aristotle made Alexamenos the first writer of dialogues.[865]
Footnote 861:
Arist. _Phys._ Η, 5. 250 a 20 (R. P. 131 a).
Footnote 862:
Simpl. _Phys._ p. 1108, 18 (R. P. 131). If this is what Aristotle
refers to, it is hardly safe to attribute the κεγχρίτης λόγος to Zeno
himself. It is worth noting that the existence of this dialogue is
another indication of Zeno’s visit to Athens at an age when he could
converse with Protagoras, which agrees very well with Plato’s
representation of the matter.
Footnote 863:
Arist. _Soph. El._ 170 b 22 (R. P. 130 b).
Footnote 864:
Chap. V. p. 231, _n._ 512.
Footnote 865:
Diog. iii. 48. It is certain that the authority whom Diogenes follows
here took the statement of Aristotle to mean that Alexamenos was the
first writer of prose dialogues.
Plato gives us a clear idea of what Zeno’s youthful work was like. It
contained more than one “discourse,” and these discourses were
subdivided into sections, each dealing with some one presupposition of
his adversaries.[866] We owe the preservation of Zeno’s arguments on the
one and many to Simplicius.[867] Those relating to motion have been
preserved by Aristotle himself;[868] but, as usual, he has restated them
in his own language.
Footnote 866:
Plato, _Parm._ 127 d. Plato speaks of the first ὑπόθεσις of the first
λόγος, which shows that the book was really divided into separate
sections. Proclus (_in loc._) says there were forty of these λόγοι
altogether.
Footnote 867:
Simplicius expressly says in one place (p. 140, 30; R. P. 133) that he
is quoting κατὰ λέξιν. I now see no reason to doubt this, as the
Academy would certainly have a copy of the work. If so, the fact that
the fragments are not written in Ionic is another confirmation of
Zeno’s residence at Athens.
Footnote 868:
Arist. _Phys._ Ζ, 9. 239 b 9 sqq.
[Sidenote: Dialectic.]
157. Aristotle in his _Sophist_[869] called Zeno the inventor of
dialectic, and this, no doubt, is substantially true, though the
beginnings at least of that method of arguing were contemporary with the
foundation of the Eleatic school. Plato[870] gives us a spirited account
of the style and purpose of Zeno’s book, which he puts into his own
mouth:—
In reality, this writing is a sort of reinforcement for the argument
of Parmenides against those who try to turn it into ridicule on the
ground that, if reality is one, the argument becomes involved in many
absurdities and contradictions. This writing argues against those who
uphold a Many, and gives them back as good and better than they gave;
its aim is to show that their assumption of multiplicity will be
involved in still more absurdities than the assumption of unity, if it
is sufficiently worked out.
Footnote 869:
Cf. Diog. ix. 25 (R. P. 130).
Footnote 870:
Plato, _Parm._ 128 c (R. P. 130 d).
The method of Zeno was, in fact, to take one of his adversaries’
fundamental postulates and deduce from it two contradictory
conclusions.[871] This is what Aristotle meant by calling him the
inventor of dialectic, which is just the art of arguing, not from true
premisses, but from premisses admitted by the other side. The theory of
Parmenides had led to conclusions which contradicted the evidence of the
senses, and Zeno’s object was not to bring fresh proofs of the theory
itself, but simply to show that his opponents’ view led to
contradictions of a precisely similar nature.
Footnote 871:
The technical terms used in Plato’s _Parmenides_ seem to be as old as
Zeno himself. The ὑπόθεσις is the provisional assumption of the truth
of a certain statement, and takes the form εἰ πολλά ἐστι or the like.
The word does not mean the assumption of something as a foundation,
but the setting before one’s self of a statement as a problem to be
solved (Ionic ὑποθέσθαι, Attic προθέσθαι). If the conclusions which
necessarily follow from the ὑπόθεσις (τὰ συμβαίνοντα) are impossible,
the ὑπόθεσις is “destroyed” (cf. Plato, _Rep._ 533 c 8, τὰς ὑποθέσεις
ἀναιροῦσα). The author of the Περὶ ἀρχαίης ἰατρικῆς (c 1) knows the
word ὑπόθεσις in a similar sense.
[Sidenote: Zeno and Pythagoreanism.]
158. That Zeno’s dialectic was mainly directed against the Pythagoreans
is certainly suggested by Plato’s statement, that it was addressed to
the adversaries of Parmenides, who held that things were “a many.”[872]
Zeller holds, indeed, that it was merely the popular form of the belief
that things are many that Zeno set himself to confute;[873] but it is
surely not true that ordinary people believe things to be “a many” in
the sense required. Plato tells us that the premisses of Zeno’s
arguments were the beliefs of the adversaries of Parmenides, and the
postulate from which all his contradictions are derived is the view that
space, and therefore body, is made up of a number of discrete units,
which is just the Pythagorean doctrine. Nor is it at all probable that
Anaxagoras is aimed at.[874] We know from Plato that Zeno’s book was the
work of his youth.[875] Suppose even that it was written when he was
thirty, that is to say, about 459 B.C., Anaxagoras had just taken up his
abode at Athens at that time,[876] and it is very unlikely that Zeno had
ever heard of him. There is, on the other hand, a great deal to be said
for the view that Anaxagoras had read the work of Zeno, and that his
emphatic adhesion to the doctrine of infinite divisibility was due to
the criticism of his younger contemporary.[877]
Footnote 872:
The view that Zeno’s arguments were directed against Pythagoreanism
has been maintained in recent times by Tannery (_Science hellène_, pp.
249 sqq.), and Bäumker (_Das Problem der Materie_, pp. 60 sqq.).
Footnote 873:
Zeller, p. 589 (Eng. trans. p. 612).
Footnote 874:
This is the view of Stallbaum in his edition of the _Parmenides_ (pp.
25 sqq.).
Footnote 875:
_Parm._, _loc. cit._
Footnote 876:
Chap. VI. § 120.
Footnote 877:
Cf. for instance Anaxagoras, fr. 3, with Zeno, fr. 2; and Anaxagoras,
fr. 5, with Zeno, fr. 3.
It will be noted how much clearer the historical position of Zeno
becomes if we follow Plato in assigning him to a somewhat later date
than is usual. We have first Parmenides, then the pluralists, and then
the criticism of Zeno. This, at any rate, seems to have been the view
which Aristotle took of the historical development.[878]
Footnote 878:
Arist. _Phys._ Α, 3. 187 a 1 (R. P. 134 b). See below, § 173.
[Sidenote: What is the unit?]
159. The polemic of Zeno is clearly directed in the first instance
against a certain view of the unit. Eudemos, in his _Physics_,[879]
quoted from him the saying that “if any one could tell him what the one
was, he would be able to say what things are.” The commentary of
Alexander on this, preserved by Simplicius,[880] is quite satisfactory.
“As Eudemos relates,” he says, “Zeno the disciple of Parmenides tried to
show that it was impossible that things could be a many, seeing that
there was no unit in things, whereas ‘many’ means a number of units.”
Here we have a clear reference to the Pythagorean view that everything
may be reduced to a sum of units, which is what Zeno denied.[881]
Footnote 879:
Simpl. _Phys._ p. 138, 32 (R. P. 134 a).
Footnote 880:
Simpl. _Phys._ p. 99, 13, ὡς γὰρ ἰστορεῖ, φησίν (Ἀλέξανδρος), Εὔδημος,
Ζήνων ὁ Παρμενίδου γνώριμος ἐπειρᾶτο δεικνύναι ὅτι μὴ οἷόν τε τὰ ὄντα
πολλὰ εἶναι τῷ μηδὲν εἶναι ἐν τοῖς οὖσιν ἕν, τὰ δὲ πολλὰ πλῆθος εἶναι
ἐνάδων. This is the meaning of the statement that Zeno ἀνῄρει τὸ ἕν,
which is not Alexander’s (as implied in R. P. 134 a), but goes back to
no less an authority than Eudemos. It is perfectly correct when read
in connexion with the words τὴν γὰρ στιγμὴν ὡς τὸ ἓν λέγει (Simpl.
_Phys._ p. 99, 11).
Footnote 881:
It is quite in order that Mr. Bertrand Russell, from the standpoint of
pluralism, should accept Zeno’s arguments as “immeasurably subtle and
profound” (_Principles of Mathematics_, p. 347). We know from Plato,
however, that Zeno meant them as a _reductio ad absurdum_ of
pluralism.
[Sidenote: The Fragments.]
160. The fragments of Zeno himself also show that this was his line of
argument. I give them according to the arrangement of Diels.
(1)
If the one had no magnitude, it would not even be.... But, if it is,
each one must have a certain magnitude and a certain thickness, and
must be at a certain distance from another, and the same may be said
of what is in front of it; for it, too, will have magnitude, and
something will be in front of it.[882] It is all the same to say this
once and to say it always; for no such part of it will be the last,
nor will one thing not be compared with another.[883] So, if things
are a many, they must be both small and great, so small as not to have
any magnitude at all, and so great as to be infinite. R. P. 134.
Footnote 882:
I formerly rendered “the same may be said of what surpasses it in
smallness; for it too will have magnitude, and something will
surpass it in smallness.” This is Tannery’s rendering, but I now
agree with Diels in thinking that ἀπέχειν refers to μέγεθος and
προεχειν to πάχος. Zeno is showing that the Pythagorean point has
really three dimensions.
Footnote 883:
Reading, with Diels and the MSS., οὔτε ἕτερον πρὸς ἕτερον οὐκ ἔσται.
Gomperz’s conjecture (adopted in R. P.) seems to me arbitrary.
(2)
For if it were added to any other thing it would not make it any
larger; for nothing can gain in magnitude by the addition of what has
no magnitude, and thus it follows at once that what was added was
nothing.[884] But if, when this is taken away from another thing, that
thing is no less; and again, if, when it is added to another thing,
that does not increase, it is plain that what was added was nothing,
and what was taken away was nothing. R. P. 132.
Footnote 884:
Zeller marks a lacuna here. Zeno must certainly have shown that the
subtraction of a point does not make a thing less; but he may have
done so before the beginning of our present fragment.
(3)
If things are a many, they must be just as many as they are, and
neither more nor less. Now, if they are as many as they are, they will
be finite in number.
If things are a many, they will be infinite in number; for there will
always be other things between them, and others again between these.
And so things are infinite in number. R. P. 133.[885]
Footnote 885:
This is what Aristotle calls “the argument from dichotomy” (_Phys._ Α,
3. 187 a 1; R. P. 134 b). If a line is made up of points, we ought to
be able to answer the question, “How many points are there in a given
line?” On the other hand, you can always divide a line or any part of
it into two halves; so that, if a line is made up of points, there
will always be more of them than any number you assign.
[Sidenote: The unit.]
161. If we hold that the unit has no magnitude—and this is required by
what Aristotle calls the argument from dichotomy,[886]—then everything
must be infinitely small. Nothing made up of units without magnitude can
itself have any magnitude. On the other hand, if we insist that the
units of which things are built up are something and not nothing, we
must hold that everything is infinitely great. The line is infinitely
divisible; and, according to this view, it will be made up of an
infinite number of units, each of which has some magnitude.
Footnote 886:
See last note.
That this argument refers to points is proved by an instructive passage
from Aristotle’s _Metaphysics_.[887] We read there—
If the unit is indivisible, it will, according to the proposition of
Zeno, be nothing. That which neither makes anything larger by its
addition to it, nor smaller by its subtraction from it, is not, he
says, a real thing at all; for clearly what is real must be a
magnitude. And, if it is a magnitude, it is corporeal; for that is
corporeal which is in every dimension. The other things, _i.e._ the
plane and the line, if added in one way will make things larger, added
in another they will produce no effect; but the point and the unit
cannot make things larger in any way.
Footnote 887:
Arist. _Met._ Β, 4. 1001 b 7.
From all this it seems impossible to draw any other conclusion than that
the “one” against which Zeno argued was the “one” of which a number
constitute a “many,” and that is just the Pythagorean unit.
[Sidenote: Space.]
162. Aristotle refers to an argument which seems to be directed against
the Pythagorean doctrine of space,[888] and Simplicius quotes it in this
form:[889]
If there is space, it will be in something; for all that is is in
something, and what is in something is in space. So space will be in
space, and this goes on _ad infinitum_, therefore there is no space.
R. P. 135.
Footnote 888:
Arist. _Phys._ Δ, 1. 209 a 23; 3. 210 b 22 (R. P. 135 a).
Footnote 889:
Simpl. _Phys._ p. 562, 3 (R. P. 135). The version of Eudemos is given
in Simpl. _Phys._ p. 563, 26, ἀξιοῖ γὰρ πᾶν τὸ ὂν ποῦ εἷναι· εἱ δὲ ὁ
τόπος τῶν ὄντων, ποῦ ἂν εἴη· οὐκοῦν ἐν ἄλλῳ τόπῳ κἀκεῖνος δὴ ἐν ἄλλῳ
καὶ οὕτως εἰς τὸ πρόσω.
What Zeno is really arguing against here is the attempt to distinguish
space from the body that occupies it. If we insist that body must be
_in_ space, then we must go on to ask what space itself is in. This is a
“reinforcement” of the Parmenidean denial of the void. Possibly the
argument that everything must be “in” something, or must have something
beyond it, had been used against the Parmenidean theory of a finite
sphere with nothing outside it.
[Sidenote: Motion.]
163. Zeno’s arguments on the subject of motion have been preserved by
Aristotle himself. The system of Parmenides made all motion impossible,
and his successors had been driven to abandon the monistic hypothesis in
order to avoid this very consequence. Zeno does not bring any fresh
proofs of the impossibility of motion; all he does is to show that a
pluralist theory, such as the Pythagorean, is just as unable to explain
it as was that of Parmenides. Looked at in this way, Zeno’s arguments
are no mere quibbles, but mark a great advance in the conception of
quantity. They are as follows:—
(1) You cannot get to the end of a race-course.[890] You cannot
traverse an infinite number of points in a finite time. You must
traverse the half of any given distance before you traverse the whole,
and the half of that again before you can traverse it. This goes on
_ad infinitum_, so that there are an infinite number of points in any
given space, and you cannot touch an infinite number one by one in a
finite time.[891]
(2) Achilles will never overtake the tortoise. He must first reach the
place from which the tortoise started. By that time the tortoise will
have got some way ahead. Achilles must then make up that, and again
the tortoise will be ahead. He is always coming nearer, but he never
makes up to it.[892]
Footnote 890:
Arist. _Top._ Θ, 8. 160 b 8, Ζήνωνος (λόγος), ὅτι οὐκ ἐνδέχεται
κινεῖσθαι οὐδὲ τὸ στάδιον διελθεῖν.
Footnote 891:
Arist. _Phys._ Ζ, 9. 239 b 11 (R. P. 136). Cf. Ζ, 2. 233 a 11; a 21
(R. P. 136 a).
Footnote 892:
Arist. _Phys._ Ζ, 9. 239 b 14 (R. P. 137).
The “hypothesis” of the second argument is the same as that in the
first, namely, that the line is a series of points; but the reasoning is
complicated by the introduction of another moving object. The
difference, accordingly, is not a half every time, but diminishes in a
constant ratio. Again, the first argument shows that no moving object
can ever traverse any distance at all, however fast it may move; the
second emphasises the fact that, however slowly it moves, it will
traverse an infinite distance.
(3) The arrow in flight is at rest. For, if everything is at rest when
it occupies a space equal to itself, and what is in flight at any
given moment always occupies a space equal to itself, it cannot
move.[893]
Footnote 893:
_Phys._ Ζ, 9. 239 b 30 (R. P. 138); _ib._ 239 b 5 (R. P. 138 a). The
latter passage is corrupt, though the meaning is plain. I have
translated Zeller’s version of it εἰ γάρ, φησίν, ἠρεμεῖ πᾶν ὅταν ᾖ
κατὰ τὸ ἴσον, ἔστι δ’ ἀεὶ τὸ φερόμενον ἐν τῷ νῦν κατὰ τὸ ἴσον,
ἀκίνητον, κ.τ.λ. Of course ἀεί means “at any time,” not “always,” and
κατὰ τὸ ἴσον is, literally, “on a level with a space equal (to
itself).” For other readings, see Zeller, p. 598, n. 3; and Diels,
_Vors._ p. 131, 44.
Here a further complication is introduced. The moving object itself has
length, and its successive positions are not points but lines. The
successive moments in which it occupies them are still, however, points
of time. It may help to make this clear if we remember that the flight
of the arrow as represented by the cinematograph would be exactly of
this nature.
(4) Half the time may be equal to double the time. Let us suppose
three rows of bodies,[894] one of which (A) is at rest while the other
two (B, C) are moving with equal velocity in opposite directions (Fig.
1). By the time they are all in the same part of the course, B will
have passed twice as many of the bodies in C as in A (Fig. 2).
FIG. 1
A. ● ● ● ●
B. ● ● ● ● →
C. ← ● ● ● ●
FIG. 2
A. ● ● ● ●
B. ● ● ● ●
C. ● ● ● ●
Therefore the time which it takes to pass C is twice as long as the
time it takes to pass A. But the time which B and C take to reach the
position of A is the same. Therefore double the time is equal to the
half.[895]
Footnote 894:
The word is ὄγκοι; cf. Chap. VII. p. 338, _n._ 794. The name is very
appropriate for the Pythagorean units, which Zeno had shown to have
length, breadth, and thickness (fr. 1).
Footnote 895:
Arist. _Phys._ Ζ, 9. 239 b 33 (R. P. 139). I have had to express the
argument in my own way, as it is not fully given by any of the
authorities. The figure is practically Alexander’s (Simpl. _Phys._ p.
1016, 14), except that he represents the ὄγκοι by letters instead of
dots. The conclusion is plainly stated by Aristotle (_loc. cit._),
συμβαίνειν οἴεται ἴσον εἶναι χρόνον τῷ διπλασίῳ τὸν ἥμισυν, and,
however we explain the reasoning, it must be so represented as to lead
to this conclusion.
According to Aristotle, the paralogism here depends upon the assumption
that an equal magnitude moving with equal velocity must move for an
equal time, whether the magnitude with which it is equal is at rest or
in motion. That is certainly so, but we are not to suppose that this
assumption is Zeno’s own. The fourth argument is, in fact, related to
the third just as the second is to the first. The Achilles adds a second
moving point to the single moving point of the first argument; this
argument adds a second moving line to the single moving line of the
arrow in flight. The lines, however, are represented as a series of
units, which is just how the Pythagoreans represented them; and it is
quite true that, if lines are a sum of discrete units, and time is
similarly a series of discrete moments, there is no other measure of
motion possible than the number of units which each unit passes.
This argument, like the others, is intended to bring out the absurd
conclusions which follow from the assumption that all quantity is
discrete, and what Zeno has really done is to establish the conception
of continuous quantity by a _reductio ad absurdum_ of the other
hypothesis. If we remember that Parmenides had asserted the one to be
continuous (fr. 8, 25), we shall see how accurate is the account of
Zeno’s method which Plato puts into the mouth of Sokrates.
II. MELISSOS OF SAMOS
[Sidenote: Life.]
164. In his Life of Perikles, Plutarch tells us, on the authority of
Aristotle, that the philosopher Melissos, son of Ithagenes, was the
Samian general who defeated the Athenian fleet in 441/0 B.C.:[896] and
it was no doubt for this reason that Apollodoros fixed his _floruit_ in
Ol. LXXXIV. (444-41 B.C.).[897] Beyond this, we really know nothing
about his life. He is said to have been, like Zeno, a disciple of
Parmenides;[898] but, as he was a Samian, it is possible that he was
originally a member of the Ionic school, and we shall see that certain
features of his doctrine tend to bear out this view. On the other hand,
he was certainly convinced by the Eleatic dialectic, and renounced the
Ionic doctrine in so far as it was inconsistent with that. We note here
the effect of the increased facility of intercourse between East and
West, which was secured by the supremacy of Athens.
Footnote 896:
Plut. _Per._ 26 (R. P. 141 b), from Aristotle’s Σαμίων πολιτεία.
[Sidenote: The Fragments.]
165. The fragments which we have come from Simplicius, and are given,
with the exception of the first, from the text of Diels.[899]
Footnote 897:
Diog. ix. 24 (R. P. 141). It is possible, of course, that Apollodoros
meant the first and not the fourth year of the Olympiad. That is his
usual era, the foundation of Thourioi. But, on the whole, it is more
likely that he meant the fourth; for the date of the ναυαρχία would be
given with precision. See Jacoby, p. 270.
Footnote 898:
Diog. ix. 24 (R. P. 141).
Footnote 899:
It is no longer necessary to discuss the passages which used to appear
as frs. 1-5 of Melissos, as it has been proved by A. Pabst that they
are merely a paraphrase of the genuine fragments (_De Melissi Samii
fragmentis_, Bonn, 1889). Almost simultaneously I had independently
come to the same conclusion (see the first edition, § 138). Zeller and
Diels have both accepted Pabst’s demonstration, and the supposed
fragments have been relegated to the notes in the last edition of R.
P. I still believe, however, that the fragment which I have numbered
1_a_ is genuine. See next note.
(1_a_) If nothing is, what can be said of it as of something
real?[900]
(1) What was was ever, and ever shall be. For, if it had come into
being, it needs must have been nothing before it came into being. Now,
if it were nothing, in no wise could anything have arisen out of
nothing. R. P. 142.
(2) Since, then, it has not come into being, and since it is, was
ever, and ever shall be, it has no beginning or end, but is without
limit. For, if it had come into being, it would have had a beginning
(for it would have begun to come into being at some time or other) and
an end (for it would have ceased to come into being at some time or
other); but, if it neither began nor ended, and ever was and ever
shall be, it has no beginning or end; for it is not possible for
anything to be ever without all being. R. P. 143.
(3) Further, just as it ever is, so it must ever be infinite in
magnitude. R. P. 143.
(4) But nothing which has a beginning or end is either eternal or
infinite. R. P. 143.
(5) If it were not one, it would be bounded by something else. R. P.
144 a.
(6) For if it is (infinite), it must be one; for if it were two, it
could not be infinite; for then they would be bounded by one
another.[901] R. P. 144.
(6_a_) (And, since it is one, it is alike throughout; for if it were
unlike, it would be many and not one.)[902]
(7) So then it is eternal and infinite and one and all alike. And it
cannot perish nor become greater, nor does it suffer pain or grief.
For, if any of these things happened to it, it would no longer be one.
For if it is altered, then the real must needs not be all alike, but
what was before must pass away, and what was not must come into being.
Now, if it changed by so much as a single hair in ten thousand years,
it would all perish in the whole of time.
Further, it is not possible either that its order should be changed;
for the order which it had before does not perish, nor does that which
was not come into being. But, since nothing is either added to it or
passes away or is altered, how can any real thing have had its order
changed? For if anything became different, that would amount to a
change in its order.
Nor does it suffer pain; for a thing in pain could not all be. For a
thing in pain could not be ever, nor has it the same power as what is
whole. Nor would it be alike, if it were in pain; for it is only from
the addition or subtraction of something that it could feel pain, and
then it would no longer be alike. Nor could what is whole feel pain;
for then what was whole and what was real would pass away, and what
was not would come into being. And the same argument applies to grief
as to pain.
Nor is anything empty. For what is empty is nothing. What is nothing
cannot be.
Nor does it move; for it has nowhere to betake itself to, but is full.
For if there were aught empty, it would betake itself to the empty.
But, since there is naught empty, it has nowhere to betake itself to.
And it cannot be dense and rare; for it is not possible for what is
rare to be as full as what is dense, but what is rare is at once
emptier than what is dense.
This is the way in which we must distinguish between what is full and
what is not full. If a thing has room for anything else, and takes it
in, it is not full; but if it has no room for anything and does not
take it in, it is full.
Now, it must needs be full if there is naught empty, and if it is
full, it does not move. R. P. 145.
(8) This argument, then, is the greatest proof that it is one alone;
but the following are proofs of it also. If there were a many, these
would have to be of the same kind as I say that the one is. For if
there is earth and water, and air and iron, and gold and fire, and if
one thing is living and another dead, and if things are black and
white and all that men say they really are,—if that is so, and if we
see and hear aright, each one of these must be such as we first
decided, and they cannot be changed or altered, but each must be just
as it is. But, as it is, we say that we see and hear and understand
aright, and yet we believe that what is warm becomes cold, and what is
cold warm; that what is hard turns soft, and what is soft hard; that
what is living dies, and that things are born from what lives not; and
that all those things are changed, and that what they were and what
they are now are in no way alike. We think that iron, which is hard,
is rubbed away by contact with the finger;[903] and so with gold and
stone and everything which we fancy to be strong, and that earth and
stone are made out of water; so that it turns out that we neither see
nor know realities. Now these things do not agree with one another. We
said that there were many things that were eternal and had forms and
strength of their own, and yet we fancy that they all suffer
alteration, and that they change from what we see each time. It is
clear, then, that we did not see aright after all, nor are we right in
believing that all these things are many. They would not change if
they were real, but each thing would be just what we believed it to
be; for nothing is stronger than true reality. But if it has changed,
what was has passed away, and what was not is come into being. So
then, if there were many things, they would have to be just of the
same nature as the one. R. P. 147.
(9) Now, if it were to exist, it must needs be one; but if it is one,
it cannot have body; for, if it had body it would have parts, and
would no longer be one. R. P. 146.[904]
(10) If what is real is divided, it moves; but if it moves, it cannot
be. R. P. 144 a.[905]
Footnote 900:
These words come from the beginning of the paraphrase which was so
long mistaken for the actual words of Melissos (Simpl. _Phys._ p. 103,
18; R. P. 142 a), and Diels has accordingly removed them along with
the rest. I believe them to be genuine because Simplicius, who had
access to the complete work, introduces them by the words ἄρχεται τοῦ
συγγράμματος οὕτως, and because they are thoroughly Eleatic in
character. It is quite natural that the first words of the book should
be prefixed to the paraphrase.
Footnote 901:
This fragment is quoted by Simpl. _de Caelo_, p. 557, 16 (R. P. 144).
The insertion of the word “infinite” is justified by the paraphrase
(R. P. 144 a) and by _M.X.G._ 974 a 11, πᾶν δὲ ἄπειρον ὂν <ἓν> εἶναι·
εἰ γὰρ δύο ἢ πλείω εἴη, πέρατ’ ἂν εἶναι ταῦτα πρὸς ἄλληλα.
Footnote 902:
I have ventured to insert this, though the actual words are nowhere
quoted, and it is not in Diels. It is represented in the paraphrase
(R. P. 145 a) and in _M.X.G._ 974 a 13 (R. P. 144 a).
Footnote 903:
Reading ὁμουρέων with Bergk. Diels keeps the MS. ὀμοῦ ῥέων; Zeller (p.
613, n. 1) conjectures ὑπ’ ἰοῦ ῥέων.
Footnote 904:
I read εἰ μὲν οὖν εἴη with E F for the εἰ μὲν ὂν εἴη of D. The ἐὸν
which still stands in R. P. is a piece of local colour due to the
editors. Diels also now reads οὖν (_Vors._ p. 149, 2).
Footnote 905:
Diels now reads ἀλλὰ with E for the ἅμα of F, and attaches the word to
the next sentence.
[Sidenote: Theory of reality.]
166. It has been pointed out that Melissos was perhaps not originally a
member of the Eleatic school; but he certainly adopted all the views of
Parmenides as to the true nature of reality with one remarkable
exception. He appears to have opened his treatise with a reassertion of
the Parmenidean “Nothing is not” (fr. 1 _a_), and the arguments by which
he supported this view are those with which we are already familiar (fr.
1). Reality, as with Parmenides, is eternal, an attribute which Melissos
expressed in a way of his own. He argued that since everything that has
come into being has a beginning and an end, everything that has not come
into being has no beginning or end. Aristotle is very severe upon him
for this simple conversion of a universal affirmative proposition;[906]
but, of course, his belief was not founded on that. His whole conception
of reality made it necessary for him to regard it as eternal.[907] It
would be a more serious matter if Aristotle were right in believing, as
he seems to have done,[908] that Melissos inferred that what is must be
infinite in space, because it had neither beginning nor end in time.
This, however, seems quite incredible. As we have the fragment which
Aristotle interprets in this way (fr. 2), we are quite entitled to
understand it for ourselves, and I cannot see anything to justify
Aristotle’s assumption that the expression “without limit” means without
limit in space.[909]
Footnote 906:
Arist. _Phys._ Α, 3. 186 a 7 (R. P. 143 a). Aristotle finds two flaws
in the Eleatic reasoning: (1) ψευδῆ λαμβάνουσιν; (2) ἀσυλλόγιστοί
εἰσιν αὐτῶν οἱ λόγοι. This is the first of these flaws. It is also
mentioned in _Soph. El._ 168 b 35 (R. P. _ib._). So Eudemos _ap._
Simpl. _Phys._ p. 105, 24, οὐ γὰρ, εἰ τὸ γενόμενον ἀρχὴν ἔχει, τὸ μὴ
γενόμενον ἀρχὴν οὐκ ἔχει, μᾶλλον δὲ τὸ μὴ ἔχον ἀρχὴν οὐκ ἐγένετο.
Footnote 907:
The real reason is given in the paraphrase in Simpl. _Phys._ p. 103,
21 (R. P. 142 a), συγχωρεῖται γὰρ καὶ τοῦτο ὑπὸ τῶν φυσικῶν, though of
course Melissos himself would not have put it in that way. He regarded
himself as a φυσικός like the rest; but, from the time of Aristotle,
it was a commonplace that the Eleatics were not φυσικοί, since they
denied motion.
Footnote 908:
This has been denied by Offner, “Zur Beurtheilung des Melissos”
(_Arch._ iv. pp. 12 sqq.), but I now think he goes too far. Cf.
especially _Top._ ix. 6, ὡς ἄμφω ταὐτὰ ὄντα τῷ ἀρχὴν ἔχειν, τό τε
γεγονὸς καὶ τὸ πεπερασμένον. The same point is made in _Soph. El._ 167
b 13 and 181 a 27.
Footnote 909:
The words ἀλλ’ ἄπειρόν ἐστι mean simply “but it is without limit,” and
this is simply a repetition of the statement that it has no beginning
or end. The nature of the limit can only be determined by the context,
and accordingly, when Melissos does introduce the subject of spatial
infinity, he is careful to say τὸ μέγεθος ἄπειρον (fr. 3).
[Sidenote: Reality spatially infinite.]
167. Melissos did indeed differ from Parmenides in holding that reality
was spatially as well as temporally infinite; but he gave an excellent
reason for this belief, and had no need to support it by the
extraordinary argument just alluded to. What he said was that, if it
were limited, it would be limited by empty space. This we know from
Aristotle himself,[910] and it marks a real advance upon Parmenides. He
had thought it possible to regard reality as a finite sphere, but it
would have been difficult for him to work out this view in detail. He
would have had to say there was nothing outside the sphere; but no one
knew better than he that there is no such thing as nothing. Melissos saw
that you cannot imagine a finite sphere without regarding it as
surrounded by an infinite empty space;[911] and as, in common with the
rest of the school, he denied the void (fr. 7), he was forced to say
reality was spatially infinite (fr. 3). It is possible that he was
influenced in this by his association with the Ionic school.
Footnote 910:
Arist. _Gen. Corr._ i. 8. 325 a 14, ἓν καὶ ἀκίνητον τὸ πᾶν εἶναί φασι
καὶ ἄπειρον ἔνιοι· τὸ γὰρ πέρας περαίνειν ἂν πρὸς τὸ κενόν. That this
refers to Melissos has been proved by Zeller (p. 612, n. 2).
Footnote 911:
Note the disagreement with Zeno (§ 162).
From the infinity of reality, it follows that it must be one; for, if it
were not one, it would be bounded by something else (fr. 5). And, being
one, it must be homogeneous throughout (fr. 6_a_), for that is what we
mean by one. Reality, then, is a single, homogeneous, corporeal
_plenum_, stretching out to infinity in space, and going backwards and
forwards to infinity in time.
[Sidenote: Opposition to Ionians.]
168. Eleaticism was always critical, and we are not without indications
of the attitude taken up by Melissos towards contemporary systems. The
flaw which he found in the Ionian theories was that they all assumed
some want of homogeneity in the One, which is a real inconsistency.
Further, they all allowed the possibility of change; but, if all things
are one, change must be a form of coming into being and passing away. If
you admit that a thing can change, you cannot maintain that it is
eternal. Nor can the arrangement of the parts of reality alter, as
Anaximander, for instance, had held; any such change necessarily
involves a coming into being and passing away.
The next point made by Melissos is somewhat peculiar. Reality, he says,
cannot feel sorrow or pain; for that is always due to the addition or
subtraction of something, which is impossible. It is not easy to be sure
what this refers to. Perhaps it is to the theory of Herakleitos with its
Want and Surfeit, perhaps to something of which no record has been
preserved.
Motion in general[912] and rarefaction and condensation in particular
are impossible; for both imply the existence of empty space.
Divisibility is excluded for the same reason. These are the same
arguments as Parmenides employed.
Footnote 912:
The view of Bäumker that Melissos admitted ἀντιπερίστασις or motion
_in pleno_ (_Jahrb. f. kl. Phil._, 1886, p. 541; _Das Problem der
Materie_, p. 59) depends upon some words of Simplicius (_Phys._ p.
104, 13), οὐχ ὅτι μὴ δυνατὸν διὰ πλήρους κινεῖσθαι, ὡς ἐπὶ τῶν σωμάτων
λέγομεν κ.τ.λ. These words were formerly turned into Ionic and passed
off as a fragment of Melissos. They are, however, part of Simplicius’s
own argument against Alexander, and have nothing to do with Melissos
at all.
[Sidenote: Opposition to Pythagoreans.]
169. In nearly all accounts of the system of Melissos, we find it stated
that he denied the corporeality of what is real,—an opinion which is
supported by a reference to fr. 9, which is certainly quoted by
Simplicius to prove this very point.[913] If, however, our general view
as to the character of early Greek Philosophy is correct, the statement
must seem incredible. And it will seem even more surprising when we find
that in the _Metaphysics_ Aristotle says that, while the unity of
Parmenides seemed to be ideal, that of Melissos was material.[914] Now
the fragment, as it stands in the MSS. of Simplicius,[915] puts a purely
hypothetical case, and would most naturally be understood as a disproof
of the existence of something on the ground that, if it existed, it
would have to be both corporeal and one. This cannot refer to the
Eleatic One, in which Melissos himself believed; and, as the argument is
almost verbally the same as one of Zeno’s,[916] it is natural to suppose
that it also was directed against the Pythagorean assumption of ultimate
units. The only possible objection is that Simplicius, who twice quotes
the fragment, certainly took it in the sense usually given to it.[917]
But it was very natural for him to make this mistake. “The One” was an
expression that had two senses in the middle of the fifth century B.C.;
it meant either the whole of reality or the point as a spatial unit. To
maintain it in the first sense, the Eleatics were obliged to disprove it
in the second; and so it sometimes seemed that they were speaking of
their own “One” when they really meant the other. We have seen that the
very same difficulty was felt about Zeno’s denial of the “one.”[918]
Footnote 913:
See, however, Bäumker, _Das Problem der Materie_, pp. 57 sqq., who
remarks that ἐόν (or ὄν) in fr. 9 must be the predicate, as it has no
article. In his fifth edition (p. 611, n. 2) Zeller has adopted the
view here taken. He rightly observes that the hypothetical form εἰ μὲν
ὂν εἴη speaks for it, and that the subject to εἴη must be ἕκαστον τῶν
πολλῶν, as with Zeno.
Footnote 914:
_Met._ Α, 5. 986 b 18 (R. P. 101).
Footnote 915:
Brandis changed the εἴη to ἔστι, but there is no warrant for this.
Footnote 916:
Cf. Zeno, fr. 1, especially the words εἰ δὲ ἔστιν, ἀνάγκη ἕκαστον
μέγεθός τι ἔχειν καὶ πάχος.
Footnote 917:
Simpl. _Phys._ pp. 87, 6, and 110, 1.
Footnote 918:
See above, § 159, p. 363, _n._ 880.
[Sidenote: Opposition to Anaxagoras.]
170. The most remarkable fragment of Melissos is, perhaps, the last (fr.
8). It seems to be directed against Anaxagoras; at least the language
used seems more applicable to him than to any one else. Anaxagoras had
admitted (§ 137, _fin._) that, so far as our perceptions go, they do not
entirely agree with his theory, though he held this was due solely to
their weakness. Melissos, taking advantage of this admission, urges
that, if we give up the senses as the ultimate test of reality, we are
not entitled to reject the Eleatic theory. With wonderful penetration he
points out that if we are to say, with Anaxagoras, that things are a
many, we are bound also to say that each one of them is such as the
Eleatics declared the One to be. In other words, the only consistent
pluralism is the atomic theory.
Melissos has long been unduly depreciated owing to the criticisms of
Aristotle; but these, we have seen, are based mainly on a somewhat
pedantic objection to the false conversion in the early part of the
argument. Melissos knew nothing about the rules of conversion; and if he
had, he could easily have made his reasoning formally correct without
modifying his system. His greatness consisted in this, that not only was
he the real systematiser of Eleaticism, but he was also able to see,
before the pluralists saw it themselves, the only way in which the
theory that things are a many could be consistently worked out.[919] It
is significant that Polybos, the nephew of Hippokrates, reproaches those
“sophists” who taught there was only one primary substance with “putting
the doctrine of Melissos on its feet.”[920]
Footnote 919:
Bäumker, _op. cit._ p. 58, n. 3: “That Melissos was a weakling is a
_fable convenue_ that people repeat after Aristotle, who was unable to
appreciate the Eleatics in general, and in particular misunderstood
Melissos not inconsiderably.”
Footnote 920:
Περὶ φύσιος ἀνθρώπου, c. 1, ἀλλ’ ἔμοιγε δοκέουσιν οἱ τοιοῦτοι ἄνθρωποι
αὐτοὶ ἑωυτοὺς καταβάλλειν ἐν τοῖσιν ὀνόμασι τῶν λόγων αὐτῶν ὑπὸ
ἀσυνεσίης, τὸν δὲ Μελίσσου λόγον ὀρθοῦν. The metaphors are taken from
wrestling, and were current at this date (cf. the καταβάλλοντες of
Protagoras). Plato implies a more generous appreciation of Melissos
than Aristotle’s. In _Theaet._ 180 e 2, he refers to the Eleatics as
Μέλισσοί τε καὶ Παρμενίδαι, and in 183 e 4 he almost apologises for
giving the pre-eminence to Parmenides.