theory of Empedokles as to the sun’s light. The meaning is that the central fire really was the sun, but that Philolaos unnecessarily duplicated it hy supposing the visible sun to be its reflexion.
* Chap. VI. § 113.
2 Aet. i. 7,7 (R. P. 81). Procl. 2 Zim. p. 106, 22, Diehl (R. P. 83 e).
The Pythagoreans 349
for Herakleides of Pontos and Aristarchos of Samos
to reach the heliocentric hypothesis,’ and it was
certainly Aristotle’s reversion to the geocentric theory
which made it necessary for Copernicus to discover the
truth afresh. We have his own word for it that the
Pythagorean theory put him on the right track.”
151. The existence of the antichthon was also a
hypothesis intended to account for the phenomena of
eclipses. In one place, indeed, Aristotle says that the
Pythagoreans invented it in order to bring the number
of revolving bodies up to ten;* but that is a mere
sally, and Aristotle really knew better. In his work
on the Pythagoreans, we are told, he said that eclipses
of the moon were caused sometimes by the interven-
tion of the earth and sometimes by that of the
antichthon; and the same statement was made by
Philip of Opous, a very competent authority on the
matter. Indeed, Aristotle shows in another passage
exactly how the theory originated. He tells us that
some thought there might be a considerable number
of bodies revolving round the centre, though invisible
1 On these points, see Staigmiiller, Bectrage zur Gesch. der Naturwissen- schaften im klassichen Altertume (Progr., Stuttgart, 1899); and ‘‘ Herakleides Pontikos und das heliokentrische System” (Arch. xv. pp. 141 sqq.). Though, for reasons which will partly appear from the following pages, I should not put the matter exactly as Staigmiiller does, I have no doubt that he is sub- stantially right. Diels had already expressed his adhesion to the view that Herakleides was the real author of the heliocentric hypothesis (Ber/. S7tzé., 1893, p. 18).
2 In his letter to Pope Paul III., Copernicus quotes Plut. Plac. iii. 13, 2-3(R. P. 83 a), and adds “‘ Inde igitur occasionem nactus, coepi et ego de terrae mobilitate cogitare.” The whole passage is paraphrased by Dreyer, Planetary Systems, p. 311. Cf. also the passage from the original MS., which was first printed in the edition of 1873, translated by Dreyer, 2. pp. 314 5464. 3 Arist. Met. A, 5. 986 a 3 (R. P. 83 b).
* Aet. ii. 29, 4, τῶν Πυθαγορείων τινὲς κατὰ τὴν ᾿Αριστοτέλειον ἱστορίαν καὶ τὴν Φιλίππου τοῦ ᾿Οπουντίου ἀπόφασιν ἀνταυγείᾳ καὶ ἀντιφράξει τοτὲ μὲν τῆς γῆς, τοτὲ δὲ τῆς ἀντίχθονος (ἐκλείπειν τὴν σελήνην).
The antichthon-
Planetary motions.
350 Early Greek Philosophy
to us because of the intervention of the earth, and that
they accounted in this way for there being more
eclipses of the moon than of the sun.’ This is
mentioned in close connexion with the antzchthon, so
there is no doubt that Aristotle regarded the two
hypotheses as of the same nature. The history of the
theory seems to be this. Anaximenes had assumed
the existence of dark planets to account for the
frequency of lunar eclipses (§ 29), and Anaxagoras
had revived that view (δ 135). Certain Pythagoreans *
had placed these dark planets between the earth and
the central fire in order to account for their invisibility,
and the next stage was to reduce them to a single
body. Here again we see how the Pythagoreans tried
to simplify the hypotheses of their predecessors.
152. We must not assume that even the later Pytha- goreans made the sun, moon, and planets, including the earth, revolve in the opposite direction to the heaven of the fixed stars. It is true that Alkmaion is said to have agreed with “some of the mathematicians” ?® in holding this view, but it is never ascribed to Pythagoras or even to Philolaos, The old theory was, as we have seen (§ 54), that all the heavenly bodies revolved in the same direction, from east to west, but that the planets revolved more slowly the further they were removed
1 Arist. de Caelo, B, 13. 293 b21, ἐνίοις δὲ δοκεῖ καὶ πλείω σώματα τοιαῦτα ἐνδέχεσθαι φέρεσθαι περὶ τὸ μέσον ἡμῖν ἄδηλα διὰ τὴν ἐπιπρόσθησιν τῆς γῆς. διὸ καὶ τὰς τῆς σελήνης ἐκλείψεις πλείους ἢ τὰς τοῦ ἡλίου γίγνεσθαί φασιν * τῶν γὰρ φερομένων ἕκαστον ἀντιφράττειν αὐτήν, ἀλλ᾽ οὐ μόνον τὴν γῆν.
2 It is not expressly stated that they were Pythagoreans, but it is natural to suppose so. Such, at least, was Alexander’s opinion (Simpl. de Caelo, Ρ. 515, 25)
3 The term οἱ μαθηματικοί is that used by Poseidonios for the Chaldzean astrologers (Berossos). Diels, Elementum, Ὁ. 11, n. 3. As we have seen, the Babylonians knew the planets better than the Greeks.
The Pythagoreans 351
from the heavens, so that those which are nearest the
earth are “overtaken” by those that are further away.
This view was still maintained by Demokritos, and that
it was also Pythagorean, seems to follow from what we
are told about the “harmony of the spheres.” We
have seen (§ 54) that we cannot attribute this theory
in its later form to the Pythagoreans of the fifth
century, but we have the express testimony of Aristotle
to the fact that those Pythagoreans whose doctrine he
knew believed that the heavenly bodies produced
musical notes in their courses. Further, the velocities
of these bodies depended on the distances between
them, and these corresponded to the intervals of the
octave. He distinctly implies that the heaven of the
fixed stars takes part in the concert; for he mentions
“the sun, the moon, and the stars, so great in magnitude
and in number as they are,” a phrase which cannot
refer solely or chiefly to the remaining five planets.’
Further, we are told that the slower bodies give out
a deep note and the swifter a high note. Now the
prevailing tradition gives the high note of the octave to
the heaven of the fixed stars,? from which it follows
1 Arist. de Caelo, B, 9. 290 Ὁ 12 544. (R. P. 82).
? Alexander, zz Met. p. 39, 24 (from Aristotle’s work on the Pytha- goreans), τῶν yap σωμάτων τῶν περὶ τὸ μέσον φερομένων ἐν ἀναλογίᾳ τὰς ἀποστάσεις ἐχόντων... ποιούντων δὲ καὶ ψόφον ἐν τῷ κινεῖσθαι τῶν μὲν βραδυτέρων βαρύν, τῶν δὲ ταχυτέρων ὀξύν. We must not attribute the identification of the seven planets with the seven strings of the heptachord to the Pythagoreans of this date. Mercury and Venus have in the long run the same velocity as the sun, and we must take in the earth and the fixed stars. We can even find room for the antichthon as προσλαμβανόμενος.
3 For the various systems, see Boeckh, Avezne Schriften, vol. iii. pp. 169 sqq., and Carl v. Jan, ‘‘ Die Harmonie der Sphiren ” (Pz/o/. 1893, pp- 13 sqq.). They vary with the astronomy of their authors, but they bear witness to the fact stated in the text. Many give the highest note to Saturn and the lowest to the Moon, while others reverse this. The system which
corresponds best, however, with the Pythagorean planetary system must inciude the heaven of the fixed stars and the earth. It is that upon which
352 Early Greek Philosophy
that all the heavenly bodies revolve in the same
direction, and that their velocity increases in proportion
to their distance from the centre.
The theory. that the proper motion of the sun,
moon, and planets is from west to east, and that they
also share in the motion from east to west of the
heaven of the fixed stars, makes its first appearance in
the Myth of Er in Plato’s Republic, and is fully worked
out in the 7zmaeus. In the Repudlic it is still associated
with the “ harmony of the spheres,” though we are not
told how it is reconciled with that theory in detail.’
In the 7zmaeus we read that the slowest of the heavenly
bodies appear the fastest and vzce versa; and, as this
statement is put into the mouth of a Pythagorean, we
might suppose the theory of a composite movement to
have been anticipated by some members at least of
that school.” That is, of course, possible; for the
the verses of Alexander of Ephesos quoted by Theon of Smyrna, p. 140, 4, are based :
The ‘‘ base οἵ Heaven’s deep Organ” in Milton’s “‘ ninefold harmony ” (Zlymn on the Nativity, xiii.) implies the reverse of this.
1 The difficulty appears clearly in Adam’s note on Republic, 617 Ὁ (vol. ii. p. 452). There the ἀπλανής appears rightly as the νήτη, while Saturn, which comes next to it, is the drdrn. It is inconceivable that this should have been the original scale. Aristotle touches upon the point (de Cae/o, B, 10. 291 a 29 sqq.); and Simplicius sensibly observes (de Caelo, p. 476, I1), οἱ δὲ πάσας τὰς σφαίρας τὴν αὐτὴν λέγοντες κίνησιν τὴν ἀπ᾽ ἀνατολῶν κινεῖσθαι καθ᾽ ὑπόληψιν (ought not the reading to be ὑπόλειψιν ?), ὥστε τὴν μὲν Kpoviay σφαῖραν συναποκαθίστασθαι καθ᾽ ἡμέραν TH ἀπλανεῖ παρ ὀλίγον, τὴν δὲ τοῦ Διὸς παρὰ πλέον καὶ ἐφεξῆς οὕτως, οὗτοι πολλὰς μὲν ἄλλας ἀπορίας ἐκφεύγουσι, but their ὑπόθεσις is ἀδύνατος. This is what led to the return to the geocentric hypothesis and the exclusion of earth and ἀπλανής from the ἁρμονία. The only solution would have been to make the earth rotate on its axis or revolve round the central fire in twenty-four hours, leaving only precession for the ἀπλανής. As we have seen, Boeckh attributed this to Philolaos, but without evidence. If he had thought of it, these difficulties would not have arisen.
2 Tim. 39 a 5- 2, especially the words τὰ τάχιστα περιιόντα ὑπὸ τῶν
The Pythagoreans 353
Pythagoreans were singularly open to new ideas. At
the same time, we must note that the theory is even
more emphatically expressed by the Athenian Stranger
in the Laws, who is in a special sense Plato himself.
If we were to praise the runners who come in last in
the race, we should not do what is pleasing to the
competitors; and in the same way it cannot be pleasing
to the gods when we suppose the slowest of the
heavenly bodies to be the fastest. The passage un-
doubtedly conveys the impression that Plato is ex-
pounding a novel theory.’
153. We have still to consider a view, which
Aristotle sometimes attributes to the Pythagoreans,
that things were “like numbers.” He does not appear
to regard this as inconsistent with the doctrine that
things ave numbers, though it is hard to see how he
could reconcile the two.2, There is no doubt, however,
that Aristoxenos represented the Pythagoreans as
teaching that things were /zke numbers,’ and there are
other traces of an attempt to make out that this was
the original doctrine. A letter was produced, purport-
ing to be by Theano, the wife of Pythagoras, in which
she says that she hears many of the Hellenes think
Pythagoras said things were made of number, whereas
βραδυτέρων ἐφαίνετο καταλαμβάνοντα καταλαμβάνεσθαι (‘‘they appear to be overtaken, though they overtake”).
1 Plato, Laws, 822 ἃ 4sqq. The Athenian says of the theory that he had not heard of it in his youth nor long before (821 e€ 3). Ifso, it can hardly have been taught by Philolaos, though it may have been by Archytas.
8 Aristoxenos af. Stob. i. pr. 6 (p. 20), Πυθαγόρας. . . πάντα τὰ πράγματα ἀπεικάζων τοῖς ἀριθμοῖς.
Things
likenesses of
numbers.
354 Early Greek Philosophy
he really said they were made according to number.’
It is amusing to notice that this fourth-century theory
had to be explained away in its turn later on, and
Iamblichos actually tells us that it was Hippasos who
said number was the exemplar of things.”
When this view is uppermost in his mind, Aristotle
seems to find only a verbal difference between Plato
and the Pythagoreans. The metaphor of “ participa-
tion” was merely substituted for that of “imitation.”
This is not the place to discuss the meaning of Plato’s
so-called “theory of ideas”; but it must be pointed
out that Aristotle’s ascription of the doctrine of
“imitation” to the Pythagoreans is abundantly
justified by the Phaedo. The arguments for immortality
given in the early part of that dialogue come from
various sources. Those derived from the doctrine of
Reminiscence, which has sometimes been supposed to
be Pythagorean, are only known to the Pythagoreans
by hearsay, and Simmias requires to have the whole
psychology of the subject explained to him.* When,
however, we come to the question what it is that our
sensations remind us of, his attitude changes. The
view that the equal itself is alone real, and that what
we call equal things are imperfect imitations of it, is
quite familiar to him.* _ He requires no proof of it, and
is finally convinced of the immortality of the soul just
because Sokrates makes him see that the theory of
forms implies it.