Early Greek Philosophy — John Burnet (Heraclitus fragments)

95. Cf. the ὑποζώματα of Plato, Rep, 616c 3. As ὕλη generally means ‘timber ” for shipbuilding (when it does not mean firewood), I suggest that we should look in this direction for an explanation of the technical use of the word in later philosophy. Cf. Plato, Phzleb. 54 ¢ 1, yevéoews .. . évexa . . . πᾶσαν ὕλην παρατίθεσθαι πᾶσιν, which is part of the answer to the question πότερα πλοίων ναυπηγίαν ἕνεκα φὴς γίγνεσθαι μᾶλλον ἢ πλοῖα ἕνεκα ναυπηγίας ; (2b. Ὁ 2); Zim. 69 a 6, οἷα τέκτοσιν ἡμῖν ὕλη παράκειται.

3 Plato, Phd. 110 Ὁ 6, ὥσπερ οἱ δωδεκάσκυτοι σφαῖραι with Wyttenbach’s note,

4 Plato, Zim. 554. Neither this passage nor the last can refer to the Zodiac, which would be described by a dodecagon, not a dodecahedron. What is implied is the division of the heavens into twelve pentagonal fields.

® Gow, Short History of Greek Mathematics, pp. 164 564.

The Pythagoreans 343 -

that it is not too high, is shown by the fact that the
famous lunules of Hippokrates date from the middle
of the fifth century. The inclusion of straight
and curved in the “table of opposites” under the
head of Limit and Unlimited points in the same
direction.’

The tradition confirms in an interesting way the
importance of the dodecahedron in the Pythagorean
system. According to one account, Hippasos was
drowned at sea for revealing its construction and claim-
ing the discovery as his ονη What that construction
was, we may partially infer from the fact that the
Pythagoreans adopted the pentagram or fentalpha as
their symbol. The use of this figure in later magic is
well known; and Paracelsus still employed it as a
symbol of health, which is exactly what the Pytha-
goreans called it.°

149. The view that the soul is a “harmony,” or
rather an attunement, is intimately connected with the
theory of the four elements. It cannot have belonged
to the earliest form of Pythagoreanism ; for, as shown
in Plato’s Phaedo, it is quite inconsistent with the idea
that the soul can exist independently of the body. It
is the very opposite of the belief that “any soul can
enter any body.”* On the other hand, we know also
from the Phaedo that it was accepted by Simmias and
Kebes, who had heard Philolaos at Thebes, and by
Echekrates of Phleious, who was the disciple of

1 This is pointed out by Kinkel, Gesch. der Phil. vol. i. p. 121.

2 Tambl. V. Pyth. 247. Cf. above, Chap. II. p. 117, ἢ. 3.

* See Gow, Short History of Greek Mathematics, p. 151, and the passages there referred to, adding Schol. Luc. p. 234, 21, Rabe, rd πεντάγραμμον ὅτι τὸ ἐν τῇ συνηθείᾳ λεγόμενον πένταλφα σύμβολον ἣν πρὸς ἀλλήλους Πυθαγορείων ἀναγνὼριστικὸν καὶ τούτῳ ἐν ταῖς ἐπιστολαῖς ἐχρῶντο.

* Arist. de An. A, 3. 407 Ὁ 20 (ΕΒ. P. 86 ο).

The Soul a “ὁ harmony.”

‘The central fire.

344 Early Greek Philosophy

Philolaos and Eurytos.' The account of the doctrine
given by Plato is quite in accordance with the view
that it was of medical origin. Simmias says: “Our
body being, as it were, strung and held together by
the warm and the cold, the dry and the moist, and
things of that sort, our soul is a sort of temperament
and attunement of these, when they are mingled with
one another well and in due proportion. If, then, our
soul is an attunement, it is clear that, when the body
has been relaxed or strung up out of measure by
diseases and other ills, the soul must necessarily perish

2 This is clearly an application of the theory

at once.
of Alkmaion (§ 96), and is in accordance with the
views of the Sicilian school of medicine. It completes
the evidence that the Pythagoreanism of the end of
the fifth century was an adaptation of the old doctrine
to the new principles introduced by Empedokles.

150. The planetary system which Aristotle attributes
to “the Pythagoreans” and Aetios to Philolaos is
sufficiently remarkable. The earth is no longer in
the middle of the world; its place is taken by a
central fire, which is not to be identified with the sun.
Round this fire revolve ten bodies. First comes the
Antichthon or Counter-earth, and next'the earth, which
thus becomes one of the planets. After the earth
comes the moon, then the sun, the five planets, and
the heaven of the fixed stars. We do not see the
central fire and the antichthon because the side of the
earth on which we live is always turned away from

1 Plato, Phd. 85 ε 544. ; and for Echekrates, 2d. 88 ἃ.

2 Plato, Phd. 86 Ὁ 7-c 5.

3 For the authorities, see R. P. 81-83. The attribution of the theory to Philolaos is perhaps due to Poseidonios. The ‘‘three books” were doubtless in existence by his time.

¥ “ THE PYTHAGOREANS 345

them. ‘This is to be explained by the analogy of the
moon. That body always presents the same face to
us ; and men living on the other side of it would never
see the earth. This implies, of course, that all these
bodies rotate on their axes in the same time as they
revolve round the central fire.’

It is not very easy to accept the view that this
system was taught by Philolaos. Aristotle nowhere
- mentions him in connexion with it, and in the Phaedo
‘Plato gives a description of the earth and its position
in the world which is entirely opposed to it, but is
accepted without demur by Simmias the disciple of
Philolaos.? It is undoubtedly a Pythagorean theory,
however, and marks a noticeable advance on the
Ionian views then current at Athens. It is clear too
that Plato states it as something of a novelty that the
earth does not require the support of air or anything
of the sort to keep it in its place. Even Anaxagoras
had not been able to shake himself free of that idea,
and Demokritos still held it. The natural inference
from the Phaedo would certainly be that the theory of
a spherical earth, kept in the middle of the world by
its equilibrium, was that of Philolaos himself. If so,
the doctrine of the central fire would belong to a some-
what later generation of the school, and Plato may

1 Plato attributes an axial rotation to the heavenly bodies (77m. 40 a 7), which must be of this kind. It is quite likely that the Pythagoreans already did so, though Aristotle was unable to see the point. He says (de Caelo, B, 8. 290 a 24), ἀλλὰ μὴν ὅτι οὐδὲ κυλίεται τὰ ἄστρα, φανερόν " τὸ μὲν γὰρ κυλιόμενον στρέφεσθαι ἀνάγκη, τῆς δὲ σελήνης ἀεὶ δηλόν ἐστι τὸ καλούμενον πρόσωπον. This, of course, is just what proves it does rotate.

2 Plato, Phd. 108 e 4 sqq. Simmias assents to this doctrine in the emphatic words Kal ὀρθῶς γε.

% The primitive character of the astronomy taught by Demokritos as compared with that of Plato is the best evidence of the value of the Pytha- gorean researches.

346 Early Greek Philosophy

have learnt it from Archytas and his friends after he
had written the Phaedo. However that may be, it is
of such importance that it cannot be omitted here.

It is commonly supposed that the revolution of the
earth round the central fire was intended to account
for the alternation of day and night, and it is clear that
an orbital motion of the kind just described would
have the same effect as the rotation of the earth on its
axis. As the same side of the earth is always turned
to the central fire, the side upon which we live will
be turned towards the sun when the earth is on the
same side of the central fire, and turned away from it
when the earth and sun are on opposite sides. This
view appears to derive some support from the state-
ment of Aristotle that the earth “being in motion
round the centre, produces day and night.”* That
remark, however, would prove too much; for in the
Ttmaeus Plato calls the earth “the guardian and
artificer of night and day,” while at the same time he
declares that the alternation of day and night is caused
by the diurnal revolution of the heavens.” That is
explained, no doubt quite rightly, by saying that, even
if the earth were regarded as at rest, it could still be
said to produce day and night; for night is due to
the intervention of the earth between the sun and the
hemisphere opposite to it. If we remember how recent
was the discovery that night was the shadow of the
earth, we shall see how it may have been worth while
to say this explicitly.

In any case, it is wholly incredible that the heaven

1 Arist. de Caelo, B, 13. 293 ἃ 18 sqq. (R. P. 83).

2 Plato, Zim. 40 c 1, (γῆν) φύλακα καὶ δημιουργὸν νυκτός Te καὶ ἡμέρας ἐμηχανήσατο. On the other hand, νὺξ μὲν οὖν ἡμέρα τε γέγονεν οὕτως καὶ διὰ ταῦτα, ἣ τῆς μιᾶς καὶ φρονιμωτάτης κυκλήσεως περίοδος (39 c I).

The Pythagoreans 347

of the fixed stars should have been regarded as
stationary. That would have been the most startling
paradox that any scientific man had yet propounded,
and we should have expected the comic poets and
popular literature generally to raise the cry of atheism
at once. Above all, we should have expected Aris-
totle to say something about it. He made the circular
motion of the heavens the very keystone of his system,
and would have regarded the theory of a stationary
heaven as blasphemous. Now he argues against those
who, like the Pythagoreans and Plato, regarded the
earth as in motion;' but he does not attribute the
view that the heavens are stationary to any one. There
is no necessary connexion between the two ideas. All
the heavenly bodies may be moving as rapidly as we
please, provided that their relative motions are such
as to account for the phenomena.’

It seems probable that the theory of the earth’s
revolution round the central fire really originated in
the account given by Empedokles of the sun’s light.
The two things are brought into close connexion by
Aetios, who says that Empedokles believed in two
suns, while Philolaos believed in two or even in three.*

1 Arist. de Caelo, B, 13. 293 Ὁ 15 sqq.

2 Boeckh admitted a very slow motion of the heaven of the fixed stars, which he at first supposed to account for the precession of the equinoxes, though he afterwards abandoned that hypothesis (Untersuchungen, p. 93). But, as Dreyer admits (Planetary Systems, Ὁ. 49), it is ‘not . . . necessary with Boeckh to suppose the motion of the starry sphere to have been an exceedingly slow one, as it might in any case escape direct observation.”

3 Aet. ii. 20, 13 (Chap. IV. p. 275, ἢ. 1); cf. 2b. 12 (of Philolaos), ὥστε τρόπον τινὰ διττοὺς ἡλίους γίγνεσθαι, τό Te ἐν τῷ οὐρανῷ πυρῶδες καὶ τὸ ἀπ᾽ αὐτοῦ πυροειδὲς κατὰ τὸ ἐσοπτροειδές " εἰ μή τις καὶ τρίτον λέξει τὴν ἀπὸ τοῦ ἐνόπτρου κατ᾽ ἀνάκλασιν διασπειρομένην πρὸς ἡμᾶς αὐγήν. Here τὸ ἐν τῷ οὐρανῷ πυρῶδες is the central fire, in accordance with the use of the word οὐρανός explained in another passage of Aetios, Stob. Zc/. i. p. 196, 18 (R. P. 81). It seems to me that these strange notices must be fragments of an attempt to show how the heliocentric hypothesis arose from the

348 Early Greek Philosophy

The theory of Empedokles is unsatisfactory in so far
as it gives two inconsistent explanations of night. It
is, we have seen, the shadow of the earth; but at the
same time Empedokles recognised a fiery diurnal
hemisphere and a nocturnal hemisphere with only a
little fire in it.’ All this could be simplified by the
hypothesis of a central fire which is the true source of
light. Such a theory would, in fact, be the natural
issue of the recent discoveries as to the moon’s light
and the cause of eclipses, if that theory were extended
so as to include the sun.

The central fire received a number of mythological
names. It was called the Hestia or “hearth of the
universe,” the “house” or “ watch-tower” of Zeus, and
the “mother of the gods.” That was in the manner
of the school; but these names must not blind us to
the fact that we are dealing with a real scientific
hypothesis. It was a great thing to see that the
phenomena could best be “saved” by ἃ central
luminary, and that the earth must therefore be a re-
volving sphere like the planets. Indeed, we are almost
tempted to say that the identification of the central
fire with the sun, which was suggested for the first time
in the Academy, is a mere detail in comparison. The
great thing was that the earth should definitely take
its place among the planets ; for once it has done so,
we can proceed to search for the true “hearth” of
the planetary system at our leisure. It is probable, at
any rate, that it was this theory which made it possible