Early Greek Philosophy — John Burnet (Heraclitus fragments)

3 This version of the tradition is mentioned in Iamblichos, V. Pyth. 247, and looks older than the other, which we shall come to later (§ 148). . Hippasos is the exfant terrible of Pythagoreanism, and the traditions about him are full of instruction.

_ Things are numbers.

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indeed the work of Eudoxos. Yet it is clear that the early Pythagoreans, and probably Pythagoras himself, studied proportion in their own way, and that the three “medieties” in particular go back to the founder, especially as the most complicated of them, the “harmonic,” stands in close relation to his discovery of the octave. If we take the harmonic proportion 12:8:6,' we find that 12:6 is the octave, 12:8 the fifth, and 8 : 6 the fourth, and it can hardly be doubted that it was Pythagoras himself who discovered these intervals. The stories which have come down to us about his observing the harmonic intervals in a smithy, and then weighing the hammers that produced them, or of his suspending weights corresponding to those of the hammers to equal. strings, are, indeed, impossible and absurd ; but it is sheer waste of time to rationalise them.2. For our purpose their absurdity is their chief merit. They are not stories which any Greek mathematician or musician could possibly have in- vented, but genuine popular tales bearing witness to the existence of a real tradition that Pythagoras was the author of this momentous discovery.

52. It was this too, no doubt, that led Pythagoras to
say all things were numbers. We shall see that, at a
later date, the Pythagoreans identified these numbers
with geometrical figures; but the mere fact that they

1 Plato (772m. 36 a 3) defines the harmonic mean as τὴν . . . ταὐτῷ μέρει τῶν ἄκρων αὐτῶν ὑπερέχουσαν καὶ ὑπερεχομένην. The harmonic mean of 12 and 6 is therefore 8; for 8=12—42=6+ 8.

2 For these stories and a criticism of them, see Max C. P. Schmidt, Kulturhistorische Beitrige, i. pp. 78 sqq. The smith’s hammers belong to the region of J/archen, and it is not true either that the notes would be determined by the weight of the hammers, or that, if they were,

the weights hung to equal strings would produce the notes. These inaccuracies were pointed out by Montucla (Martin, Etudes sur le Timée,

i. p. 391).

Science and Religion [19

called them “numbers,” when taken in connexion with what we are told about the method of Eurytos, is sufficient to show this was not the original sense of the doctrine. It is enough to suppose that Pythagoras reasoned somewhat as follows. If musical sounds can be reduced to numbers, why should not everything else? There are many likenesses to number in things, and it may well be that a lucky experiment, like that by which the octave was discovered, will reveal their true numerical nature. The Neopythagorean writers, going back in this as in other matters to the earliest tradition of the school, indulge their fancy in tracing out analogies between things and numbers in endless variety; but we are fortunately dispensed from following them in these vagaries. Aristotle tells us distinctly that the Pythagoreans explained only a few things by means of numbers,’ which means that Pythagoras himself left no developed doctrine on the sub- ject, while the Pythagoreans of the fifth century did not care to add anything of the sort to the school tradition. ᾿ς Aristotle does imply, however, that, according to them the “right time” (καιρός) was seven, justice was four, and marriage three. These identifications, with a few others like them, we may safely refer to Pythagoras or his immediate successors; but we must not attach much importance to them. They are mere sports of the analogical fancy. If we wish to understand the cosmology of Pythagoras, we must start, not from them, but from any statements we can find that present points of contact with the teaching of the

1 Arist. AZet. M, 4. 1078 Ὁ 21 (R. P. 78); Zeller, p. 390, n. 2. The Theologumena Arithmetica, wrongly attributed to Nikomachos of Gerasa, is full of fanciful doctrine on this subject (R. P. 78 a). Alexander 7 Met.

p. 38, 8, gives a few definitions which may be old (R. P. 78 c).

Cosmology.

120 Early Greek Philosophy

Milesian school. These, we may fairly infer, belong to the system in its most primitive form.

53. Now the most striking statement of this kind is
one of Aristotle’s. The Pythagoreans held, he tells us,
that there was “ boundless breath ” outside the heavens,
and that it was inhaled by the world. In substance,
this is the doctrine of Anaximenes, and it becomes
practically certain that it was that of Pythagoras,
when we find that Xenophanes denied it.2 We may
infer, then, that the further development of the idea is
also due to Pythagoras himself. We are told that, after
the first unit had been formed—however that may
have taken place—the nearest part of the Boundless
was first drawn in and limited ;* and further, that it is
just the Boundless thus inhaled that keeps the units

separate from each other.* It represents the interval

.between them. This is a very primitive way of

\describing the nature of discrete quantity.

i In the passages of Aristotle just referred to, the
Boundless is also spoken of as the void or empty.
This identification of air and the void is a confusion
which we have already met with in Anaximenes, and
it need not surprise us to find it here too. We find

1 Arist. Phys. A, 6. 213 Ὁ 22 (R. P. 75).

2 Diog. ix. 19 (R. P. 103 c). It is true that Diogenes is here drawing from a biographical rather than a doxographical source (Dox. p. 168), but this touch can hardly be an invention.

3 Arist. Met. M, 3. 1091 a 13 (R. P. 74).

* Arist. Phys. A, 6. 213 Ὁ 23 (R. P. 75 a). The words διορίζει τὰς φύσεις have caused unnecessary difficulty, because they have been supposed to attribute the function of limiting to the ἄπειρον. Aristotle makes it quite clear that his meaning is that stated in the text. Cf. especially the words χωρισμοῦ τινος τῶν ἐφεξῆς Kal διορίσεως. The term διωρισμένον is the proper antithesis to συνεχές. In his work on the Pythagorean philosophy, Aristotle used instead the phrase διορίζει ras χώρας (Stob. i. p. 156, 8; R. P. 75), which is also quite intelligible if we remember what the Pytha- goreans meant by χώρα (cf. p. 115, ἢ. 2).

5 Cf. Arist. Phys. A, 6. 213 ἃ 27, of δ᾽ ἄνθρωποι. .. φασὶν ἐν ᾧ ὅλως

Science and Religion 121

also, as we might expect, distinct traces of the other confusion, that of air and vapour. It seems certain, in fact, that Pythagoras identified the Limit with fire, and the Boundless with darkness. We are told by Aristotle that Hippasos made Fire the first principle,’ and we shall see that Parmenides, in discussing the opinions of his contemporaries, attributes to them the view that there were two primary “forms,” Fire and Night.2. We also find that Light and Darkness appear in the Pythagorean table of opposites under the heads of the Limit and the Unlimited respectively. The identification of breath with darkness here implied is a strong proof of the primitive character of the doctrine ; for in the sixth century darkness was supposed to be a sort of vapour, while in the fifth, its true nature was well known. Plato, with his usual historical tact, makes the Pythagorean Timaios describe mist and _ darkness as condensed air. We must think, then, of a “field” of darkness or breath marked out by luminous units, an imagination which the starry heavens would naturally suggest, It is even probable that we should ascribe to Pythagoras the Milesian view of a plurality of worlds, though it would not have been natural for him to speak of an infinite number. We know, at least, that Petron, one of the early Pythagoreans, said ἘΞ there were just a hundred and eighty-three worlds arranged in a triangle;> and Plato makes Timaios

μηδέν ἐστι, τοῦτ᾽ εἶναι κενόν, διὸ τὸ πλῆρες ἀέρος κενὸν εἶναι; de Part, An. Β, 10. 656 Ὁ 15, τὸ γὰρ κενὸν καλούμενον ἀέρος πλῆρές ἐστι ; de An. Β, 10. 419 b 34, δοκεῖ γὰρ εἶναι κενὸν ὁ ἀήρ.

1 Arist. Met. A, 3. 984 ἃ 7 (ΚΕ. P. 56 ο).

2 See Chap. IV. 8 91.

3 Arist. Met. A, 5. 986 ἃ 25 (R. P. 66).

4 Plato, Zim. 58 ἃ 2.

5 This is quoted by Plutarch, de def. orac. 422 Ὁ, ἃ, from Phanias of Eresos, who gave it on the authority of Hippys of Rhegion. If we may

The heavenly 20d ies.

122 Early Greek Philosophy

admit, when laying down that there is only one world,
that something might be urged in favour of the view
that there are five, as there are five regular solids.’

54. Anaximander had regarded the heavenly bodies
” filled with fire which escapes
through certain openings (§ 19), and there is evidence
that Pythagoras adopted the same view.” We have
seen that Anaximander only assumed the existence of
three such wheels, and held that the wheel of the sun
was the lowest. It is extremely probable that
Pythagoras identified the intervals between these rings
with the three musical intervals which he had
discovered, the fourth, the fifth, and the octave. That
would be the most natural beginning for the later
doctrine of the “harmony of the spheres,” though that
expression would be doubly misleading if applied to

as wheels of “air

any theory we can properly ascribe to Pythagoras
himself. The word ἁρμονία does not mean harmony,
and the “spheres” are an anachronism. We are still
at the stage when wheels or rings were considered
sufficient to account for the motions of the heavenly
bodies. It is also to be observed that sun, moon,
planets, and fixed stars must all be regarded as moving

in the same direction from east to west. Pythagoras” ,

certainly did not ascribe to the planets an orbital motion
of their own from west toeast. The old idea was rather
that they were left behind more or less every day. As
compared with the fixed stars, Saturn is left behind
least of all, and the Moon most; so, instead of saying

follow Wilamowitz (Hermes, xix. p. 444) in supposing that this really means Hippasos of Metapontion (and it was in Rhegion that the Pythagoreans took refuge), this is a very valuable piece of evidence.

1 Plato, Zim. 55 c 7 sqq.

2 This will be found in Chap. IV. § 93.

Science and Religion 123

that the Moon took a shorter time than Saturn to
complete its path through the signs of the Zodiac, men
said Saturn travelled quicker than the Moon, because
it more nearly succeeds in keeping up with the signs.
Instead of holding that Saturn takes thirty years to
complete its revolution, they said it took the fixed stars
thirty years to pass Saturn, and only twenty-nine days
and a half to pass the Moon. This is one of the
most important points to bear in mind regarding the
planetary systems of the Greeks, and we shall return
to it again.

The account just given of the views of Pythagoras is, no doubt, conjectural and incomplete. We have simply assigned to him those portions of the Pythagorean system which appear to be the oldest, and it has not even been possible at this stage to cite fully the evidence on which our discussion is based. It will only appear in its true light when we have examined the second part of the poem of Parmenides and the system of the later Pythagoreans.2_ For reasons which will then be apparent, I do not venture to ascribe to Pythagoras himself the theory of the earth’s revolution round the central fire. It seems safest to suppose that he still adhered to the geocentric hypothesis of Anaximander. In spite of this, however, it will be clear that he opened a new period in the development of Greek science, and it was certainly to his school that its greatest discoveries were directly or indirectly due.

1 For a clear statement of this view (which was still that of Demokritos), see Lucretius, v. 621 sqq. The view that the planets had an orbital motion from west to east is attributed by Aetios, ii. 16, 3, to Alkmaion (§ 96), which certainly implies that Pythagoras did not hold it. As we shall see (§ 152), it is far from clear that any of the Pythagoreans did. It seems rather to be Plato’s discovery.

2 See Chap. IV. §§ 92-93, and Chap. VII. 88 150-152.

Life.

124 Early Greek Philosophy

When Plato deliberately attributes some of his own
most important discoveries to the Pythagoreans, he
was acknowledging in a characteristic way the debt he
owed them.

Il. XENOPHANES OF KOLOPHON

55. We have seen how Pythagoras identified himself
with the religious movement of his time ; we have now
to consider a very different manifestation of the reaction
against that view of the gods which the poets had
made familiar to every one. Xenophanes denied the
anthropomorphic gods altogether, but was quite
unaffected by the revival of more primitive ideas that
was going on all round him. We still have a fragment
of an elegy in which he ridiculed Pythagoras and the
doctrine of transmigration. “Once, they say, he was
passing by when a dog was being ill-treated. ‘Stop!’
he said, ‘don’t hit it! It is the soul of a friend! I
knew it when I heard its voice””’ We are also told
that he opposed the views of Thales and Pythagoras,
and attacked Epimenides, which is likely enough,
though no fragments of the kind have come down to
us.” His chief importance lies in the fact that he was
the author of the quarrel between philosophy and
poetry which culminated in Plato’s Republic. |

It is not easy to determine the date of Xenophanes.
Timaios said he was a contemporary of Hieron
and Epicharmos, and he certainly seems to have