Early Greek Philosophy by John Burnet, with Burnet's notes
52. Things Are Numbers 54. The Heavenly Bodies

From Chapter II., Science and Religion

53. Cosmology
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.92 In substance, that is the doctrine of Anaximenes, and it becomes practically certain that it was taught by Pythagoras, when we find that Xenophanes denied it.93 We may infer that the further development of the idea is also due to Pythagoras. 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;94 and that it is the Boundless thus inhaled that keeps the units separate from each other.95 It represents the interval between them. This is a primitive way of describing discrete quantity.

In these passages of Aristotle, the "breath" is also spoken of as the void or empty. This is a confusion we have already met with in Anaximenes, and it need not surprise us to find it here.96 We find also clear 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,97 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.98 We also find that Light and Darkness appear in the Pythagorean table of opposites under the heads of the Limit and the Unlimited respectively.99 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 known. Plato, with his usual historical tact, makes the Pythagorean Timaios describe mist and darkness as condensed air.100 We must think, then, of a "field" of darkness or breath marked out by luminous units, an imagination 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 there were just a hundred and eighty-three worlds arranged in a triangles.101

Burnet's Notes


92. Arist. Phys. Δ, 6. 213 b 22 (R. P. 75).

93. Diog. ix. 119 (R. P, 103 c), ὅλον δ' ὁρᾶν καὶ ὅλον ἀκούειν, μὴ μέντοι ἀναπνεῖν (φησι Ξενοφάνης) So in [Plut.] Strom. fr. 4 we read that Xenophanes held μὴ κατὰ πᾶν μέρος περιέχεσθαι ὑπὸ ἀέρος (τὴν γῆν). We may therefore ascribe the statement to Theophrastos without hesitation, in spite of the fact that Diogenes is here drawing on an inferior (biographical) source, as shown by Diels (Dox. p. 168). Cf. also Hipp. Ref. i. 14, 2,τὴν δὲ γῆν ἄπειρον εἶναι καὶ μήτε ὑπ' ἀέρος μήτε ὑπὸ τοῦ οὐρανοῦ περιέχεσθαι (Ξενοφάνης λέγει).

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

95. Arist. Phys. Δ, 6. 213 b 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 καὶ διορίσεως. The term διωρισμένον, "discrete," is the proper antithesis to συνεχές, "continuous." In his work on the Pythagorean philosophy, Aristotle used instead the phrase διορίζει τὰς χώρας (Stob. i. p. 156, 8 ; R. P. 75), which is also quite intelligible if we remember what the Pythagoreans meant by χώρα (cf. p. 104, n. 2).

96. Cf. Arist. Phys. Δ, 6. 213 a 27, οἱ δ' ἄνθρωποι . . . φασὶν ἐν ᾧ ὅλως μηδέν ἐστι, τοῦτ' εἶναι κενόν, διὸ τὸ πλῆρες ἀέρος κενὸν εἶναι ; De part. an. B, 10. 656 b 15, τὸ γὰρ κενὸν καλούμενον ἀέρος πλῆρές ἐστι; De an. B, 10. 419 b 34, δοκεῖ γὰρ εἶναι κενὸν ὁ ἀήρ.

97. Arist. Met. A, 3. 984 a 7 (R. P. 56 c).

98. See Chap. IV. § 91.

99. Arist. Met. A, 5. 986 a 25 (R. P. 66).

100. Plato, Tim. 58 d 2.

101. This is quoted by Plutarch, De def. orac. 422 b, d, from Phanias of Eresos, who gave it on the authority of Hippys of Rhegion. If we may 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.

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