The revolutions of such grand bodies could not take place, in the opinion of the Pythagoreans, without producing a loud and powerful sound; and as their distances from the central fire were supposed to be arranged in musical ratios,[40] so the result of all these separate sounds was full and perfect harmony. To the objection — Why were not these sounds heard by us? — they replied, that we had heard them constantly and without intermission from the hour of our birth; hence they had become imperceptible by habit.[41]
[40] Playfair observes (in his dissertation on the Progress of Natural Philosophy, p. 87) respecting Kepler — “Kepler was perhaps the first person who conceived that there must be always a law capable of being expressed by arithmetic or geometry, which connects such phenomena as have a physical dependence on each other”. But this seems to be exactly the fundamental conception of the Pythagoreans: or rather a part of their fundamental conception, for they also considered their numbers as active forces bringing such law into reality. To illustrate the determination of the Pythagoreans to make up the number of Ten celestial bodies, I transcribe another passage from Playfair (p. 98). Huygens, having discovered one satellite of Saturn, “believed that there were no more, and that the number of the planets was now complete. The planets, primary and secondary, thus made up twelve — the double of six, the first of the perfect numbers.”
[41] Aristot. De Cœlo, ii. 9; Pliny, H.N. ii. 20.
See the Pythagorean system fully set forth by Zeller, Die Philosophie der Griechen, vol. i. p. 302-310, ed. 2nd.
Pythagorean list of fundamental Contraries — Ten opposing pairs.
Ten was, in the opinion of the Pythagoreans, the perfection and consummation of number. The numbers from One to Ten were all that they recognised as primary, original, generative. Numbers greater than ten were compounds and derivatives from the decad. They employed this perfect number not only as a basis on which to erect a bold astronomical hypothesis, but also as a sum total for their list of contraries. Many Hellenic philosophers[42] recognised pairs of opposing attributes as pervading nature, and as the fundamental categories to which the actual varieties of the sensible world might be reduced. While others laid down Hot and Cold, Wet and Dry, as the fundamental contraries, the Pythagoreans adopted a list of ten pairs. 1. Limit and Unlimited; 2. Odd and Even; 3. One and Many; 4. Right and Left; 5. Male and Female; 6. Rest and Motion; 7. Straight and Curve; 8. Light and Darkness; 9. Good and Evil; 10. Square and Oblong.[43] Of these ten pairs, five belong to arithmetic or to geometry, one to mechanics, one to physics, and three to anthropology or ethics. Good and Evil, Regularity and Irregularity, were recognised as alike primordial and indestructible.[44]
[42] Aristot. Metaphys. Γ. 2, p. 1004, b. 30. τὰ δ’ ὄντα καὶ τὴν οὐσιαν ὁμολογοῦσιν ἐξ ἐναντίων σχεδὸν ἅπαντες συγκεῖσθαι.
[43] Aristot. Metaphys. A. 5, p. 986, a. 22. He goes on to say that Alkmæon, a semi-Pythagorean and a younger contemporary of Pythagoras himself, while agreeing in the general principle that “human affairs were generally in pairs,” (εἶναι δύο τὰ πολλὰ τῶν ἀνθρωπίνων), laid down pairs of fundamental contraries at random (τὰς ἐναντιότητας τὰς τυχούσας) — black and white, sweet and bitter, good and evil, great and little. All that you can extract from these philosophers is (continues Aristotle) the general axiom, that “contraries are the principia of existing things” — ὅτι τἀνάντια ἀρχαὶ τῶν ὄντων.
This axiom is to be noted as occupying a great place in the minds of the Greek philosophers.