structed.[1] This construction of the world out of numbers was a real process in time, which the Pythagoreans described in detail.[2]
Further, the numbers were intended to be mathematical numbers, though they were not separated from the things of sense.[3] On the other hand, they were not mere predicates of something else, but had an independent reality of their own. "They did not hold that the limited and the unlimited and the one were certain other substances, such as fire, water, or anything else of that sort; but that the unlimited itself and the one itself were the reality of the things of which they are predicated, and that is why they said that number was the reality of everything."[4] Accordingly the numbers are, in Aristotle's own language, not only the formal, but also the material, cause of things.[5]
Lastly, Aristotle notes that the point in which the Pythagoreans agreed with Plato was in giving numbers an independent reality of their own; while Plato differed from the Pythagoreans in holding that this reality was distinguishable from that of sensible things.[6] Let us consider these statements in detail.
144.The elements of numbers. Aristotle speaks of certain "elements" (στοιχεῖα) of numbers, which were also the elements of things. That is clearly the key to the problem, if we can discover what it means. Primarily, the "elements of number" are the Odd and the Even, but that does not seem to help us much. We find, however, that the Odd and Even were identified with the Limit and the Unlimited, which we have seen reason to regard as the original principles of the Pythagorean cosmo-
- ↑ Met. A, 5. 986 a 2, τὸν ὅλον οὐρανὸν ἁρμονίαν εἶναι καὶ ἀριθμόν; A, 8. 990 a 21, τὸν ἀριθμὸν τοῦτον ἐξ οὗ συνέστηκεν ὁ κόσμος; M. 6. 1080 b 18, τὸν γὰρ ὅλον οὐρανὸν κατασκευάζουσιν ἐξ ἀριθμῶν; De caelo, Γ. 1. 300 a 15, τοῖς ἐξ ἀριθμῶν συνιστᾶσι τὸν οὐρανόν· ἔνιοι γὰρ τὴν φύσιν ἐξ ἀριθμῶν συνιστᾶσιν, ὥσπερ τῶν Πυθαγορείων τινές.
- ↑ Met. N, 3. 1091 a 18, κοσμοποιοῦσι καὶ φυσικῶς βούλονται λέγειν.
- ↑ Met. M, 6. 1080 b 16; N, 3. 1090 a 20.
- ↑ Arist. Met. A, 5. 987 a 15.
- ↑ Met. ib. 986 a 15 (R. P. 66).
- ↑ Met. A, 6. 987 b 27, ὁ μὲν (Πλάτων) τοὺς ἀριθμοὺς παρὰ τὰ αἰσθητά, οἱ δ' (οἱ Πυθαγόρειοι) ἀριθμοὺς εἶναί φασιν αὐτὰ τὰ αἰσθητά.
