Early Greek Philosophy by John Burnet, with Burnet's notes
141. The "Fragments of Philolaus" 143. Aristotle on the Numbers

From Chapter VII., The Pythagoreans

142. The Problem
We must look, then, for other evidence. From what has been said, it will be clear that it is above all from Plato we can learn to regard Pythagoreanism sympathetically. Aristotle was out of sympathy with Pythagorean ways of thinking, but he took great pains to understand them. This was because they played so great a part in the philosophy of Plato and his successors, and he had to make the relation of the two doctrines as clear as he could to himself and his disciples. What we have to do, then, is to interpret what Aristotle tells us in the spirit of Plato, and then to consider how the doctrine we thus arrive at is related to the systems which preceded it. It is a delicate operation, no doubt, but it has been made much safer by recent discoveries in the early history of mathematics and medicine.

Zeller has cleared the ground by eliminating the Platonic elements which have crept into later accounts of the system. These are of two kinds. First of all, we have genuine Academic formulae, such as the identification of the Limit and the Unlimited with the One and the Indeterminate Dyad;38 and secondly, there is the Neoplatonic doctrine which represents the opposition between them as one between God and Matter.39 It is not necessary to repeat Zeller's arguments here, as no one will now attribute the doctrine in that form to the Pythagoreans.

This simplifies the problem, but it is still very difficult. According to Aristotle, the Pythagoreans said Things are numbers, though that is not the doctrine of the fragments of "Philolaos." According to them, things have number, which makes them knowable, while their real essence is something unknowable.40 We have seen reason for believing that Pythagoras himself said Things are numbers (§ 52), and there is no doubt as to what his followers meant by the formula; for Aristotle says they used it in a cosmological sense. The world, according to them, was made of numbers in the same sense as others had said it was made of "four roots" or "innumerable seeds." It will not do to dismiss this as mysticism. The Pythagoreans of the fifth century were scientific men, and must have meant something quite definite. We shall, no doubt, have to say that they used the words Things are numbers in a somewhat non-natural sense, but there is no difficulty in that. The Pythagoreans had a great veneration for the actual words of the Master (αὐτὸς ἔφα); but such veneration is often accompanied by a singular licence of interpretation. We shall start, then, from what Aristotle tells us about the numbers.

Burnet's Notes


38. Aristotle says distinctly (Met. A, 6. 987 b 25) that "to set up a dyad instead of the unlimited regarded as one, and to make the unlimited consist of the great and small, is distinctive of Plato."

39. Zeller, p. 369 sqq. (Eng. trans. p. 397 sqq.).

40. For the doctrine of "Philolaos," cf. fr. 1 (R. P. 64); and for the unknowable ἐστὼ τῶν πραγμάτων, see fr. 3 (R. P. 67). It has a suspicious resemblance to the later ὕλη, which Aristotle would hardly have failed to note. He is always on the look-out for anticipations of ὕλη.

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