This simplifies the problem very considerably, but it is still extremely difficult. According to Aristotle, the Pythagoreans said _Things are numbers_, though that does not appear to be the doctrine of the fragments of “Philolaos.” According to them, things _have_ number, which make them knowable, while their real essence is something unknowable.[770] That would be intelligible enough, but the formula that things _are_ numbers seems meaningless. We have seen reason for believing that it is due to Pythagoras himself (§ 52), though we did not feel able to say very clearly what he meant by it. There is no such doubt as to his school. Aristotle says they used the formula 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. Whatever we may think of Pythagoras, the Pythagoreans of the fifth century were scientific men, and they 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 such a supposition. We have seen already how the friends of Aristoxenos reinterpreted the old _Akousmata_ (§ 44). The Pythagoreans had certainly 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. Footnote 770: For the doctrine of “Philolaos,” cf. fr. 1 = 2 Ch. (R. P. 64); and for the unknowable ἐστὼ τῶν πραγμάτων, see fr. 3 = 4 Ch. (R. P. 67). It has a suspicious resemblance to the later ὕλη, which Aristotle would hardly have failed to note if he had ever seen the passage. He is always on the lookout for anticipations of ὕλη. [Sidenote: Aristotle on the Numbers.] 143. In the first place, Aristotle is quite decided in his opinion that Pythagoreanism was intended to be a cosmological system like the others. “Though the Pythagoreans,” he tells us, “made use of less obvious first principles and elements than the rest, seeing that they did not derive them from sensible objects, yet all their discussions and studies had reference to nature alone. They describe the origin of the heavens, and they observe the phenomena of its parts, all that happens to it and all it does.”[771] They apply their first principles entirely to these things, “agreeing apparently with the other natural philosophers in holding that reality was just what could be perceived by the senses, and is contained within the compass of the heavens,”[772] though “the first principles and causes of which they made use were really adequate to explain realities of a higher order than the sensible.”[773] Footnote 771: Arist. _Met._ Α, 8. 989 b 29 (R. P. 92 a). Footnote 772: