In the attempt which Plato makes to connect them, we easily trace the influences of ancient Pythagorean notions.

There is no reason to suppose that he is speaking of the ideal numbers; but he is describing numbers which are pure abstractions, to which he assigns a real and separate existence, which, as 'the teachers of the art' (meaning probably the Pythagoreans) would have affirmed, repel all attempts at subdivision, and in which unity and every other number are conceived of as absolute.

The truth and certainty of numbers, when thus disengaged from phenomena, gave them a kind of sacredness in the eyes of an ancient philosopher.

Nor is it easy to say how far ideas of order and fixedness may have had a moral and elevating influence on the minds of men, 'who,' in the words of the Timaeus, 'might learn to regulate their erring lives according to them.' It is worthy of remark that the old Pythagorean ethical symbols still exist as figures of speech among ourselves.

And those who in modern times see the world pervaded by universal law, may also see an anticipation of this last word of modern philosophy in the Platonic idea of good, which is the source and measure of all things, and yet only an abstraction (Philebus).
Two passages seem to require more particular explanations.