It is clear at any rate that the great contribution of Pythagoras to science was his discovery that the concordant intervals could be expressed by simple numerical ratios. In principle, at least, that suggests an entirely new view of the relation between the traditional "opposites." If a perfect attunement (ἁρμονία) of the high and the low can be attained by observing these ratios, it is clear that other opposites may be similarly harmonised. The hot and the cold, the wet and the dry, may be united in a just blend (κρᾶσις), an idea to which our word "temperature" still bears witness.[1] The medical doctrine of the "temperaments" is derived from the same source. Moreover, the famous doctrine of the Mean is only an application of the same idea to the problem of conduct.[2] It is not too much to say that Greek philosophy was henceforward to be dominated by the notion of the perfectly tuned string.
II. Xenophanes of Kolophon
55.Life. We have seen how Pythagoras gave a deeper meaning to the religious movement of his time; we have now to consider a very different manifestation of the reaction against the view of the gods which the poets had made familiar. Xenophanes denied the anthropomorphic gods altogether, but was quite unaffected by the revival of religion going on all round him. We still have a fragment of an elegy in which he ridiculed Pythagoras and the doctrine of transmigration.[3] We are also told that he opposed the views of Thales and Pythagoras, and attacked Epimenides,
- ↑ It is impossible not to be struck by the resemblance between this doctrine and Dalton's theory of chemical combination. A formula like H₂O is a beautiful example of a μεσότης. The diagrams of modern stereochemistry have also a curiously Pythagorean appearance. We sometimes feel tempted to say that Pythagoras had really hit upon the secret of the world when he said, "Things are numbers."
- ↑ Aristotle derived his doctrine of the Mean from Plato's Philebus, where it is clearly expounded as a Pythagorean doctrine.
- ↑ See fr. 7, below.
