3), he was an adherent of the Heraclitean firedoctrine, whereas the Pythagoreans maintained the theory that number is the principle of everything.
He means that the logical analysis of demonstration in the Analytics would teach them beforehand that there cannot be demonstration, though there must be induction, of an axiom, or any other principle; whereas, if they are not logically prepared for metaphysics, they will expect a demonstration of the axiom, as Heraclitus, the Heraclitean Cratylus and the Sophist Protagoras actually did, - and in vain.
The nihilism of Gorgias from the Eleatic point of view of bare identity, and the speechlessness of Cratylus from the Heraclitean ground of absolute difference, are alike disowned.
Received at his hands an extension throughout the natural world, in which Heraclitean influence is unmistakable.
On and completed the assimilation of Heraclitean doctrine; but his own contributions were more distinctive and original.
Yet under this poetical Heraclitean mystic the school was far from flourishing.
Moreover, the commentaries of Cleanthes, Aristo and Sphaerus on Heraclitean writings (Diog.