Anaximander, answered from the texts and cited to the page.
The disagreement is not a quarrel between teacher and student over personal doctrine — it is a philosophical consequence that follows from taking the cosmological problem seriously. Thales said the arche is water. The report is preserved, and I do not dispute that it was his position. But consider what the claim entails: if water is the source of all things, then water is prior to and more fundamental than its opposites — the hot, the dry, the fiery.
Yet fire is the contrary of water, and if water were the unlimited source, fire would already have been destroyed by it. The opposites stand in contrariety to one another; if any one of them were the unlimited, the others would already have perished.1 This is not a minor technical objection. It is a demonstration that no named element — water, air, fire, earth — can serve as the arche of all things without immediately undermining the existence of its own contraries.
The apeiron is the answer to that problem. The principle of existing things must be neither water nor any of the so-called elements, but a certain other unlimited nature from which all the heavens and the worlds in them come to be.2 It is unlimited precisely because any limit — any specific quality, any named element — would place it in opposition to something else, and the source of all things cannot be in opposition to anything it generates.
The apeiron is eternal, ageless, surrounding and encompassing all.3 The opposites — hot and cold, wet and dry — separate out from it in the cosmogonic process; the seed of the warm and the cold, coming from the eternal, was detached at the birth of this world, and a sphere of fire grew around the surrounding air like the bark around a tree.4
The apeiron itself is none of these; it is that from which they all emerge. So the disagreement with Thales is structural, not temperamental. He had the right question — what is the source of all things? — and the wrong answer, because naming a specific element as the source creates the very problem of opposites that a genuine arche must dissolve.
For there are some who identify the unlimited with this, and not with air or water, so that the other things are not destroyed by their being unlimited. For they stand in contrariety to one another, for example air is cold, water moist, fire hot; and if one of them were unlimited, the others would already have been destroyed.Early Greek Philosophy Vol II, Anaximander chapter, pp. 49–50
He says that it is neither water nor any other of what are called elements, but a certain other unlimited nature from which come about all the heavens and the worlds in them.Early Greek Philosophy Vol II, Anaximander chapter, pp. 13–14
this he says that the heavens are separated out and in general all the worlds, which are unlimited... ταύτην δὲ ἀίδιον εἶναι καὶ ἀγήρω, ἣν καὶ πάντας περιέχειν τοὺς κόσμους.Early Greek Philosophy Vol II, Anaximander chapter, pp. 13–14
He says that the seed of the warm and the cold, coming from the eternal, was detached at the birth of this world and that a certain sphere of fire coming from this grew around the air surrounding the earth like the bark around a tree.Early Greek Philosophy Vol II, Anaximander chapter, pp. 18–19