Anaximander, answered from the texts and cited to the page.
The question names a principle formulated centuries after my time, associated above all with Leibniz — the claim that nothing exists or occurs without a sufficient reason why it is so and not otherwise. But the principle is not foreign to my thought. It is, in fact, the silent engine of my cosmology. Consider how I argued for the position of the Earth.
The Earth hangs free, supported by nothing, held in place at the center of the cosmos.1 Why does it not fall? Because there is no reason for it to fall in any one direction rather than another: all directions from the center to the cosmic boundary are equivalent, and where no direction is privileged, no motion toward any direction is compelled.
The argument is precisely the principle of sufficient reason in action — without a sufficient reason for motion in a particular direction, no such motion occurs. No Atlas, no roots into Tartarus, no physical support is needed. Equidistance from all points of the boundary is the sufficient reason for rest, and rest follows from it necessarily.
The same logic governs the apeiron itself. It is ungenerated and indestructible, for there is no sufficient reason that could generate or destroy it — anything that could generate it would itself require a prior source, and the apeiron is precisely that-from-which all other things are generated.2 It surrounds all and steers all; it is deathless and imperishable.3
The argument is not mythological; it is the recognition that a first principle, to function as a first principle, must stand outside the cycle of generation and destruction that everything else is subject to. If it could be destroyed, something more fundamental would destroy it, and that something would be the real principle. The apeiron is real because the reasoning leaves no alternative.
From the apeiron, the opposites — hot and cold, wet and dry — are separated out.4 The seed of the warm and the cold, detached from the eternal, produced a sphere of fire that grew around the surrounding air like bark around a tree; when this was torn away and enclosed within certain circles, the sun, the moon, and the stars were formed.5 Each step is reasoned: the cosmogonic process is not narrated as myth but derived from what the principle requires. Sufficient reason is not a formula I named; it is the method by which I built the system.
τὴν δὲ γῆν εἶναι μετέωρον, ὑπὸ μηδενὸς κρατουμένην, μένουσαν <δὲ> διὰ τὴν ὁμοίαν πάντων ἀπόστασιν.Early Greek Philosophy Vol II, Anaximander chapter, pp. 13–14
it [i.e. the unlimited] is ungenerated and indestructible, inasmuch as it is a principle. For what is generated must necessarily have an end, and there is an ending to every destruction.Early Greek Philosophy Vol II, Anaximander chapter, pp. 19–20
it itself is [scil. a principle] for everything else and surrounds all things and steers all... And the divine is this: for it is deathless and imperishable, as Anaximander says and most of the natural philosophers.Early Greek Philosophy Vol II, Anaximander chapter, pp. 21–23
The others say that the opposites are present in the one and are separated out from it, as Anaximander says.Early Greek Philosophy Vol II, Anaximander chapter, pp. 21–23
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. When this was torn away and enclosed within certain circles, the sun, the moon, and the stars were formed.Early Greek Philosophy Vol II, Anaximander chapter, pp. 18–19