Plato's order of creation is deliberate and philosophically loaded. In ordinary speech we describe the soul as something added to an already existing body — an animating principle that arrives after the physical structure is in place. Plato insists the reverse is true, and that our habit of speaking otherwise reflects our own subjection to chance rather than any natural priority of the material.
The world-soul is composed of three ingredients blended together: the indivisible and unchangeable (the realm of the Forms), the divisible and material (the realm of bodies), and an intermediate third kind that partakes of both. To these Plato adds the natures of the Same and the Other — the principles by which a thing recognises identity and difference. The result is a substance that can understand both the eternal and the changeable, because it shares in both.
From this compound the Demiurge cut strips according to harmonic ratios derived from the numbers 1, 2, 3, 4, 8, 9, and 27 — the framework of the Pythagorean musical scale. He bent these strips into circles, nested within each other, and set them spinning. The outer circle, moving with the nature of the Same, is the circle of the fixed stars. The inner circles, moving with the nature of the Other, are the orbits of the planets. This is not mere poetry: the mathematical structure of the soul is meant to explain why the heavens move as they do.
The world-soul perceives both the intelligible and the sensible by rotating its circles and comparing what they encounter. When the circle of the Same turns against an eternal Form, knowledge results; when it turns against a changing thing, true belief results. The cosmos is, on this account, not just alive but cognisant — a vast thinking being whose thoughts are the regular motions of the heavens. Human souls, made from the leftover material of the world-soul, share this structure at a diminished level: our capacity to reason is our participation in the same divine proportion that governs the universe.
The world-soul is constructed in Chapter 2 of the Timaeus. It was one of the most intensely discussed passages in ancient philosophy: the Neoplatonists, beginning with Plotinus, developed the world-soul into a distinct metaphysical hypostasis. The idea that the cosmos is itself intelligent — a living creature with a rational soul — stood in sharp contrast to Aristotle's cosmology and later to mechanical views of the universe.