[22] Plato, Timæus, p. 30 A. Compare the Republic, vi. p. 506, Philêbus, pp. 65-66, and the investigation in the Euthydêmus, pp. 279-293, which ends in no result.
Process of demiurgic construction — The total Kosmos comes logically first, constructed on the model of the Αὐτοζῶον.
These are the fundamental ideas which Plato expands into a detailed Kosmology. The first application which he makes of them is, to construct the total Kosmos. The total is here the logical Prius, or anterior to the parts in his order of conception. The Kosmos is one vast and comprehensive animal: just as in physiological description, the leading or central idea is, that of the animal organism as a whole, to which each and all the parts are referred. The Kosmos is constructed by the Demiurgus according to the model of the Αὐτοζῶον,[23] — (the Form or Idea of Animal — the eternal Generic or Self-Animal,) — which comprehends in itself the subordinate specific Ideas of different sorts of animals. This Generic Idea of Animal comprehended four of such specific Ideas: 1. The celestial race of animals, or Gods, who occupied the heavens. 2. Men. 3. Animals living in air — Birds. 4. Animals living on land or in water.[24] In order that the Kosmos might approach near to its model the Self-animal, it was required to contain all these four species. As there was but one Self-Animal, so there could only be one Kosmos.
[23] Plato, Timæus, p. 30 D.
[24] Plat. Timæus, pp. 39 E-40 A. ἧπερ οὖν νοῦς ἐνούσας ἰδέας τῷ ὃ ἔστι ζῶον, οἷαί τε ἔνεισι καὶ ὅσαι, καθορᾷ, τοιαύτας καὶ τοσαύτας διενοήθη δεῖν καὶ τόδε σχεῖν. Εἰσὶ δὲ τέτταρες, μία μὲν οὐράνιον θεῶν γένος, ἄλλη δὲ πτηνὸν καὶ ἀεροπόρον, τρίτη δὲ ἔνυδρον εἶδος, πεζὸν δὲ καὶ χερσαῖον τέταρτον.
We see thus, that the primary and dominant idea, in Plato’s mind, is, not that of inorganic matter, but that of organised and animated matter — life or soul embodied. With him, biology comes before physics.
The body of the Kosmos was required to be both visible and tangible: it could not be visible without fire: it could not be tangible without something solid, nor solid without earth. But two things cannot be well put together by themselves, without a third to serve as a bond of connection: and that is the best bond which makes them One as much as possible. Geometrical proportion best accomplishes this object. But as both Fire and Earth were solids and not planes, no one mean proportional could be found between them. Two mean proportionals were necessary. Hence the Demiurgus interposed air and water, in such manner, that as fire is to air, so is air to water: and as air is to water, so is water to earth.[25] Thus the four elements, composing the body of the Kosmos, were bound together in unity and friendship. Of each of the four, the entire total was used up in the construction: so that there remained nothing of them apart, to hurt the Kosmos from without, nor anything as raw material for a second Kosmos.[26]
[25] Plato, Tim. pp. 31-32. The comment of Macrobius on this passage (Somn. Scip. i. 6, p. 30) is interesting, if not conclusive. But the language in which Plato lays down this doctrine about mean proportionals is not precise, and has occasioned much difference of opinion among commentators. Between two solids (he says), that is, solid numbers, or numbers generated out of the product of three factors, no one mean proportional can be found. This is not universally true. The different suggestions of critics to clear up this difficulty will be found set forth in the elaborate note of M. Martin (Études sur le Timée, vol. 1, note xx. pp. 337-345), who has given what seems a probable explanation. Plato (he supposes) is speaking only of prime numbers and their products. In the language of ancient arithmeticians linear numbers, par excellence or properly so-called, were the prime numbers, measurable by unity only; plane numbers were the products of two such linear numbers or prime numbers; solid numbers were the products of three such. Understanding solid numbers in this restricted sense, it will be perfectly true that between any two of them you can never find any one solid number or any whole number which shall be a mean proportional, but you can always find two solid numbers which shall be mean proportionals. One mean proportional will never be sufficient. On the contrary, one mean proportional will be sufficient between two plane numbers (in the restricted sense) when these numbers are squares, though not if they are not squares. It is therefore true, that in the case of two solid numbers (so understood) one such mean proportional will never be sufficient, while two can always be found; and that between two plane numbers (so understood) one such mean proportional will in certain cases be sufficient and may be found. This is what is present to Plato’s mind, though in enunciating it he does not declare the restriction under which alone it is true. M. Boeckh (Untersuchungen über das Kosmische System des Platon, p. 17) approves of Martin’s explanation. At the same time M. Martin has given no proof that Plato had in his mind the distinction between prime numbers and other numbers, for his references in p. 338 do not prove this point; moreover, the explanation assumes such very loose expression, that the phrase of M. Cousin in his note (p. 334) is, after all, perfectly just: “Platon n’a pas songé à donner à sa phrase une rigueur mathématique”: and the more simple explanation of M. Cousin (though Martin rejects it as unworthy) may perhaps include all that is really intended. “Si deux surfaces peuvent être unies par un seul terme intermédiaire, il faudra deux termes intermédiaires pour unir deux solides: et l’union sera encore plus parfaite si la raison des deux proportions est la même.”
[26] Plat. Timæus, p. 32 E.