We must assume (says Plato, after a certain brief argument which he himself does not regard as quite complete) the Forms or Ideas of Fire, Air, Water, Earth, as distinct and self-existent, eternal, indestructible, unchangeable — neither visible nor tangible, but apprehended by Reason or Intellect alone — neither receiving anything else from without, nor themselves moving to anything else. Distinct from these — images of these, and bearing the same name — are the sensible objects called Fire, Water, &c. — objects of sense and opinion — always in a state of transition — generated and destroyed, but always generated in some place and destroyed out of some place. There is to be assumed, besides, distinct from the two preceding — as a third fundamentum — the place or receptacle in which these images are localised, generated, and nursed up. This place, or formless primitive receptivity, is indestructible, but out of all reach of sense, and difficult to believe in, inasmuch as it is only accessible by a spurious sort of ratiocination.[68]
[68] Plato, Timæus, p. 52 B. αὐτὸ δὲ μετ’ ἀναισθησίας ἁπτὸν λογισμῷ τινὶ νόθῳ, μόγις πιστόν.
Primordial Chaos — Effect of intervention by the Demiurgus.
Anterior to the construction of the Kosmos, the Forms or Ideas of the four elements had already begun to act upon this primitive recipient or receptacle, but in a confused and irregular way. Neither of the four could impress itself in a special and definite manner: there were some vestiges of each, but each was incomplete: all were in stir and agitation, yet without any measure or fixed rule. Thick and heavy, however, were tending to separate from thin and light, and each particle thus tending to occupy a place of its own.[69] In this condition (the primordial moving chaos of the poets and earlier philosophers), things were found by the Demiurgus, when he undertook to construct the Kosmos. There was no ready made Fire, Water, &c. (as Plato had assumed at the opening of the Timæus), but an agitated imbroglio of all, with the portions tending to separate from each other, and to agglomerate each in a place of its own. The Demiurgus brought these four elements out of confusion into definite bodies and regular movements. He gave to each a body, constructed upon the most beautiful proportions of arithmetic and geometry, as far as this was possible.[70]
[69] Plato, Timæus, pp. 52-53. 53 A: τὰ τέτταρα γένη σειόμενα ὑπὸ τῆς δεξαμένης, κινουμένης αὐτῆς οἷον ὀργάνου σεισμὸν παρέχοντος, τὰ μὲν ἀνομοιότατα πλεῖστον αὐτὰ ἀφ’ αὑτῶν ὁρίζειν, τὰ δ’ ὁμοιότατα μάλιστα εἰς ταὐτὸν ξυνωθεῖν· διὸ δὴ καὶ χώραν ταῦτα ἄλλα ἄλλην ἴσχειν, πρὶν καὶ τὸ πᾶν ἐξ αὐτῶν διακοσμηθὲν γενέσθαι. 57 C: διέστηκε μὲν γὰρ τοῦ γένους ἑκάστου τὰ πλήθη κατὰ τόπον ἴδιον διὰ τὴν τῆς δεχομένης κίνησιν. 58 C.
[70] Plato, Timæus, p. 53 B. τὸ δὲ ᾗ δυνατὸν ὡς κάλλιστα ἄριστά τε ἐξ οὐχ οὕτως ἐχόντων τὸν θεὸν αὐτὰ ξυνιστάναι, παρὰ πάντα ἡμῖν, ὡς ἀεί, τοῦτο λεγόμενον ὑπαρχέτω.
This is the hypothesis pervading all the Timæus — construction the best and finest which the case admitted. The limitations accompany the assumed purpose throughout.
Geometrical theory of the elements — fundamental triangles — regular solids.
Respecting such proportions, the theory which Plato here lays out is admitted by himself to be a novel one; but it is doubtless borrowed, with more or less modification, from the Pythagoreans. Every solid body is circumscribed by plane surfaces: every plane surface is composed of triangles: all triangles are generated out of two — the right-angled isoskeles triangle — and the right-angled scalene or oblong triangle. Of this oblong there are infinite varieties: but the most beautiful is a right-angled triangle, having the hypotenuse twice as long as the lesser of the two other sides.[71] From this sort of oblong triangle are generated the tetrahedron or pyramid — the octahedron — and the eikosihedron: from the equilateral triangle is generated the cube. The cube, as the most stable and solid, was assigned by the Demiurgus for the fundamental structure of earth: the pyramid for that of fire: the octahedron for that of air: the eikosihedron for that of water. The purpose was that the four should be in continuous geometrical proportion: as Fire to Air, so Air to Water: as Air to Water, so Water to Earth. Lastly, the Dodekahedron was assigned as the basis of structure for the spherical Kosmos itself or universe.[72] Upon this arrangement each of the three elements — fire, water, air — passes into the other; being generated from the same radical triangle. But earth does not pass into either of the three (nor either of these into earth), being generated from a different radical triangle. The pyramid, as thin, sharp, and cutting, was assigned to fire as the quickest and most piercing of the four elements: the cube as most solid and difficult to move, was allotted to earth, the stationary element. Fire was composed of pyramids of different size, yet each too small to be visible by itself, and becoming visible only when grouped together in masses: the earth was composed of cubes of different size, each invisible from smallness: the other elements in like manner, each from its respective solid,[73] in exact proportion and harmony, as far as Necessity could be persuaded to tolerate. All the five regular solids were thus employed in the configuration and structure of the Kosmos.[74]
[71] Plato, Timæus, pp. 53-54. 53 C: ἀηθεῖ λόγῳ δηλοῦν.