Timaeus — Plato
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to pass into it. Not only Buddhism, but Greek as well as Christian philosophy, show that it is quite possible that the human mind should retain an enthusiasm for mere negations. In different ages and countries there have been forms of light in which nothing could be discerned and which have nevertheless exercised a lifegiving and illumining power.
For the higher intelligence of man seems to require, not only something above sense, but above knowledge, which can only be described as Mind or Being or Truth or God or the unchangeable and eternal element, in the expression of which all predicates fail and fall short.
Eternity or the eternal is not merely the unlimited in time but the truest of all Being, the most real of all realities, the most certain of all knowledge, which we nevertheless only see through a glass darkly. The passionate earnestness of Parmenides contrasts with the vacuity of the thought which he is revolving in his mind. Space is said by Plato to be the ' containing vessel or nurse of generation.
Reflecting on the simplest kinds of external objects, which to the ancients were the four elements, he was led to a more general notion of a substance, more or less like themselves, out of which they were fashioned. He would not have them too precisely distinguished. Thus seems to have arisen the first dim perception of v^ri or matter, which has played so great a part in the metaphysical philosophy of Aristotle and his followers.
But besides the material out of which the elements are made, there is also a space in which they are contained. There arises thus a second nature which the senses are incapable of discerning and which can hardly be referred to the intelligible class. For it is and it is not, it is nowhere when filled, it is nothing when empty.
Hence it is said to be discerned by a kind of spurious or analogous reason, partaking so feebly of existence as to be hardly perceivable, yet always reappearing as the containing mother or nurse of all things. It had not that sort of consistency to Plato which has been given to it in modern times by geometry and metaphysics.
Neither of the Greek words by which it is described are so purely abstract as the English word 'space' or the Latin 'spatium. Neither Plato nor any other Greek would have spoken of jp(it'Of koX Toiroc^ or x^P^ ill the same manner as we speak of ' time ' and * space. Yet space is also of a very permanent or even eternal nature ;
The elements in a rude fashion pre-existed in chaos. 399 and Plato seems more willing to admit of the unreality of time Timaats. than of the unreality of space ; because, as he says, all things Introducmust necessarily exist in space. We, on the other hand, are disposed to fancy that even if space were annihilated time might still survive.
He admits indeed that our knowledge of space is of a dreamy kind, and is given by a spurious reason without the help of sense. (Cp. the hypotheses and images of Rep. vi. 511.) It is true that it does not attain to the clearness of ideas. But like them it seems to remain, even if all the objects contained in it are supposed to have vanished away. Hence it was natural for Plato to conceive of it as eternal.
We must remember further that in his attempt to realize either space or matter the two abstract ideas of weight and extension, which are familiar to us, had never passed before his mind.
Thus far God, working according to an eternal pattern, out of his goodness has created the same, the other, and the essence (compare the three principles of the Philebus — the finite, the infinite, and the union of the two), and out of them has formed the outer circle of the fixed stars and the inner circle of the planets, divided according to certain musical intervals ; he has also created time, the moving image of eternity, and space, existing by a sort of necessity and hardly distinguishable from matter.
The matter out of which the world is formed is not absolutely void, but retains in the chaos certain germs or traces of the elements. These Plato, like Empedocles, supposed to be four in number — fire, air, earth, and water. They were at first mixed together; but already in the chaos, before God fashioned them by form and number, the greater masses of the elements had an appointed place.
Into the confusion {jily^a) which preceded Plato does not attempt further to penetrate. They are called elements, but they are so far from being'elements {proix^'ui) or letters in the higher sense that they are not even syllables or first compounds. The real elements are two triangles, the rectangular isosceles which has but one form, and the most beautiful of the many forms of scalene, which is half of an equilateral triangle.
By the combination of these triangles which exist in an infinite variety of sizes, the surfaces of the four elements are constructed. That there were only five regular solids was already known to the ancients ; and out of the surfaces which he has formed Plato proceeds to generate the four first of the five. He perhaps forgets that he is only putting together surfaces and has not provided for their transformation into solids. The first solid is a regular pyramid, of which the base and sides are formed by four equilateral or twenty-four scalene triangles.
Each of the four solid angles in this figure is a little larger than the largest of obtuse angles. The second solid is composed of the same triangles, which unite as eight equilateral triangles, and make one solid angle out of four plane angles — six of these angles form a regular octahedron. The third solid is a regular icosahedron, having twenty triangular equilateral bases, and therefore 120 rectangular scalene triangles.
The fourth regular solid, or cube, is formed by the combination of four isosceles triangles into one square and of six squares into a cube. The fifth regular solid, or dodecahedron, cannot be formed by a combination of either of these triangles, but each of its faces may be regarded as composed of thirty triangles of another kind.
Probably Plato notices this as the only remaining regular polyhedron, which from its approximation to a globe, and possibly because, as Plutarch remarks, it is composed of 12 x 30 = 360 scalene triangles (Platon. Quaest. 5), representing thus the signs and degrees of the Zodiac, as well as the months and days of the year, God may be said to have ' used in the delineation of the universe.
According to Plato earth was composed of cubes, fire of regular pyramids, air of regular octahedrons, water of regular icosahedrons. The stability of the last three increases with the number of their sides.
The elements are supposed to pass into one another, but we must remember that these transformations are not the transformations of real solids, but of imaginary geometrical figures ; in other words, we are composing and decomposing the faces of substances and not the substances themselves — it is a house of cards which we are pulling to pieces and putting together again (cp. however Laws x. 894 A).
Yet perhaps Plato may regard these sides or faces as only the forms which are impressed on pre-existent matter. It is remarkable that he should speak of each of these solids as a possible world in itself, though upon the whole he inclines to the opinion that they form one world and not five. To suppose that there is an infinite number of worlds,
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