Timaeus
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 (Greek) which preceded
Plato does not attempt further to penetrate. They are called
elements, but they are so far from being elements (Greek) 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.), 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 (compare however
Laws). 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, as Democritus
(Hippolyt. Ref. Haer. I.) had said, would be, as he satirically
observes, ‘the characteristic of a very indefinite and ignorant
mind.’
The twenty triangular faces of an icosahedron form the faces or
sides of two regular octahedrons and of a regular pyramid (20 = 8
x 2 + 4); and therefore, according to Plato, a particle of water
when decomposed is supposed to give two particles of air and one
of fire. So because an octahedron gives the sides of two pyramids
(8 = 4 x 2), a particle of air is resolved into two particles of
fire.
The transformation is effected by the superior power or number of
the conquering elements. The manner of the change is (1) a
separation of portions of the elements from the masses in which
they are collected; (2) a resolution of them into their original
triangles; and (3) a reunion of them in new forms. Plato himself
proposes the question, Why does motion continue at all when the
elements are settled in their places? He answers that although
the force of attraction is continually drawing similar elements
to the same spot, still the revolution of the universe exercises
a condensing power, and thrusts them again out of their natural
places. Thus want of uniformity, the condition of motion, is
produced. In all such disturbances of matter there is an
alternative for the weaker element: it may escape to its kindred,
or take the form of the stronger—becoming denser, if it be
denser, or rarer if rarer. This is true of fire, air, and water,
which, being composed of similar triangles, are interchangeable;
earth, however, which has triangles peculiar to itself, is
capable of dissolution, but not of change. Of the interchangeable
elements, fire, the rarest, can only become a denser, and water,
the densest, only a rarer: but air may become a denser or a
rarer. No single particle of the elements is visible, but only
the aggregates of them are seen. The subordinate species depend,
not upon differences of form in the original triangles, but upon
differences of size. The obvious physical phenomena from which
Plato has gathered his views of the relations of the elements
seem to be the effect of fire upon air, water, and earth, and the
effect of water upon earth. The particles are supposed by him to
be in a perpetual process of circulation caused by inequality.
This process of circulation does not admit of a vacuum, as he
tells us in his strange account of respiration.
Of the phenomena of light and heavy he speaks afterwards, when
treating of sensation, but they may be more conveniently
considered by us in this place. They are not, he says, to be
explained by ‘above’ and ‘below,’ which in the universal globe
have no existence, but by the attraction of similars towards the
great masses of similar substances; fire to fire, air to air,
water to water, earth to earth. Plato’s doctrine of attraction
implies not only (1) the attraction of similar elements to one
another, but also (2) of smaller bodies to larger ones. Had he
confined himself to the latter he would have arrived, though,
perhaps, without any further result or any sense of the greatness
of the discovery, at the modern doctrine of gravitation. He does
not observe that water has an equal tendency towards both water
and earth. So easily did the most obvious facts which were
inconsistent with his theories escape him.
The general physical doctrines of the Timaeus may be summed up as
follows: (1) Plato supposes the greater masses of the elements to
have been already settled in their places at the creation: (2)
they are four in number, and are formed of rectangular triangles
variously combined into regular solid figures: (3) three of them,
fire, air, and water, admit of transformation into one another;
the fourth, earth, cannot be similarly transformed: (4) different
sizes of the same triangles form the lesser species of each
element: (5) there is an attraction of like to like—smaller
masses of the same kind being drawn towards greater: (6) there is
no void, but the particles of matter are ever pushing one another
round and round (Greek). Like the atomists, Plato attributes the
differences between the elements to differences in geometrical
figures. But he does not explain the process by which surfaces
become solids; and he characteristically ridicules Democritus for
not seeing that the worlds are finite and not infinite.
Section 4.
The astronomy of Plato is based on the two principles of the same
and the other, which God combined in the creation of the world.
The soul, which is compounded of the same, the other, and the
essence, is diffused from the centre to the circumference of the
heavens. We speak of a soul of the universe; but more truly
regarded, the universe of the Timaeus is a soul, governed by
mind, and holding in solution a residuum of matter or evil, which
the author of the world is unable to expel, and of which Plato
cannot tell us the origin. The creation, in Plato’s sense, is
really the creation of order; and the first step in giving order
is the division of the heavens into an inner and outer circle of
the other and the same, of the divisible and the indivisible,
answering to the two spheres, of the planets and of the world
beyond them, all together moving around the earth, which is their
centre. To us there is a difficulty in apprehending how that
which is at rest can also be in motion, or that which is
indivisible exist in space. But the whole description is so ideal
and imaginative, that we can hardly venture to attribute to many
of Plato’s words in the Timaeus any more meaning than to his
mythical account of the heavens in the Republic and in the
Phaedrus. (Compare his denial of the ‘blasphemous opinion’ that
there are planets or wandering stars; all alike move in
circles—Laws.) The stars are the habitations of the souls of men,
from which they come and to which they return. In attributing to
the fixed stars only the most perfect motion—that which is on the
same spot or circulating around the same—he might perhaps have
said that to ‘the spectator of all time and all existence,’ to
borrow once more his own grand expression, or viewed, in the
language of Spinoza, ‘sub specie aeternitatis,’ they were still
at rest, but appeared to move in order to teach men the periods
of time. Although absolutely in motion, they are relatively at
rest; or we may conceive of them as resting, while the space in
which they are contained, or the whole anima mundi, revolves.
The universe revolves around a centre once in twenty-four hours,
but the orbits of the fixed stars take a different direction from
those of the planets. The outer and the inner sphere cross one
another and meet again at a point opposite to that of their first
contact; the first moving in a circle from left to right along