Timaeus
The entire compound was divided by the Creator in certain
proportions and reunited; it was then cut into two strips, which
were bent into an inner circle and an outer, both moving with an
uniform motion around a centre, the outer circle containing the
fixed, the inner the wandering stars. The soul of the world was
diffused everywhere from the centre to the circumference. To this
God gave a body, consisting at first of fire and earth, and
afterwards receiving an addition of air and water; because solid
bodies, like the world, are always connected by two middle terms
and not by one. The world was made in the form of a globe, and
all the material elements were exhausted in the work of creation.
The proportions in which the soul of the world as well as the
human soul is divided answer to a series of numbers 1, 2, 3, 4,
9, 8, 27, composed of the two Pythagorean progressions 1, 2, 4, 8
and 1, 3, 9, 27, of which the number 1 represents a point, 2 and
3 lines, 4 and 8, 9 and 27 the squares and cubes respectively of
2 and 3. This series, of which the intervals are afterwards
filled up, probably represents (1) the diatonic scale according
to the Pythagoreans and Plato; (2) the order and distances of the
heavenly bodies; and (3) may possibly contain an allusion to the
music of the spheres, which is referred to in the myth at the end
of the Republic. The meaning of the words that ‘solid bodies are
always connected by two middle terms’ or mean proportionals has
been much disputed. The most received explanation is that of
Martin, who supposes that Plato is only speaking of surfaces and
solids compounded of prime numbers (i.e. of numbers not made up
of two factors, or, in other words, only measurable by unity).
The square of any such number represents a surface, the cube a
solid. The squares of any two such numbers (e.g. 2 squared, 3
squared = 4, 9), have always a single mean proportional (e.g. 4
and 9 have the single mean 6), whereas the cubes of primes (e.g.
3 cubed and 5 cubed) have always two mean proportionals (e.g.
27:45:75:125). But to this explanation of Martin’s it may be
objected, (1) that Plato nowhere says that his proportion is to
be limited to prime numbers; (2) that the limitation of surfaces
to squares is also not to be found in his words; nor (3) is there
any evidence to show that the distinction of prime from other
numbers was known to him. What Plato chiefly intends to express
is that a solid requires a stronger bond than a surface; and that
the double bond which is given by two means is stronger than the
single bond given by one. Having reflected on the singular
numerical phenomena of the existence of one mean proportional
between two square numbers are rather perhaps only between the
two lowest squares; and of two mean proportionals between two
cubes, perhaps again confining his attention to the two lowest
cubes, he finds in the latter symbol an expression of the
relation of the elements, as in the former an image of the
combination of two surfaces. Between fire and earth, the two
extremes, he remarks that there are introduced, not one, but two
elements, air and water, which are compared to the two mean
proportionals between two cube numbers. The vagueness of his
language does not allow us to determine whether anything more
than this was intended by him.
Leaving the further explanation of details, which the reader will
find discussed at length in Boeckh and Martin, we may now return
to the main argument: Why did God make the world? Like man, he
must have a purpose; and his purpose is the diffusion of that
goodness or good which he himself is. The term ‘goodness’ is not
to be understood in this passage as meaning benevolence or love,
in the Christian sense of the term, but rather law, order,
harmony, like the idea of good in the Republic. The ancient
mythologers, and even the Hebrew prophets, had spoken of the
jealousy of God; and the Greek had imagined that there was a
Nemesis always attending the prosperity of mortals. But Plato
delights to think of God as the author of order in his works,
who, like a father, lives over again in his children, and can
never have too much of good or friendship among his creatures.
Only, as there is a certain remnant of evil inherent in matter
which he cannot get rid of, he detaches himself from them and
leaves them to themselves, that he may be guiltless of their
faults and sufferings.
Between the ideal and the sensible Plato interposes the two
natures of time and space. Time is conceived by him to be only
the shadow or image of eternity which ever is and never has been
or will be, but is described in a figure only as past or future.
This is one of the great thoughts of early philosophy, which are
still as difficult to our minds as they were to the early
thinkers; or perhaps more difficult, because we more distinctly
see the consequences which are involved in such an hypothesis.
All the objections which may be urged against Kant’s doctrine of
the ideality of space and time at once press upon us. If time is
unreal, then all which is contained in time is unreal—the
succession of human thoughts as well as the flux of sensations;
there is no connecting link between (Greek) and (Greek). Yet, on
the other hand, we are conscious that knowledge is independent of
time, that truth is not a thing of yesterday or tomorrow, but an
‘eternal now.’ To the ‘spectator of all time and all existence’
the universe remains at rest. The truths of geometry and
arithmetic in all their combinations are always the same. The
generations of men, like the leaves of the forest, come and go,
but the mathematical laws by which the world is governed remain,
and seem as if they could never change. The ever-present image of
space is transferred to time—succession is conceived as
extension. (We remark that Plato does away with the above and
below in space, as he has done away with the absolute existence
of past and future.) The course of time, unless regularly marked
by divisions of number, partakes of the indefiniteness of the
Heraclitean flux. By such reflections we may conceive the Greek
to have attained the metaphysical conception of eternity, which
to the Hebrew was gained by meditation on the Divine Being. No
one saw that this objective was really a subjective, and involved
the subjectivity of all knowledge. ‘Non in tempore sed cum
tempore finxit Deus mundum,’ says St. Augustine, repeating a
thought derived from the Timaeus, but apparently unconscious of
the results to which his doctrine would have led.
The contradictions involved in the conception of time or motion,
like the infinitesimal in space, were a source of perplexity to
the mind of the Greek, who was driven to find a point of view
above or beyond them. They had sprung up in the decline of the
Eleatic philosophy and were very familiar to Plato, as we gather
from the Parmenides. The consciousness of them had led the great
Eleatic philosopher to describe the nature of God or Being under
negatives. He sings of ‘Being unbegotten and imperishable,
unmoved and never-ending, which never was nor will be, but always
is, one and continuous, which cannot spring from any other; for
it cannot be said or imagined not to be.’ The idea of eternity
was for a great part a negation. There are regions of speculation
in which the negative is hardly separable from the positive, and
even seems 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 life-giving 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 (Greek) 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 (Greek) or (Greek) in the same manner as we
speak of ‘time’ and ‘space.’
Yet space is also of a very permanent or even eternal nature; and
Plato seems more willing to admit of the unreality of time than
of the unreality of space; because, as he says, all things must
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. (Compare the hypotheses and images of Rep.) 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