Plato's Timaeus

TIMAEUS

by Plato

Translated by Benjamin Jowett

Section 3.

Plato's account of the soul is partly mythical or figurative, and partly
literal. Not that either he or we can draw a line between them, or say,
'This is poetry, this is philosophy'; for the transition from the one to
the other is imperceptible. Neither must we expect to find in him absolute
consistency. He is apt to pass from one level or stage of thought to
another without always making it apparent that he is changing his ground.
In such passages we have to interpret his meaning by the general spirit of
his writings. To reconcile his inconsistencies would be contrary to the
first principles of criticism and fatal to any true understanding of him.

There is a further difficulty in explaining this part of the Timaeus--the
natural order of thought is inverted. We begin with the most abstract, and
proceed from the abstract to the concrete. We are searching into things
which are upon the utmost limit of human intelligence, and then of a sudden
we fall rather heavily to the earth. There are no intermediate steps which
lead from one to the other. But the abstract is a vacant form to us until
brought into relation with man and nature. God and the world are mere
names, like the Being of the Eleatics, unless some human qualities are
added on to them. Yet the negation has a kind of unknown meaning to us.
The priority of God and of the world, which he is imagined to have created,
to all other existences, gives a solemn awe to them. And as in other
systems of theology and philosophy, that of which we know least has the
greatest interest to us.

There is no use in attempting to define or explain the first God in the
Platonic system, who has sometimes been thought to answer to God the
Father; or the world, in whom the Fathers of the Church seemed to recognize
'the firstborn of every creature.' Nor need we discuss at length how far
Plato agrees in the later Jewish idea of creation, according to which God
made the world out of nothing. For his original conception of matter as
something which has no qualities is really a negation. Moreover in the
Hebrew Scriptures the creation of the world is described, even more
explicitly than in the Timaeus, not as a single act, but as a work or
process which occupied six days. There is a chaos in both, and it would be
untrue to say that the Greek, any more than the Hebrew, had any definite
belief in the eternal existence of matter. The beginning of things
vanished into the distance. The real creation began, not with matter, but
with ideas. According to Plato in the Timaeus, God took of the same and
the other, of the divided and undivided, of the finite and infinite, and
made essence, and out of the three combined created the soul of the world.
To the soul he added a body formed out of the four elements. The general
meaning of these words is that God imparted determinations of thought, or,
as we might say, gave law and variety to the material universe. The
elements are moving in a disorderly manner before the work of creation
begins; and there is an eternal pattern of the world, which, like the 'idea
of good,' is not the Creator himself, but not separable from him. The
pattern too, though eternal, is a creation, a world of thought prior to the
world of sense, which may be compared to the wisdom of God in the book of
Ecclesiasticus, or to the 'God in the form of a globe' of the old Eleatic
philosophers. The visible, which already exists, is fashioned in the
likeness of this eternal pattern. On the other hand, there is no truth of
which Plato is more firmly convinced than of the priority of the soul to
the body, both in the universe and in man. So inconsistent are the forms
in which he describes the works which no tongue can utter--his language, as
he himself says, partaking of his own uncertainty about the things of which
he is speaking.

We may remark in passing, that the Platonic compared with the Jewish
description of the process of creation has less of freedom or spontaneity.
The Creator in Plato is still subject to a remnant of necessity which he
cannot wholly overcome. When his work is accomplished he remains in his
own nature. Plato is more sensible than the Hebrew prophet of the
existence of evil, which he seeks to put as far as possible out of the way
of God. And he can only suppose this to be accomplished by God retiring
into himself and committing the lesser works of creation to inferior
powers. (Compare, however, Laws for another solution of the difficulty.)

Nor can we attach any intelligible meaning to his words when he speaks of
the visible being in the image of the invisible. For how can that which is
divided be like that which is undivided? Or that which is changing be the
copy of that which is unchanging? All the old difficulties about the ideas
come back upon us in an altered form. We can imagine two worlds, one of
which is the mere double of the other, or one of which is an imperfect copy
of the other, or one of which is the vanishing ideal of the other; but we
cannot imagine an intellectual world which has no qualities--'a thing in
itself'--a point which has no parts or magnitude, which is nowhere, and
nothing. This cannot be the archetype according to which God made the
world, and is in reality, whether in Plato or in Kant, a mere negative
residuum of human thought.

There is another aspect of the same difficulty which appears to have no
satisfactory solution. In what relation does the archetype stand to the
Creator himself? For the idea or pattern of the world is not the thought
of God, but a separate, self-existent nature, of which creation is the
copy. We can only reply, (1) that to the mind of Plato subject and object
were not yet distinguished; (2) that he supposes the process of creation to
take place in accordance with his own theory of ideas; and as we cannot
give a consistent account of the one, neither can we of the other. He
means (3) to say that the creation of the world is not a material process
of working with legs and arms, but ideal and intellectual; according to his
own fine expression, 'the thought of God made the God that was to be.' He
means (4) to draw an absolute distinction between the invisible or
unchangeable which is or is the place of mind or being, and the world of
sense or becoming which is visible and changing. He means (5) that the
idea of the world is prior to the world, just as the other ideas are prior
to sensible objects; and like them may be regarded as eternal and self-
existent, and also, like the IDEA of good, may be viewed apart from the
divine mind.

There are several other questions which we might ask and which can receive
no answer, or at least only an answer of the same kind as the preceding.
How can matter be conceived to exist without form? Or, how can the
essences or forms of things be distinguished from the eternal ideas, or
essence itself from the soul? Or, how could there have been motion in the
chaos when as yet time was not? Or, how did chaos come into existence, if
not by the will of the Creator? Or, how could there have been a time when
the world was not, if time was not? Or, how could the Creator have taken
portions of an indivisible same? Or, how could space or anything else have
been eternal when time is only created? Or, how could the surfaces of
geometrical figures have formed solids? We must reply again that we cannot
follow Plato in all his inconsistencies, but that the gaps of thought are
probably more apparent to us than to him. He would, perhaps, have said
that 'the first things are known only to God and to him of men whom God
loves.' How often have the gaps in Theology been concealed from the eye of
faith! And we may say that only by an effort of metaphysical imagination
can we hope to understand Plato from his own point of view; we must not ask
for consistency. Everywhere we find traces of the Platonic theory of
knowledge expressed in an objective form, which by us has to be translated
into the subjective, before we can attach any meaning to it. And this
theory is exhibited in so many different points of view, that we cannot
with any certainty interpret one dialogue by another; e.g. the Timaeus by
the Parmenides or Phaedrus or Philebus.

The soul of the world may also be conceived as the personification of the
numbers and figures in which the heavenly bodies move. Imagine these as in
a Pythagorean dream, stripped of qualitative difference and reduced to
mathematical abstractions. They too conform to the principle of the same,
and may be compared with the modern conception of laws of nature. They are
in space, but not in time, and they are the makers of time. They are
represented as constantly thinking of the same; for thought in the view of
Plato is equivalent to truth or law, and need not imply a human
consciousness, a conception which is familiar enough to us, but has no
place, hardly even a name, in ancient Greek philosophy. To this principle
of the same is opposed the principle of the other--the principle of
irregularity and disorder, of necessity and chance, which is only partially
impressed by mathematical laws and figures. (We may observe by the way,
that the principle of the other, which is the principle of plurality and
variation in the Timaeus, has nothing in common with the 'other' of the
Sophist, which is the principle of determination.) The element of the same
dominates to a certain extent over the other--the fixed stars keep the
'wanderers' of the inner circle in their courses, and a similar principle
of fixedness or order appears to regulate the bodily constitution of man.
But there still remains a rebellious seed of evil derived from the original
chaos, which is the source of disorder in the world, and of vice and
disease in man.

But what did Plato mean by essence, (Greek), which is the intermediate
nature compounded of the Same and the Other, and out of which, together
with these two, the soul of the world is created? It is difficult to
explain a process of thought so strange and unaccustomed to us, in which
modern distinctions run into one another and are lost sight of. First, let
us consider once more the meaning of the Same and the Other. The Same is
the unchanging and indivisible, the heaven of the fixed stars, partaking of
the divine nature, which, having law in itself, gives law to all besides
and is the element of order and permanence in man and on the earth. It is
the rational principle, mind regarded as a work, as creation--not as the
creator. The old tradition of Parmenides and of the Eleatic Being, the
foundation of so much in the philosophy of Greece and of the world, was
lingering in Plato's mind. The Other is the variable or changing element,
the residuum of disorder or chaos, which cannot be reduced to order, nor
altogether banished, the source of evil, seen in the errors of man and also
in the wanderings of the planets, a necessity which protrudes through
nature. Of this too there was a shadow in the Eleatic philosophy in the
realm of opinion, which, like a mist, seemed to darken the purity of truth
in itself.--So far the words of Plato may perhaps find an intelligible
meaning. But when he goes on to speak of the Essence which is compounded
out of both, the track becomes fainter and we can only follow him with
hesitating steps. But still we find a trace reappearing of the teaching of
Anaxagoras: 'All was confusion, and then mind came and arranged things.'
We have already remarked that Plato was not acquainted with the modern
distinction of subject and object, and therefore he sometimes confuses mind
and the things of mind--(Greek) and (Greek). By (Greek) he clearly means
some conception of the intelligible and the intelligent; it belongs to the
class of (Greek). Matter, being, the Same, the eternal,--for any of these
terms, being almost vacant of meaning, is equally suitable to express
indefinite existence,--are compared or united with the Other or Diverse,
and out of the union or comparison is elicited the idea of intelligence,
the 'One in many,' brighter than any Promethean fire (Phil.), which co-
existing with them and so forming a new existence, is or becomes the
intelligible world...So we may perhaps venture to paraphrase or interpret
or put into other words the parable in which Plato has wrapped up his
conception of the creation of the world. The explanation may help to fill
up with figures of speech the void of knowledge.

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 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.