Timaeus

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.