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 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.

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 the side of a parallelogram which is supposed to be inscribed in it, the second also moving in a circle along the diagonal of the same parallelogram from right to left; or, in other words, the first describing the path of the equator, the second, the path of the ecliptic. The motion of the second is controlled by the first, and hence the oblique line in which the planets are supposed to move becomes a spiral. The motion of the same is said to be undivided, whereas the inner motion is split into seven unequal orbits—the intervals between them being in the ratio of two and three, three of either:—the Sun, moving in the opposite direction to Mercury and Venus, but with equal swiftness; the remaining four, Moon, Saturn, Mars, Jupiter, with unequal swiftness to the former three and to one another. Thus arises the following progression:—Moon 1, Sun 2, Venus 3, Mercury 4, Mars 8, Jupiter 9, Saturn 27. This series of numbers is the compound of the two Pythagorean ratios, having the same intervals, though not in the same order, as the mixture which was originally divided in forming the soul of the world.

Plato was struck by the phenomenon of Mercury, Venus, and the Sun appearing to overtake and be overtaken by one another. The true reason of this, namely, that they lie within the circle of the earth’s orbit, was unknown to him, and the reason which he gives—that the two former move in an opposite direction to the latter—is far from explaining the appearance of them in the heavens. All the planets, including the sun, are carried round in the daily motion of the circle of the fixed stars, and they have a second or oblique motion which gives the explanation of the different lengths of the sun’s course in different parts of the earth. The fixed stars have also two movements—a forward movement in their orbit which is common to the whole circle; and a movement on the same spot around an axis, which Plato calls the movement of thought about the same. In this latter respect they are more perfect than the wandering stars, as Plato himself terms them in the Timaeus, although in the Laws he condemns the appellation as blasphemous.

The revolution of the world around earth, which is accomplished in a single day and night, is described as being the most perfect or intelligent. Yet Plato also speaks of an ‘annus magnus’ or cyclical year, in which periods wonderful for their complexity are found to coincide in a perfect number, i.e. a number which equals the sum of its factors, as 6 = 1 + 2 + 3. This, although not literally contradictory, is in spirit irreconcilable with the perfect revolution of twenty-four hours. The same remark may be applied to the complexity of the appearances and occultations of the stars, which, if the outer heaven is supposed to be moving around the centre once in twenty-four hours, must be confined to the effects produced by the seven planets. Plato seems to confuse the actual observation of the heavens with his desire to find in them mathematical perfection. The same spirit is carried yet further by him in the passage already quoted from the Laws, in which he affirms their wanderings to be an appearance only, which a little knowledge of mathematics would enable men to correct.

We have now to consider the much discussed question of the rotation or immobility of the earth. Plato’s doctrine on this subject is contained in the following words:—‘The earth, which is our nurse, compacted (OR revolving) around the pole which is extended through the universe, he made to be the guardian and artificer of night and day, first and eldest of gods that are in the interior of heaven’. There is an unfortunate doubt in this passage (1) about the meaning of the word (Greek), which is translated either ‘compacted’ or ‘revolving,’ and is equally capable of both explanations. A doubt (2) may also be raised as to whether the words ‘artificer of day and night’ are consistent with the mere passive causation of them, produced by the immobility of the earth in the midst of the circling universe. We must admit, further, (3) that Aristotle attributed to Plato the doctrine of the rotation of the earth on its axis. On the other hand it has been urged that if the earth goes round with the outer heaven and sun in twenty-four hours, there is no way of accounting for the alternation of day and night; since the equal motion of the earth and sun would have the effect of absolute immobility. To which it may be replied that Plato never says that the earth goes round with the outer heaven and sun; although the whole question depends on the relation of earth and sun, their movements are nowhere precisely described. But if we suppose, with Mr. Grote, that the diurnal rotation of the earth on its axis and the revolution of the sun and outer heaven precisely coincide, it would be difficult to imagine that Plato was unaware of the consequence. For though he was ignorant of many things which are familiar to us, and often confused in his ideas where we have become clear, we have no right to attribute to him a childish want of reasoning about very simple facts, or an inability to understand the necessary and obvious deductions from geometrical figures or movements. Of the causes of day and night the pre-Socratic philosophers, and especially the Pythagoreans, gave various accounts, and therefore the question can hardly be imagined to have escaped him. On the other hand it may be urged that the further step, however simple and obvious, is just what Plato often seems to be ignorant of, and that as there is no limit to his insight, there is also no limit to the blindness which sometimes obscures his intelligence (compare the construction of solids out of surfaces in his account of the creation of the world, or the attraction of similars to similars). Further, Mr. Grote supposes, not that (Greek) means ‘revolving,’ or that this is the sense in which Aristotle understood the word, but that the rotation of the earth is necessarily implied in its adherence to the cosmical axis. But (a) if, as Mr Grote assumes, Plato did not see that the rotation of the earth on its axis and of the sun and outer heavens around the earth in equal times was inconsistent with the alternation of day and night, neither need we suppose that he would have seen the immobility of the earth to be inconsistent with the rotation of the axis. And (b) what proof is there that the axis of the world revolves at all? (c) The comparison of the two passages quoted by Mr Grote (see his pamphlet on ‘The Rotation of the Earth’) from Aristotle De Coelo, Book II (Greek) clearly shows, although this is a matter of minor importance, that Aristotle, as Proclus and Simplicius supposed, understood (Greek) in the Timaeus to mean ‘revolving.’ For the second passage, in which motion on an axis is expressly mentioned, refers to the first, but this would be unmeaning unless (Greek) in the first passage meant rotation on an axis. (4) The immobility of the earth is more in accordance with Plato’s other writings than the opposite hypothesis. For in the Phaedo the earth is described as the centre of the world, and is not said to be in motion. In the Republic the pilgrims appear to be looking out from the earth upon the motions of the heavenly bodies; in the Phaedrus, Hestia, who remains immovable in the house of Zeus while the other gods go in procession, is called the first and eldest of the gods, and is probably the symbol of the earth. The silence of Plato in these and in some other passages (Laws) in which he might be expected to speak of the rotation of the earth, is more favourable to the doctrine of its immobility than to the opposite. If he had meant to say that the earth revolves on its axis, he would have said so in distinct words, and have explained the relation of its movements to those of the other heavenly bodies. (5) The meaning of the words ‘artificer of day and night’ is literally true according to Plato’s view. For the alternation of day and night is not produced by the motion of the heavens alone, or by the immobility of the earth alone, but by both together; and that which has the inherent force or energy to remain at rest when all other bodies are moving, may be truly said to act, equally with them. (6) We should not lay too much stress on Aristotle or the writer De Caelo having adopted the other interpretation of the words, although Alexander of Aphrodisias thinks that he could not have been ignorant either of the doctrine of Plato or of the sense which he intended to give to the word (Greek). For the citations of Plato in Aristotle are frequently misinterpreted by him; and he seems hardly ever to have had in his mind the connection in which they occur. In this instance the allusion is very slight, and there is no reason to suppose that the diurnal revolution of the heavens was present to his mind. Hence we need not attribute to him the error from which we are defending Plato.

After weighing one against the other all these complicated probabilities, the final conclusion at which we arrive is that there is nearly as much to be said on the one side of the question as on the other, and that we are not perfectly certain, whether, as Bockh and the majority of commentators, ancient as well as modern, are inclined to believe, Plato thought that the earth was at rest in the centre of the universe, or, as Aristotle and Mr. Grote suppose, that it revolved on its axis. Whether we assume the earth to be stationary in the centre of the universe, or to revolve with the heavens, no explanation is given of the variation in the length of days and nights at different times of the year. The relations of the earth and heavens are so indistinct in the Timaeus and so figurative in the Phaedo, Phaedrus and Republic, that we must give up the hope of ascertaining how they were imagined by Plato, if he had any fixed or scientific conception of them at all.

The soul of the world is framed on the analogy of the soul of man, and many traces of anthropomorphism blend with Plato’s highest flights of idealism. The heavenly bodies are endowed with thought; the principles of the same and other exist in the universe as well as in the human mind. The soul of man is made out of the remains of the elements which had been used in creating the soul of the world; these remains, however, are diluted to the third degree; by this Plato expresses the measure of the difference between the soul human and divine. The human soul, like the cosmical, is framed before the body, as the mind is before the soul of either—this is the order of the divine work—and the finer parts of the body, which are more akin to the soul, such as the spinal marrow, are prior to the bones and flesh. The brain, the containing vessel of the divine part of the soul, is (nearly) in the form of a globe, which is the image of the gods, who are the stars, and of the universe.

There is, however, an inconsistency in Plato’s manner of conceiving the soul of man; he cannot get rid of the element of necessity which is allowed to enter. He does not, like Kant, attempt to vindicate for men a freedom out of space and time; but he acknowledges him to be subject to the influence of external causes, and leaves hardly any place for freedom of the will. The lusts of men are caused by their bodily constitution, though they may be increased by bad education and bad laws, which implies that they may be decreased by good education and good laws. He appears to have an inkling of the truth that to the higher nature of man evil is involuntary. This is mixed up with the view which, while apparently agreeing with it, is in reality the opposite of it, that vice is due to physical causes. In the Timaeus, as well as in the Laws, he also regards vices and crimes as simply involuntary; they are diseases analogous to the diseases of the body, and arising out of the same causes. If we draw together the opposite poles of Plato’s system, we find that, like Spinoza, he combines idealism with fatalism.

The soul of man is divided by him into three parts, answering roughly to the charioteer and steeds of the Phaedrus, and to the (Greek) of the Republic and Nicomachean Ethics. First, there is the immortal nature of which the brain is the seat, and which is akin to the soul of the universe. This alone thinks and knows and is the ruler of the whole. Secondly, there is the higher mortal soul which, though liable to perturbations of her own, takes the side of reason against the lower appetites. The seat of this is the heart, in which courage, anger, and all the nobler affections are supposed to reside. There the veins all meet; it is their centre or house of guard whence they carry the orders of the thinking being to the extremities of his kingdom. There is also a third or appetitive soul, which receives the commands of the immortal part, not immediately but mediately, through the liver, which reflects on its surface the admonitions and threats of the reason.

The liver is imagined by Plato to be a smooth and bright substance, having a store of sweetness and also of bitterness, which reason freely uses in the execution of her mandates. In this region, as ancient superstition told, were to be found intimations of the future. But Plato is careful to observe that although such knowledge is given to the inferior parts of man, it requires to be interpreted by the superior. Reason, and not enthusiasm, is the true guide of man; he is only inspired when he is demented by some distemper or possession. The ancient saying, that ‘only a man in his senses can judge of his own actions,’ is approved by modern philosophy too. The same irony which appears in Plato’s remark, that ‘the men of old time must surely have known the gods who were their ancestors, and we should believe them as custom requires,’ is also manifest in his account of divination.

The appetitive soul is seated in the belly, and there imprisoned like a wild beast, far away from the council chamber, as Plato graphically calls the head, in order that the animal passions may not interfere with the deliberations of reason. Though the soul is said by him to be prior to the body, yet we cannot help seeing that it is constructed on the model of the body—the threefold division into the rational, passionate, and appetitive corresponding to the head, heart and belly. The human soul differs from the soul of the world in this respect, that it is enveloped and finds its expression in matter, whereas the soul of the world is not only enveloped or diffused in matter, but is the element in which matter moves. The breath of man is within him, but the air or aether of heaven is the element which surrounds him and all things.

Pleasure and pain are attributed in the Timaeus to the suddenness of our sensations—the first being a sudden restoration, the second a sudden violation, of nature (Phileb.). The sensations become conscious to us when they are exceptional. Sight is not attended either by pleasure or pain, but hunger and the appeasing of hunger are pleasant and painful because they are extraordinary.

I shall not attempt to connect the physiological speculations of Plato either with ancient or modern medicine. What light I can throw upon them will be derived from the comparison of them with his general system.

There is no principle so apparent in the physics of the Timaeus, or in ancient physics generally, as that of continuity. The world is conceived of as a whole, and the elements are formed into and out of one another; the varieties of substances and processes are hardly known or noticed. And in a similar manner the human body is conceived of as a whole, and the different substances of which, to a superficial observer, it appears to be composed—the blood, flesh, sinews—like the elements out of which they are formed, are supposed to pass into one another in regular order, while the infinite complexity of the human frame remains unobserved. And diseases arise from the opposite process—when the natural proportions of the four elements are disturbed, and the secondary substances which are formed out of them, namely, blood, flesh, sinews, are generated in an inverse order.

Plato found heat and air within the human frame, and the blood circulating in every part. He assumes in language almost unintelligible to us that a network of fire and air envelopes the greater part of the body. This outer net contains two lesser nets, one corresponding to the stomach, the other to the lungs; and the entrance to the latter is forked or divided into two passages which lead to the nostrils and to the mouth. In the process of respiration the external net is said to find a way in and out of the pores of the skin: while the interior of it and the lesser nets move alternately into each other. The whole description is figurative, as Plato himself implies when he speaks of a ‘fountain of fire which we compare to the network of a creel.’ He really means by this what we should describe as a state of heat or temperature in the interior of the body. The ‘fountain of fire’ or heat is also in a figure the circulation of the blood. The passage is partly imagination, partly fact.

He has a singular theory of respiration for which he accounts solely by the movement of the air in and out of the body; he does not attribute any part of the process to the action of the body itself. The air has a double ingress and a double exit, through the mouth or nostrils, and through the skin. When exhaled through the mouth or nostrils, it leaves a vacuum which is filled up by other air finding a way in through the pores, this air being thrust out of its place by the exhalation from the mouth and nostrils. There is also a corresponding process of inhalation through the mouth or nostrils, and of exhalation through the pores. The inhalation through the pores appears to take place nearly at the same time as the exhalation through the mouth; and conversely. The internal fire is in either case the propelling cause outwards—the inhaled air, when heated by it, having a natural tendency to move out of the body to the place of fire; while the impossibility of a vacuum is the propelling cause inwards.

Thus we see that this singular theory is dependent on two principles largely employed by Plato in explaining the operations of nature, the impossibility of a vacuum and the attraction of like to like. To these there has to be added a third principle, which is the condition of the action of the other two,—the interpenetration of particles in proportion to their density or rarity. It is this which enables fire and air to permeate the flesh.

Plato’s account of digestion and the circulation of the blood is closely connected with his theory of respiration. Digestion is supposed to be effected by the action of the internal fire, which in the process of respiration moves into the stomach and minces the food. As the fire returns to its place, it takes with it the minced food or blood; and in this way the veins are replenished. Plato does not enquire how the blood is separated from the faeces.

Of the anatomy and functions of the body he knew very little,—e.g. of the uses of the nerves in conveying motion and sensation, which he supposed to be communicated by the bones and veins; he was also ignorant of the distinction between veins and arteries;—the latter term he applies to the vessels which conduct air from the mouth to the lungs;—he supposes the lung to be hollow and bloodless; the spinal marrow he conceives to be the seed of generation; he confuses the parts of the body with the states of the body—the network of fire and air is spoken of as a bodily organ; he has absolutely no idea of the phenomena of respiration, which he attributes to a law of equalization in nature, the air which is breathed out displacing other air which finds a way in; he is wholly unacquainted with the process of digestion. Except the general divisions into the spleen, the liver, the belly, and the lungs, and the obvious distinctions of flesh, bones, and the limbs of the body, we find nothing that reminds us of anatomical facts. But we find much which is derived from his theory of the universe, and transferred to man, as there is much also in his theory of the universe which is suggested by man. The microcosm of the human body is the lesser image of the macrocosm. The courses of the same and the other affect both; they are made of the same elements and therefore in the same proportions. Both are intelligent natures endued with the power of self-motion, and the same equipoise is maintained in both. The animal is a sort of ‘world’ to the particles of the blood which circulate in it. All the four elements entered into the original composition of the human frame; the bone was formed out of smooth earth; liquids of various kinds pass to and fro; the network of fire and air irrigates the veins. Infancy and childhood is the chaos or first turbid flux of sense prior to the establishment of order; the intervals of time which may be observed in some intermittent fevers correspond to the density of the elements. The spinal marrow, including the brain, is formed out of the finest sorts of triangles, and is the connecting link between body and mind. Health is only to be preserved by imitating the motions of the world in space, which is the mother and nurse of generation. The work of digestion is carried on by the superior sharpness of the triangles forming the substances of the human body to those which are introduced into it in the shape of food. The freshest and acutest forms of triangles are those that are found in children, but they become more obtuse with advancing years; and when they finally wear out and fall to pieces, old age and death supervene.

As in the Republic, Plato is still the enemy of the purgative treatment of physicians, which, except in extreme cases, no man of sense will ever adopt. For, as he adds, with an insight into the truth, ‘every disease is akin to the nature of the living being and is only irritated by stimulants.’ He is of opinion that nature should be left to herself, and is inclined to think that physicians are in vain (Laws—where he says that warm baths would be more beneficial to the limbs of the aged rustic than the prescriptions of a not over-wise doctor). If he seems to be extreme in his condemnation of medicine and to rely too much on diet and exercise, he might appeal to nearly all the best physicians of our own age in support of his opinions, who often speak to their patients of the worthlessness of drugs. For we ourselves are sceptical about medicine, and very unwilling to submit to the purgative treatment of physicians. May we not claim for Plato an anticipation of modern ideas as about some questions of astronomy and physics, so also about medicine? As in the Charmides he tells us that the body cannot be cured without the soul, so in the Timaeus he strongly asserts the sympathy of soul and body; any defect of either is the occasion of the greatest discord and disproportion in the other. Here too may be a presentiment that in the medicine of the future the interdependence of mind and body will be more fully recognized, and that the influence of the one over the other may be exerted in a manner which is not now thought possible.

In Plato’s explanation of sensation we are struck by the fact that he has not the same distinct conception of organs of sense which is familiar to ourselves. The senses are not instruments, but rather passages, through which external objects strike upon the mind. The eye is the aperture through which the stream of vision passes, the ear is the aperture through which the vibrations of sound pass. But that the complex structure of the eye or the ear is in any sense the cause of sight and hearing he seems hardly to be aware.

The process of sight is the most complicated (Rep.), and consists of three elements—the light which is supposed to reside within the eye, the light of the sun, and the light emitted from external objects. When the light of the eye meets the light of the sun, and both together meet the light issuing from an external object, this is the simple act of sight. When the particles of light which proceed from the object are exactly equal to the particles of the visual ray which meet them from within, then the body is transparent. If they are larger and contract the visual ray, a black colour is produced; if they are smaller and dilate it, a white. Other phenomena are produced by the variety and motion of light. A sudden flash of fire at once elicits light and moisture from the eye, and causes a bright colour. A more subdued light, on mingling with the moisture of the eye, produces a red colour. Out of these elements all other colours are derived. All of them are combinations of bright and red with white and black. Plato himself tells us that he does not know in what proportions they combine, and he is of opinion that such knowledge is granted to the gods only. To have seen the affinity of them to each other and their connection with light, is not a bad basis for a theory of colours. We must remember that they were not distinctly defined to his, as they are to our eyes; he saw them, not as they are divided in the prism, or artificially manufactured for the painter’s use, but as they exist in nature, blended and confused with one another.

We can hardly agree with him when he tells us that smells do not admit of kinds. He seems to think that no definite qualities can attach to bodies which are in a state of transition or evaporation; he also makes the subtle observation that smells must be denser than air, though thinner than water, because when there is an obstruction to the breathing, air can penetrate, but not smell.

The affections peculiar to the tongue are of various kinds, and, like many other affections, are caused by contraction and dilation. Some of them are produced by rough, others by abstergent, others by inflammatory substances,—these act upon the testing instruments of the tongue, and produce a more or less disagreeable sensation, while other particles congenial to the tongue soften and harmonize them. The instruments of taste reach from the tongue to the heart. Plato has a lively sense of the manner in which sensation and motion are communicated from one part of the body to the other, though he confuses the affections with the organs. Hearing is a blow which passes through the ear and ends in the region of the liver, being transmitted by means of the air, the brain, and the blood to the soul. The swifter sound is acute, the sound which moves slowly is grave. A great body of sound is loud, the opposite is low. Discord is produced by the swifter and slower motions of two sounds, and is converted into harmony when the swifter motions begin to pause and are overtaken by the slower.

The general phenomena of sensation are partly internal, but the more violent are caused by conflict with external objects. Proceeding by a method of superficial observation, Plato remarks that the more sensitive parts of the human frame are those which are least covered by flesh, as is the case with the head and the elbows. Man, if his head had been covered with a thicker pulp of flesh, might have been a longer-lived animal than he is, but could not have had as quick perceptions. On the other hand, the tongue is one of the most sensitive of organs; but then this is made, not to be a covering to the bones which contain the marrow or source of life, but with an express purpose, and in a separate mass.

We have now to consider how far in any of these speculations Plato approximated to the discoveries of modern science. The modern physical philosopher is apt to dwell exclusively on the absurdities of ancient ideas about science, on the haphazard fancies and a priori assumptions of ancient teachers, on their confusion of facts and ideas, on their inconsistency and blindness to the most obvious phenomena. He measures them not by what preceded them, but by what has followed them. He does not consider that ancient physical philosophy was not a free enquiry, but a growth, in which the mind was passive rather than active, and was incapable of resisting the impressions which flowed in upon it. He hardly allows to the notions of the ancients the merit of being the stepping-stones by which he has himself risen to a higher knowledge. He never reflects, how great a thing it was to have formed a conception, however imperfect, either of the human frame as a whole, or of the world as a whole. According to the view taken in these volumes the errors of ancient physicists were not separable from the intellectual conditions under which they lived. Their genius was their own; and they were not the rash and hasty generalizers which, since the days of Bacon, we have been apt to suppose them. The thoughts of men widened to receive experience; at first they seemed to know all things as in a dream: after a while they look at them closely and hold them in their hands. They begin to arrange them in classes and to connect causes with effects. General notions are necessary to the apprehension of particular facts, the metaphysical to the physical. Before men can observe the world, they must be able to conceive it.

To do justice to the subject, we should consider the physical philosophy of the ancients as a whole; we should remember, (1) that the nebular theory was the received belief of several of the early physicists; (2) that the development of animals out of fishes who came to land, and of man out of the animals, was held by Anaximander in the sixth century before Christ (Plut. Symp. Quaest; Plac. Phil.); (3) that even by Philolaus and the early Pythagoreans, the earth was held to be a body like the other stars revolving in space around the sun or a central fire; (4) that the beginnings of chemistry are discernible in the ‘similar particles’ of Anaxagoras. Also they knew or thought (5) that there was a sex in plants as well as in animals; (6) they were aware that musical notes depended on the relative length or tension of the strings from which they were emitted, and were measured by ratios of number; (7) that mathematical laws pervaded the world; and even qualitative differences were supposed to have their origin in number and figure; (8) the annihilation of matter was denied by several of them, and the seeming disappearance of it held to be a transformation only. For, although one of these discoveries might have been supposed to be a happy guess, taken together they seem to imply a great advance and almost maturity of natural knowledge.

We should also remember, when we attribute to the ancients hasty generalizations and delusions of language, that physical philosophy and metaphysical too have been guilty of similar fallacies in quite recent times. We by no means distinguish clearly between mind and body, between ideas and facts. Have not many discussions arisen about the Atomic theory in which a point has been confused with a material atom? Have not the natures of things been explained by imaginary entities, such as life or phlogiston, which exist in the mind only? Has not disease been regarded, like sin, sometimes as a negative and necessary, sometimes as a positive or malignant principle? The ‘idols’ of Bacon are nearly as common now as ever; they are inherent in the human mind, and when they have the most complete dominion over us, we are least able to perceive them. We recognize them in the ancients, but we fail to see them in ourselves.

Such reflections, although this is not the place in which to dwell upon them at length, lead us to take a favourable view of the speculations of the Timaeus. We should consider not how much Plato actually knew, but how far he has contributed to the general ideas of physics, or supplied the notions which, whether true or false, have stimulated the minds of later generations in the path of discovery. Some of them may seem old-fashioned, but may nevertheless have had a great influence in promoting system and assisting enquiry, while in others we hear the latest word of physical or metaphysical philosophy. There is also an intermediate class, in which Plato falls short of the truths of modern science, though he is not wholly unacquainted with them. (1) To the first class belongs the teleological theory of creation. Whether all things in the world can be explained as the result of natural laws, or whether we must not admit of tendencies and marks of design also, has been a question much disputed of late years. Even if all phenomena are the result of natural forces, we must admit that there are many things in heaven and earth which are as well expressed under the image of mind or design as under any other. At any rate, the language of Plato has been the language of natural theology down to our own time, nor can any description of the world wholly dispense with it. The notion of first and second or co-operative causes, which originally appears in the Timaeus, has likewise survived to our own day, and has been a great peace-maker between theology and science. Plato also approaches very near to our doctrine of the primary and secondary qualities of matter. (2) Another popular notion which is found in the Timaeus, is the feebleness of the human intellect—‘God knows the original qualities of things; man can only hope to attain to probability.’ We speak in almost the same words of human intelligence, but not in the same manner of the uncertainty of our knowledge of nature. The reason is that the latter is assured to us by experiment, and is not contrasted with the certainty of ideal or mathematical knowledge. But the ancient philosopher never experimented: in the Timaeus Plato seems to have thought that there would be impiety in making the attempt; he, for example, who tried experiments in colours would ‘forget the difference of the human and divine natures.’ Their indefiniteness is probably the reason why he singles them out, as especially incapable of being tested by experiment. (Compare the saying of Anaxagoras—Sext. Pyrrh.—that since snow is made of water and water is black, snow ought to be black.)

The greatest ‘divination’ of the ancients was the supremacy which they assigned to mathematics in all the realms of nature; for in all of them there is a foundation of mechanics. Even physiology partakes of figure and number; and Plato is not wrong in attributing them to the human frame, but in the omission to observe how little could be explained by them. Thus we may remark in passing that the most fanciful of ancient philosophies is also the most nearly verified in fact. The fortunate guess that the world is a sum of numbers and figures has been the most fruitful of anticipations. The ‘diatonic’ scale of the Pythagoreans and Plato suggested to Kepler that the secret of the distances of the planets from one another was to be found in mathematical proportions. The doctrine that the heavenly bodies all move in a circle is known by us to be erroneous; but without such an error how could the human mind have comprehended the heavens? Astronomy, even in modern times, has made far greater progress by the high a priori road than could have been attained by any other. Yet, strictly speaking—and the remark applies to ancient physics generally—this high a priori road was based upon a posteriori grounds. For there were no facts of which the ancients were so well assured by experience as facts of number. Having observed that they held good in a few instances, they applied them everywhere; and in the complexity, of which they were capable, found the explanation of the equally complex phenomena of the universe. They seemed to see them in the least things as well as in the greatest; in atoms, as well as in suns and stars; in the human body as well as in external nature. And now a favourite speculation of modern chemistry is the explanation of qualitative difference by quantitative, which is at present verified to a certain extent and may hereafter be of far more universal application. What is this but the atoms of Democritus and the triangles of Plato? The ancients should not be wholly deprived of the credit of their guesses because they were unable to prove them. May they not have had, like the animals, an instinct of something more than they knew?

Besides general notions we seem to find in the Timaeus some more precise approximations to the discoveries of modern physical science. First, the doctrine of equipoise. Plato affirms, almost in so many words, that nature abhors a vacuum. Whenever a particle is displaced, the rest push and thrust one another until equality is restored. We must remember that these ideas were not derived from any definite experiment, but were the original reflections of man, fresh from the first observation of nature. The latest word of modern philosophy is continuity and development, but to Plato this is the beginning and foundation of science; there is nothing that he is so strongly persuaded of as that the world is one, and that all the various existences which are contained in it are only the transformations of the same soul of the world acting on the same matter. He would have readily admitted that out of the protoplasm all things were formed by the gradual process of creation; but he would have insisted that mind and intelligence—not meaning by this, however, a conscious mind or person—were prior to them, and could alone have created them. Into the workings of this eternal mind or intelligence he does not enter further; nor would there have been any use in attempting to investigate the things which no eye has seen nor any human language can express.

Lastly, there remain two points in which he seems to touch great discoveries of modern times—the law of gravitation, and the circulation of the blood.

(1) The law of gravitation, according to Plato, is a law, not only of the attraction of lesser bodies to larger ones, but of similar bodies to similar, having a magnetic power as well as a principle of gravitation. He observed that earth, water, and air had settled down to their places, and he imagined fire or the exterior aether to have a place beyond air. When air seemed to go upwards and fire to pierce through air—when water and earth fell downward, they were seeking their native elements. He did not remark that his own explanation did not suit all phenomena; and the simpler explanation, which assigns to bodies degrees of heaviness and lightness proportioned to the mass and distance of the bodies which attract them, never occurred to him. Yet the affinities of similar substances have some effect upon the composition of the world, and of this Plato may be thought to have had an anticipation. He may be described as confusing the attraction of gravitation with the attraction of cohesion. The influence of such affinities and the chemical action of one body upon another in long periods of time have become a recognized principle of geology.

(2) Plato is perfectly aware—and he could hardly be ignorant—that blood is a fluid in constant motion. He also knew that blood is partly a solid substance consisting of several elements, which, as he might have observed in the use of ‘cupping-glasses’, decompose and die, when no longer in motion. But the specific discovery that the blood flows out on one side of the heart through the arteries and returns through the veins on the other, which is commonly called the circulation of the blood, was absolutely unknown to him.

A further study of the Timaeus suggests some after-thoughts which may be conveniently brought together in this place. The topics which I propose briefly to reconsider are (a) the relation of the Timaeus to the other dialogues of Plato and to the previous philosophy; (b) the nature of God and of creation (c) the morality of the Timaeus:—

(a) The Timaeus is more imaginative and less scientific than any other of the Platonic dialogues. It is conjectural astronomy, conjectural natural philosophy, conjectural medicine. The writer himself is constantly repeating that he is speaking what is probable only. The dialogue is put into the mouth of Timaeus, a Pythagorean philosopher, and therefore here, as in the Parmenides, we are in doubt how far Plato is expressing his own sentiments. Hence the connexion with the other dialogues is comparatively slight. We may fill up the lacunae of the Timaeus by the help of the Republic or Phaedrus: we may identify the same and other with the (Greek) of the Philebus. We may find in the Laws or in the Statesman parallels with the account of creation and of the first origin of man. It would be possible to frame a scheme in which all these various elements might have a place. But such a mode of proceeding would be unsatisfactory, because we have no reason to suppose that Plato intended his scattered thoughts to be collected in a system. There is a common spirit in his writings, and there are certain general principles, such as the opposition of the sensible and intellectual, and the priority of mind, which run through all of them; but he has no definite forms of words in which he consistently expresses himself. While the determinations of human thought are in process of creation he is necessarily tentative and uncertain. And there is least of definiteness, whenever either in describing the beginning or the end of the world, he has recourse to myths. These are not the fixed modes in which spiritual truths are revealed to him, but the efforts of imagination, by which at different times and in various manners he seeks to embody his conceptions. The clouds of mythology are still resting upon him, and he has not yet pierced ‘to the heaven of the fixed stars’ which is beyond them. It is safer then to admit the inconsistencies of the Timaeus, or to endeavour to fill up what is wanting from our own imagination, inspired by a study of the dialogue, than to refer to other Platonic writings,—and still less should we refer to the successors of Plato,—for the elucidation of it.