On Plato’s ‘Timaeus’​ — The World Soul

The story goes that Georg Wilhelm Friedrich Hegel, (1770–1831), demonstrated the impossibility of there being an eighth planet at the very moment that an eighth planet was being discovered. (Neptune, actually discovered in 1846, independently by John Couch Adams, (1819–1892), in England and Urbain-Jean-Joseph Le Verrier, (1811–1877), in France, based upon mathematical calculations of its predicted position due to observed perturbations in the orbit of the planet Uranus, though it was Johann Gottfried Galle, (1812–1910), in Germany, who was the first to see it based on their calculations). It is said that in his dissertation, ‘De orbitis planetarum’, Hegel demonstrated by the clearest logic that the number of planets could not exceed seven. Typically of good stories it is in fact not true. There is a short section in the dissertation where Hegel is not concerned with the total number of the planets, but only with whether there is a planet, yet to be discovered, between Mars and Jupiter, and he offers no proof that the gap between Mars and Jupiter must be empty, but only a criticism of the argument that was leading contemporary astronomers to think that it was likely to be occupied. Hegel cites another series that roughly matched the orbits of the then known planets, but unlike Bode’s Law, (formulaic prediction of spacing between planets in any given solar system, after Johann Elert Bode, (1747–1826), who was also responsible for giving Uranus its name), did not have any term that corresponded to an apparent gap in the solar system, and albeit this other series did not turn out to be the correct one Hegel makes no claim to the effect that it is, rather ‘if this series should be the truer order of nature …’ (‘Quae series si verior naturae ordo sit …’):

‘It remains to add some observations on the relations of planetary displacements, which appear to be a matter of experience alone. In truth, they cannot be measures or numbers of nature alien to reason. For our pursuit of the laws of nature, and our knowledge of them, is founded on nothing other than the belief that nature is shaped by reason, and that we are convinced of the identity of all natural laws. Whenever those who seek laws through experience and induction happen upon something that looks like a law, they rejoice at their find and the identity of nature and reason therein, and when other appearances are difficult to accommodate with that they feel some doubt in the earlier experiments and try in every way to establish harmony between the findings. Our topic, the planets’ orbits, offers a case in point: While the displacements of the planets suggest an arithmetic progression in which、unfortunately, no planet in nature corresponds to the fifth member in the series, it is supposed that there really does exist between Mars and Jupiter, unbeknown to us, a planet moving through outer space. It is now being eagerly looked for’.

‘Since this progression is arithmetic and does not follow a number series that generates them itself, i.e. not by powers, it is of no interest to philosophy. The extensive work of the Pythagoreans on the relations of philosophical numbers is well-known; so I will now, if I may, consider the traditional number series presented in the two Timaeus texts. For although Timaeus does not refer to the planets, he thinks the demiurge formed the universe according to this series. The number series is: 1, 2, 3, 4, 9, 16, 27, if I may take 16 instead of 8, which we find in the Timaeus. If this series really does give the true order of nature as an arithmetic series, then there is a great space between the fourth and fifth places where no planet appears to be missing’.

- Hegel, ‘On the Orbit of the Planets’.

There is another issue of great interest here however. Timaeus of Locri, (5th century BC, if he ever existed), from whom Plato’s, (428/427 or 424/423–348/347 BC), dialogue the ‘Timaeus’, referred to by Hegel, gets its name, is presented by Plato as a philosopher of the Pythagorean school, and Pythagoras, (c. 570 — c. 495 BC), laid great stress upon the mystic properties of number and had a particularly high regard for the number seven. Philolaus of Croton, (ca. 470 — ca. 385 BC), a contemporary of Socrates, (c. 470–399 BC), and the first to set forth in writing an extended exposition of Pythagorean doctrine, said concerning God, the author and governor of all things, that ‘he is without variation, ever like himself and like no other, even as the number seven’. Throughout history, there have been two principle ways humanity has endeavoured to acquire knowledge about the world, top-down, beginning with certain principles and insisting upon logical self-consistency, and bottom-up, obtaining empirical information about the world and synthesizing it together into a larger, self-consistent framework. The top-down approach is frequently credited to Plato and is reasoning a priori, everything being derivable as long as one has an accurate set of postulates, while the bottom-up approach is attributed to Aristotle, (384–322 BC), and is reasoning a posteriori, starting from known facts rather than postulates. Clearly, logical reasoning on its own is not enough for science but if it used on its own the results obtained may be very far removed from what the world is actually like. Has not nature shown herself to defy logic, her arcane rules unable to be intuited without the performing of experiments? Indeed, why assume that nature is shaped by reason?

Another means of explaining natural or social phenomena is through myth, which, albeit it is made up fables, can reveal much concerning human nature. In Plato’s dialogue Timaeus, who it seems had a serious interest in philosophy alongside serious political commitments, delivers a long monologue which has to be understood in the context of this dialogue having followed on from the ‘Republic’ that gave an account of the best city. (See my article On Plato’s ‘Republic’ Philosopher Kings). Before Critias, (c. 460–403 BC), delivers an account of Atlantis, victory over which redounded to the glory of Athens, the latter hence an ideal city in action (albeit we assume Atlantis to be legendary), Timaeus gives an account of the generation of the cosmos itself, this ordered whole within which we live, and an account of the generation of human nature, with the objective of locating humanity as a citizen of the world before Critias praises the citizens of ancient Athens. Timaeus informs us of, among other things, about the musical construction of the soul, the geometric construction of body, about how we came to have a sphere-shaped head, (we evolved bodies because our heads rolled around and got stuck in cracks in the ground), a neck and torso, eyes and ears, liver and spleen, bone and flesh, an upright posture, about the manifold diseases that afflict body and soul, about where sex came from, (I believe the current scientific theory is that sex was invented around 385 million years ago in the lakes of Scotland by an armoured species of fish or placoderm called Microbrachius dicki (thankfully the brachius is in the name) but according to Timaeus: ‘Of the men who came into the world, those who were cowards or led unrighteous lives may with reason be supposed to have changed into the nature of women in the second generation. And this was the reason why at that time the gods created in us the desire of sexual intercourse’), and about how birds evolved from feather-brained astronomers.

‘Around the turn of the Twentieth Century’, said Christian apologist John Lennox, (1943 — ), ‘as far as I understand it, the Aristotelian view still prevailed, and that is that the universe was eternal, and people believed essentially that it was static. They didn’t think the stars moved very much, they weren’t aware of other galaxies other than the Milky Way. So essentially it was eternal static universe, and that of course was about to be changed. the Big bang does not disprove the need for God, or Creator, that’s a confusion of thought. The Big Bang is simply telling us: we believe there was a beginning. That is what Genesis has been saying for thousands of years. The point is that Genesis is not only telling us that there was a beginning, it is also telling us, what science cannot tell us, the ultimate cause of that beginning, which is God. So a Christian has nothing to fear from people using the words Big Bang … let us grasp this central thing which I think is marvellous. As I have often said to physicists, look, it took you till the 1960s to come to believe that the universe had a beginning. I actually believed it myself before you did because I have reasons for thinking that the Biblical revelation is true. And, what is more, if you had taken seriously the world view of the Bible and weren’t so committed to Aristotle you might have looked for evidence for a beginning to space/time much earlier than you did’.

‘In the beginning God created the heaven and the earth’.

‘And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters’.

‘And God said, Let there be light: and there was light’.

- ‘Genesis’, 1.1–3

Lennox’s assertions are so bizarre I hardly know know what to say in response, but I will just make two points. One wonders how a professor of mathematics at Oxford University seemingly has zero understanding about how myths work. ‘Genesis’ has been telling us? This mythical account of creation has been telling us what precisely? The eternity of the world, whether the world has a beginning in time or has existed from eternity, was a question that certainly exercised the minds of both ancient philosophers and the medieval theologians and medieval philosophers and became a focus of a dispute in the 13th century when some of the works of Aristotle, who believed in the eternity of the world, were rediscovered in the Latin West, a view conflicting with the view of the Catholic Church that the world had a beginning in time. Hence the Aristotelian view was prohibited in the ‘Condemnations’ of 1210–1277. And it was Aristotle who rejected the cosmology of the ‘Timaeus’ on the ground that it, nonsensically in his view, required not just a beginning of the universe in time, but a beginning of time itself. Defenders of the ‘Timaeus’, perhaps wishing to nullify Aristotle’s critique while conceding its point, have claimed that the creation story is not to be read literally, but metaphorically. Platonic philosophy is certainly more in harmony with Christianity than Aristotelianism. Christian apologist William Lane Craig, (1949 — ), however, in a response to a question about abstract objects (the ontological abstract/concrete distinction is a fundamental importance in philosophy albeit a standard account of how it should be drawn is notably lacking. Numbers are taken to be abstract objects. Are they though?) argues against a Platonist account of mathematical objects in virtue of the fact that Platonism entails the existence of necessary objects independently of God, and since these are inconsistent with John 1:3 (‘All things were made by him; and without him was not any thing made that was made’) and the creedal statements that God created all things, visible and invisible, Craig concludes that Platonism is inconsistent with Christianity. Whatever else Christian apologetics may be it is not philosophy but nonsensical reasoning from unchallenged postulates (whatever the Bible says) intended to give apologetics a veneer of intellectual credibility and profundity and achieving just the opposite. For Plato whatever is apprehended by intelligence and reason always exists and has no becoming, (see below). Abstract objects neither exist (though they have reality) nor were ever made, a simple enough point that Craig either cannot grasp or he is being disingenuous.

So quite what Lennox means by a commitment to Aristotle I do not know, and furthermore, not only ‘Genesis’ but Timaeus has also, through myth, been ‘telling us’ that there was a beginning and also telling us ‘what science cannot tell us’, the ultimate cause of that beginning, well, a demiurge as it happens, according to Timaeus. And how literally or seriously are we to take the myths of the Bible or of Timaeus?

‘For God… Thou didst divide the sea by thy strength: thou brakest the heads of the dragons in the waters. Thou brakest the heads of leviathan in pieces, and gavest him to be meat to the people inhabiting the wilderness. Thou didst cleave the fountain and the flood: thou driedst up mighty rivers. The day is thine, the night also is thine: thou hast prepared the light and the sun. Thou hast set all the borders of the earth: thou hast made summer and winter’.

- ‘Isaiah’, 74.12–17

‘Untitled’ (‘Sun State’). 1974. Joseph Beuys. (Illustrating an ideal state in which the natural and social orders are balanced, the ‘Sun State’ blazes at the base of the composition, creating energy that radiates in looping white lines that alchemy turns into a system of culture with three branches: religion, art and science. At the centre of the image, an androgynous human figure represents the Earth, accompanied by a delicate stag that symbolizes humans’ animalistic and spiritualist nature. Further loops of chalk connect written references to myth, the economy, socialism and astrology, balancing life force with the forces of death.

Now here is a crucial point concerning the ‘Timaeus’ and one that Lennox and Craig would do well to take note of. The purpose of its creation myth is to give an account of the nature of man and of the universe to serve as the background for another mythical account, the purpose of which will be to show that the ideal state is superior and ultimately more powerful than an adversary that has greater material resources and skill but is morally inferior, hence the purpose of the creation myth is to give a systematic account of the nature of human beings. In the dialogue investigation and inquiry are foregone in favour of long speeches that take the form of myths and Socrates is for the most part silent. That is the crucial point. His silence is like the receptacle Timaeus talks about (see below) providing a receptive space for the stories and images we are presented with, and Socrates is silent because this is not philosophy. We are drawn beyond a mere pageant of mortal opinion to a godlike vision of what eternally is, our attention is directed to a form of thumos or spiritedness, a will to order glorified in the ‘likely story’ (as he calls it) of Timaeus in which craftsmanship over contemplation is given due honour.

Philosophy makes an appearance in a manner of speaking, understood as the command over distinct disciplines, the systematic presentation of theories, the building of models, the resolving of problems, philosophy rendered technical and effective, philosophy, if one may so designate it as such, in which all of the divine madness has been filtered out, endeavoring to transcend the Socratic self-knowledge concerning knowledge itself or lack of it to veer beyond the knowledge of ignorance, the claim of not teaching and treating of virtue as perpetually in question, beyond the tension between philosophy and civic life, endeavouring to capture our interest at a profound level in an experiment displacing the love of wisdom with that of the will to order.

The principal ideas advanced in the ‘Timaeus’ are as follows.

1. Whatever is apprehended by intelligence and reason always exists and has no becoming.

2. The world (the universe) must have been created, for it is a sensible, and not an intelligible, thing, the world is a living creature endowed with soul and intelligence.

3. The soul of the world is prior in existence and excellence to the body of the world, the soul’s function is to know the rational and to rule the body.

4. The universal nature which receives all things without changing its own nature is ‘that which is’, is eternal, formless space.

5. The three natures which make up reality are the Ideas (the eternal forms of things), the sensible copies of Ideas (existing objects), and space.

In most of the Socratic dialogues Socrates is either the central figure or one of the central figures, and for all of his assumed deference Socrates knew himself to be the superior of his contemporaries in the art of philosophical elucidation and debate, and Plato so honoured him by making him the consistently victorious examiner of the pretenders to wisdom. But the ‘Timaeus’ is one of the dialogues in which Socrates assumes a minor role, his personality is off to the slide, glowing as usual, but only by grace of earlier dialogues in which he figures as an intellectual hero. And the ‘Timaeus’ is not so much a dialogue,although there is some conversation, as it is a solo display of Pythagorean ideas about the origin and character of the universe by Timaeus, an enthusiastic Pythagorean astronomer. The ‘Timaeus’ is interesting as an exhibition of the fantastic lengths to which the imagination of human beings can go in the attempt to understand this mysterious universe. It is a characteristically curious mixture of immature science and mature invention, and it may appear as having little relevance to the scientific and philosophical problems of contemporary human beings. Nevertheless, as part of the portrait of Greek thought, as a facet in the complex entity that was Plato’s realm of Ideas, and as the one dialogue which, thanks to a translation by Cicero, was influential in the Middle Ages, the ‘Timaeus’ continues to hold a place in the significant literature of philosophy.

As the dialogue begins Socrates reminds Timaeus of a conversation on the previous day concerning the various kinds of citizens required in an ideal state. The main points of the Republic are reviewed, the citizens will be husbandmen, or artisans, or defenders of the state, the defenders will be warriors or political leaders, guardians of the state, the guardians are to be passionately dedicated to their tasks and philosophical by temperament and training. Gymnastics and music will play important parts in their education, there will be no private wives or children, but all will work together in a communal way. An effort will be made, by contrived lot, to mate the good with the good, the bad with the bad, and only the good children, morally and intellectually superior, are to be educated. Socrates, having reviewed the principle points, then invites Timaeus, Critias, and Hermocrates, (c. 5th cent. — 407 BC), as persons with practical experience in the art of politics, to tell something of their adventures, so that the portrait of the ideal state can begin to take on a living character.

Critias begins by telling a story about ancient Athens, a tale told to him by his great-grandfather, Dropides, who heard it from Solon, (c. 630 — c. 560 BC), the lawgiver. Socrates told of hearing from a priest of Sais that Athens was a thousand years older than Sais, which had been founded eight thousand years before the time of Solon. Both Sais and Athens were founded by Athene, the goddess, so that, both in the division of classes and in laws, the two were alike. Athens became the leader of the Hellenes against the threatening forces from the great island of Atlantis, a powerful empire larger than Libya and Asia combined. Athens defeated Atlantis, but soon afterward both empires were utterly destroyed and hidden by earthquakes and floods. Critias suggests that Socrates regard the citizens of the imaginary city (as outlined in the Republic) as being, not imaginary, but the citizens of the actual city of ancient Athens. The justification of this would be that the ancient city and the imagined one agree in their general features. Socrates is charmed by the idea, and it is agreed by Timaeus will give an account commencing with the generation of the world and ending with the creation of human beings. Critias is then to continue the account in order to complete the process of making actual the state which has so far figured in their conversation as an imaginary one. The remainder of the dialogue is devoted to Timaeus’ account. The dialogue ‘Critias’ continues the conversation by giving Critias his turn in the historical philosophical account of man’s origins and progress.

After invoking the gods, Timaeus asks the intriguing and complex question: ‘What is that which always is and has no becoming, and what is that which is always becoming and never is?’ The answer is thoroughly Platonic (although it is also consistently Pythagorean): ‘That which is apprehended by intelligence and reason is always in the same state; but that which is conceived by opinion with the help of sensation and without reason, is always in a process of becoming and perishing and never really is’. This answer, that idea (whatever is apprehended by intelligence) is constant, while what is sensed is inconstant and consequently unreal, is Platonic in its giving priority to idea and in its identification of reality with whatever is constant and prior. The next important question to be settled is whether the world did or did not have a beginning. The answer by now is clear enough, if whatever can be sensed is not eternal, but comes into being or is destroyed, and if the world is sensible, then it must have come into being. But whatever comes into being must have a cause. Furthermore, since the world is fair and the maker of it must have been the best of causes, the pattern to which the artificer referred in making the copy which is the world must have been the pattern of the unchangeable, the Ideas (although the word does not feature here).

Timaeus continues by stating that the world must have been patterned after a perfect, intelligent animal (an Idea), for the Deity could not have been satisfied with the imperfect, the unintelligent, or the inanimate. The world, then, became a living creature ‘endowed with soul and intelligence by the providence of God’. In order to make the word visible, God had to use fire, in order to make it tangible, he had to use earth. Then, in order to supply two means by which a union of elements could be achieved and a world of solidity created, God introduced the elements of water and air. Since the world had to have shape which would comprehend all others, God made the world (the living animal), in the form of a globe. The world is one, for it is a copy of the eternal form, which is one. It has no hands or feet, but revolves in a circle.

‘Planet Set’, Tête Etoilée, Giuditta Pasta (Dédicace), 1950, Joseph Cornell. (At the top the white balls balance on rods and roll along prescribed pathways, resembling planets in their orbits. The glasses at the bottom of the box might correspond to the six planets visible to naked eye observers from Earth, or the blue marble may be a reference to Earth itself).

The soul of the world was made by God to be prior in existence and excellence to the body. The soul’s function is to rule the body. To compose the soul God made an essence in between the indivisible and the divisible. He then mixed this intermediate essence with the indivisible (the same) and the divisible (the other), and then divided the compound into parts, each of which contained each of the three essences. The division was very complicated, but orderly. The formula is provided but rather too complicated to go into here. The material was then made into strips, and an outer and an inner circle were formed which joined to form X’s. The one circle became the circle of the same and was, consequently, undivided, the other, the circle of the other, was divided into seven circles having different orbits. (Thus the seven planets are accounted for, see the Hegel passage above).

The soul and the corporeal universe were joined together. Since the soul partakes of the essences of the same, the other, and the intermediate, it alone knows the characters of the sensible world and attains to perfect knowledge of the rational. God wanted the world to be everlasting, but eternity is not possible for a corporeal being. Hence, he created time as the image of eternity. Stars were placed in the seven orbits to make time possible. God then made a great fire, the sun, to light up the heavens so that animals (human beings) might learn arithmetic by observing the stars in their courses. The created animal was then made to have four species corresponding to the four kinds of idea involved in the original, heavenly bodies (creatures of fire), birds (creatures of air), creatures of the water, and creatures of the earth.

Knowledge of the gods comes by tradition from those who were the children of the gods. From Earth and Heaven were born Oceanus and Tethys. Phorcys, Cronos, and Rhea were the children of the latter pair, and from Cronos and Rhea were generated Zeus and Hera. God then used a dilution of the essence of the universe soul to prepare the souls of living things. Souls that lived properly were destined to return to their native stars, but others would be forced to reside in women or brute animals. Human beings had their bodies fashioned by those gods who were the children of the father of the gods, and the bodies were made of the four elements welded together with tiny invisible pegs. Motions within the body or upon it from external motions were carried to the soul, and the motions came to be called sensations. Only when the soul is able to free itself from the influence of bodily motions can it begin to revolve as it should, acquiring knowledge.

‘A Universe’, 1934, Alexander Calder. (A motor in the base causes the two small red and white globes to glide at different speeds along the undulating wires in a pattern that takes forty minutes to complete. The abstract spheres, circles, lines and ellipses conjure an impression of planetary motion through the Solar System. A black iron pipe provides a central axis that eventually curves as a helix, around which thinner lines arc to recall the rings of Saturn).

The courses of the soul are contained in the head, which is a spherical body emulating the spherical body emulating the spherical body of the universe. All the other appendages of the human being are instrumental to the soul’s functioning within the head. Light is a gentle fire which merges in the eye with the fire within the body, finally affecting the soul in an act of perception. The causes of sight must be distinguished from the purpose of sight. Sight exists to make knowledge possible, by observing heavenly bodies human beings acquire knowledge of time then of numbers and of philosophy. Human beings learn by analogy, identifying the courses of heavenly bodies with the courses of individual souls.

Having given an account of the genesis and development of the soul and of the mind in terms of the soul’s activity, Timaeus considers the consequences of the presence of the four elements (earth, water, air, fire) in the universe. In addition to the changeless, eternal pattern of things and the copies of the pattern there is the ‘receptacle’ and ‘nurse’ of all generation. Since the elements can pass into each other, water, for example, changing into a vapour, or air, no element is primary, in fact one should not refer to fire, or water, or any element as ‘that’ which is, but one should say of that which is that it is of ‘such a nature, for example, fire. The universal nature which receives all things without changing its own nature is alone truly designated as ‘that’ which is, it is formless, it is eternal space. Thus, there are three kinds of natures, the uncreated, indestructible kind of being (the eternal Ideas), the sensible copies of the eternal (the objects of opinion and sense); and space, the ‘home of all created things’. These are called, respectively, being, generation, and space.

Originally the four elements were tossed about in space, and they were neither fair nor good, but God, by the use of form and number, brought order and goodness. The elements were made up of triangles, for they are solids, and all solids are made up of planes which are, in turn, composed of triangles. Triangles are either isosceles or scalene (with unequal sides), of these, the most beautiful is that which is such that its double is an equilateral triangle. To achieve the most beauty, the isosceles, which has but a single form, and that one of the scalene forms which is such that, doubled, an equilateral triangle is formed, must have been used by God in the creation of the elements.

Timaeus retracts his earlier statement that the elements can all pass into one another. Earth can never become anything but earth. The other three, however, can pass into one another. Since earth is the most immovable of the four elements, it must be composed of cubical forms. Water is harder to move than either fire or air; hence, it must be composed of icosahedron forms (‘made up of 120 triangular elements, forming twelve solid angles, each of them included in five plane equilateral triangles, having altogether twenty bases, each of which is an equilateral triangle’). Fire is made up of the smallest and most acute bodies, pyramids, while air is composed of octahedron solids. It can now be understood why earth cannot be come something other than earth, its solids cannot assume the forms necessary to the other elements.

After a discussion of the kinds of fire (flaming fire, light, and glow), the kinds of water (liquid and fusile, the latter divisible into gold, adamant, and copper, and the former into such various liquids as wine, oil, honey, and the like), and the kinds of earth (rock, stones, chemicals), Timaeus considers the effects of the elements on bodies and souls. Fire is sharp and cutting in its heat because its made up of sharp pointed solids (pyramids: tetrahedra). Other sensations are accounted for by reference to contraction, compression, expansion, and so forth, caused by the impingement of various bodies on the sensing body. Pain is the result of a sudden change which disturbs the particles of the body, pleasure is the effect of the body’s return to its natural condition.

The sensations resulting from the stimulation of the sense organs are explained as affectations caused by contractions and dilations, or by moistening or drying up , or by smothering or roughening of parts caused by the entrance of the particles of exterior objects. Sounds are blows which are transmitted to the soul, and hearing is a vibration which begins in the head and ends in the liver. Colours are flames coming from things which join with the streams of light within the body. (With great care Timaeus explains how various colours are formed by the combination of fires). Returning to the account of humanity’s origin, Timaeus argues that umanity’s immortal soul comes from God, but humanity has another, mortal soul given to him and her by the gods who fashioned his and her body. Humanity’s mortal soul is that in him and her which is subject to various destructive passions, among which are the love of pleasure, and rashness and fear. The immortal soul is in the head, but the mortal soul is in the breast and thorax and is so divided that the part which has courage and passion is nearer the head, so that it might be better subject to reason.

Robert Rauschenburg, ‘Arena II’ (‘Stoned Moon’), 1969.(after witnessing the 1969 launch of Apollo 11, Rauschenberg produced his ‘Stoned Moon’ series, a group of lithographs based on NASA archival materials).

The heart was designed by the gods to be a guard in the service of reason, sending the fire of passion to all parts of the body, and the lungs were designed to enclose the heart, thus cushioning its exertions and cooling it. The liver, solid and smooth like a mirror, was intended to distort the images of things of unworthy nature, giving them the distressing colour of bile, while it also suffuses the images of worthy things with its natural sweetness. The spleen was made to keep the liver clean in order that it may function properly as the seat of divination. All parts of the body, the bowels,the bones, the marrow of the bones (which unites the soul with the body), the joints and flesh, were fashioned in such a manner as to encourage human beings to be a creature of reason, not appetite. Fire travels through the body, giving the red colour to blood and performing such necessary tasks as the digestion of food by cutting the food with the pyramidal solids which are the material of fire. Eventually, however, as the body grows older, the triangles are blunted, and digestion becomes more difficult. Disease and death are the results of the loosening or dissolving of the bonds by which the marrow holds the body and soul together.When death results the soul ‘obtaining a natural release, flies away with joy’.

The diseases of the mind are of two kinds, madness and ignorance. If anyone is bad, he or she is so involuntarily as the result of an indisposition of the body, and indisposition is simply the lack of that fair and good proportion which means health and sanity. To achieve a proper harmony of body and soul, exercise is necessary, gymnastics for the body, music and body for the soul.The human being needs the food and motion which will encourage the growth and harmony of his and her body and soul, and the motions most worth studying and emulating are the motions of the universe as revealed in the revolutions of the heavenly bodies. In human beings intellect is supposed to be superior to desire, and thus he and she must give particular attention to the exercise of that divine part of his soul.

Cowardly men change into women in the second generation, simple, light-minded men give rise to the race of birds, and those without philosophy, who allow the breast to rule the head, become beasts. Those who become foolish are made to crawl on the ground, devoid of feet, while the senseless and ignorant become animals of the sea. The generation of animals is the result of desire resulting from the respiration of the seed of life rising in the marrow. When the desire of man and woman is satisfied, unseen animals pass from the man to the woman, and they mature in her.

Timaeus concludes his account by summarizing in the following manner, ‘The world has received animals, mortal and immortal, and is fulfilled with them, and has become a visible animal containing the visible — the sensible God who is the image of the intellectual, the greatest, best, fairest, most perfect — the one only begotten heaven’. Thus, by giving the centre of the stage to a Pythagorean, Plato sketched out a conception of the origin of the universe. Perhaps he found the analysis of things in terms of triangles a reasonable, even probable, anatomy of nature, perhaps he was intrigued,but not convinced. In any case, Plato gave full allegiance to the theory of forms, or eternal essences, and he never wavered in his endorsement of the rational mode of life. Despite the bizarre character of the philosophy contained in the ‘Timaeus’, the Greek love of wisdom makes itself felt and gives to the whole an enduring fascination.

‘Constellations’, 1924, Pablo Picasso. (Delicate, intricate shapes, delineated like variations on a musical score, small black circles of ink connected with thin pen lines, glimmers of figurative moments amid the curving forms and irregular patterns of the four groupings, at top right an otherworldly square-headed being, with straightened arms and legs, at bottom right, the curvature of a planet interrupted by intersecting geometric shapes such as triangles and rectangles).

Plato’s ‘Timaeus’ includes a complex of contemporary arithmetic, geometry and Pythagorean musical theory making up the framework of Timaeus’ likely story concerning the craftsman or demiurge that had brought order to the cosmos out of its initial state of disorder and who desired everything to be good and nothing bad, who brought order to an out-of-tune, plemmelos, disorderly state, shaping the cosmos into a single living animal of which all other living things formed parts, both individually and as kinds. As to how the parts are combined, Timaeus explains:

‘But two things cannot be rightly put together without a third; there must be some bond of union between them. And the fairest bond is that which makes the most complete fusion of itself and the things which it combines; and proportion is best adapted to effect such a union. For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean-then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one’.

In accordance with Franz von Baader’s, (1765–1841), connecting of the three-part trinity structure to the Pythagorean tetraktys, (a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number, a mystical symbol, very important to the clandestine worship of Pythagoreanism, there are four seasons and the number was also associated with planetary motions and music), Hegel focuses upon how this seemingly trinary structure becomes complicated by the notion that not one but two middle terms are needed to unify its extremes. The Pythagoreans had an arithmetic worldview, the principle of all number being the monas which, besides the unit used in counting was also meant to play the role of a spatial point, conceived as a monadic unit in position. In this manner a line could then be conceived as composed of such units, two-dimensional figures such as squares and rectangles could be conceived as compounded of arrays of two-dimensional lines, and three dimensional solid figures as compounded of those planar ones. Which is to say, square numbers, numbers multiplied by themselves, were for the Pythagoreans literally square, determinations of areas rather than lengths, and cubic numbers were similarly cubic. In Plato’s day this reduction of geometric continuous magnitudes to arithmetic ones was being challenged by a new geometrical approach in which such continua were understood as in some sense primary, a view reflected in Aristotle’s thought as well as in his logic.

Plato continued to be more attuned to Pythagorean mathematics within which the four rows of the tetraktys were intended to represent the four spatial dimensions of point, line, area and volume, the series of exponential powers associated with them, as well as the four fundamental elements, fire, air, water and earth. Like the kinds of the four substances with which they were associated, numbers raised to different exponential powers were understood as different kinds of numbers, with the notion of different and incommensurable kinds of magnitude being a deeply held belief within Greek mathematics after the discovery of incommensurable numbers sometime in the fifth century BC. This was the type of incommensurability holding between curves and straight lines that Hegel alluded in his critique of Isaac Newton’s, (1642–1727), reduction of curves to straight lines and ultimately points. Taking heed that anything with bodily form must be both visible and tangible, Plato has the demiurge compose the body of the cosmic animal out of the elements of visible fire and tangible earth, elements existing at the extremes of the tetraktic structure, and so having two intermediaries. Along with this, Timaeus points out that were the cosmos planar rather than three-dimensional, there would be needed only a single middle term, but as it actually is three-dimensional, there is a need for two middle terms standing between the monadic elements themselves and the solids into which they were compounded. The demiurge had thus ‘set water and air between fire and earth, and made them as proportionate to one another as was possible, so that what fire is to air, air is to water, and what air is to water, water is to earth. He then bound them together and thus he constructed the visible and tangible universe … making it a symphony of proportion’.

In relation to Plato’s rational syllogism with its Pythagorean structure, Hegel portrays Aristotle’s formal syllogism as a type of corrupted form with only a single middle term. Aristotle seems to have been heavily influenced by contemporary geometers who were reacting against the Pythagoreans reduction of continuous to discrete magnitudes. As with continuous magnitudes, the relations among its three terms, A, B and C, are understood comparatively according to the idea of the containment of the smaller in the larger, the transitivity of which means if C is contained in B and B in A, then C is contained in A. This is how we how we are to understand how the combination of two premises, A-B and B-C, can result in the conclusion, A-C. All of Aristotle’s terms must be general, as each must be able to play the role of subject (container) or predicate (contained) in a judgment and singular terms such as proper names cannot be predicates. There are, then, no remnants of the Pythagorean monas (Hegel’s singularities), in Aristotle’s logic. Thus, there is nothing in Aristotle’s logic to properly capture the absolute singularities of external nature as understood by Hegel.

Hegel’s ‘Logic’ is intended as an entirely internal project in which thought determinations are generated from the operations of thought itself. In the ‘Logic’’s ‘Subjective Logic’, we find Hegel’s analogue of Aristotle’s syllogistic but modified such that Aristotle’s terms designated by A, B, and C are now identified with Hegel’s three fundamental conceptual determinations (moments of the concept), universality, particularity, and singularity. Perhaps the distinction between singularity and particularity is defined by the different ways in which a thought can be related to an object, the former, as expressed in a singular term such as a demonstrative phrase or a proper name picking out something in its specificity, the latter as in a definite description that is satisfied by whatever worldly object or objects it is true of. This is a distinction that had been used by Gottfried Ploucquet (1716–1790), who described the distinction as between exclusive and comprehensive forms of particularity, and it incorporates the innovation of earlier nominalist logicians so to give a type of extensional interpretation to judgments. On the other hands this is at odds with the methodology of the ‘Logic’ for in virtue of its entirely internal constitution as the self-articulation of pure thought there is no equivalent of any extensional semantics within it, and from a logical point of view singularity is to be understood as somehow different to particularity and universality while related to both.

Such extensional semantic considerations begin to come into focus in Hegel’s ‘Philosophy of Nature’ wherein the concept of nature is introduced with the statement that: ‘Nature has yielded itself as the Idea in the form of otherness … nature is not merely external relative to this Idea (and to the subjective existence of the same, spirit), but is embodied as nature in the determination of externality’, and this theme of the externality of nature is further elaborated thus: ‘In this externality, the determinations of the concept have the appearance of an indifferent subsistence and isolation with regard to one another’. This combination of externality and singularity gives a dimension to every actual natural thing thathat Hegel later refers to as its ‘infinite singularization or separation’. From a logical point of view, the difference between the conceptual determinations of singularity and particularity cannot be accounted for by the question of how they pick out worldly objects, but now, in the context of the Philosophy of Nature this internally articulated system of thought faces a world with its own inherent logical structure, including the element of ‘infinite singularization or separation’. This status possessed by a natural thing in respect of being natural plainly resists the type of conceptually articulated unification upon which intelligibility relies. Where something is grasped as a particular it is grasped in terms of what it has in common with other instances of a universal. This rose grasped in the judgment ‘this rose is red’ can be grasped in terms of what it has in common with other roses or other red things. But when grasped as singular such connections must be put in abeyance. Hegel’s split middle term signals the paradox of the conceptual determinacy of singularity. When I grasp this rose in a judgment, I abstract from its specificity and weave it as a rose into the fabric of my understanding. This comes at the price of annulling its ‘infinite singularization’, however.

Hegel refers to this as the contradiction at the heart of theoretical reason. I seek to understand the thing as it is and yet:

‘… the more thought predominates in ordinary perceptiveness, so much the more does the naturalness, individuality, and immediacy of things vanish away. As thoughts invade the limitless multiformity of nature, its richness is impoverished, its spring-times die, and there is a fading in the play of its colours. That which in nature was noisy with life, falls silent in the quietude of thought; its warm abundance, which shaped itself into a thousand intriguing wonders, withers into acrid forms and shapeless generalities, which resemble a dull northern fog’.

This is the price paid by Newtonian thought in which abstractions come to completely replace the specific entities, Johannes Kepler’s (1571 –1630), observed elliptical orbits, for instance, that had been concretely perceived. As with understanding the role of mathematics within science, one might advise against confusing purely conceptual relations with the physical ones, for the infinite singularization or separation of things in nature does not mean they are unconnected, if nature is ‘noisy with life’ then clearly there are real physical relations at work in the world. What it suggests is that these physical relations cannot be simply reduced to the types of relations existing among the determinate concepts we bring to it, concepts mutually determined within the fixed oppositions of the logic of the understanding. Because of such consequences, Johann Wolfgang von Goethe, (1749–1832), Friedrich Wilhelm Joseph Schelling (1775–1854), Baader and various other philosophers of Nature had sought forms of science that preserved the immediacy of living nature, but Hegel’s solution was different: ‘what has been dismembered may be restored to simple universality through thought’ rather than intuition. By our becoming more self-aware of what we are doing when employing concepts in our practical and theoretical engagements with the world we may return to a proper grasp of the living processes implicit in nature itself. In this way Hegel’s philosophy of nature does not aim to challenge the results of the working scientist’s investigations with an account of how the world they are investigating really is. Rather, as based upon a correct understanding of the logic implicit in the empirical investigation of the natural world, philosophy of nature will assist the working scientist to avoid the pitfalls brought about by the contradictions implicit within the mind’s own theorizing. Examples of such pitfalls can be recognized in Newton’s projections of concepts onto the world, such as the concept of the infinitesimal, that, not reflecting empirically detectable existences in the world itself, have to be understood as mere posits of the mind. It is then in this indirect sense that Hegel’s defence of Kepler over Newton is premised upon the Platonic cosmology to which Kepler had been attracted, for inn it, Plato had given the first concrete expression to the logic implicit in the activity of empirical science itself.

Which is all very fascinating and esoteric but what is of especial interest for me in the ‘Timaeus’ , aside from the universe being a cosmic animal with no sex organs and eating its own excreta (I didn’t really explain that in detail) is the receptacle, or chora, a word for the the territory of the polis outside the city proper and used by Timaeus to designate a receptacle as a third kind, triton genos, a space, a material substratum, or an interval, a formless interval akin to a non-being in between which the Forms were received from the intelligible realm where they were originally held and were copied shaping into the transitory forms of the sensible realm. It gives space and has maternal overtones (a womb, a matrix), it rests between the sensible and intelligible, through which everything passes and in which nothing remains. An oddly obscure notion yet capturing the imagination of modern philosophers hence testifying to the power of the philosophical imagination.

Martin Heidegger, (1889–1976), refers to a clearing in which Being happens or takes place. Julia Kristeva, (1941 — ), deploys the term as part of her analysis of the difference between the semiotic and symbolic realms, for the Platonic chora is said to anticipate the emancipatory employment of semiotic activity as a way of evading the allegedly phallocentric character of symbolic activity (signification through language), considered as an inherently limiting and oppressive form of praxis. The chora is to be understood in a condition of pre-signifying: ‘Although the chora can be designated and regulated’, said Kristeva, ‘it can never be definitively posited: as a result, one can situate the chora and, if necessary, lend it a topology, but one can never give it axiomatic form’. Jacques Derrida, (1930–2004), uses chora to name a radical otherness that gives place for Being. For Derrida argues that the subjectile (a kind of ground used in artistic painting, a theory, not a fact, a tool that can be employed to analyse art objects to generate hypotheses concerning the relationship between subject and object in art), is like Plato’s chora. For instance an image needs to be held by something, just as a mirror will hold a reflection. The chora defies attempts at naming or either/or logic, which he deconstructs, and Derrida has collaborated with architect Peter Eisemann, (1930 -), on a project proposing the construction of a garden in the Parc de la Villette, Paris, which included a sieve, or harp-like structure that Derrida envisaged as a physical metaphor for the receptacle-like properties of the chora. Chora, an interesting space that ‘at times appears to be neither this nor that, at times both this and that’, wavering ‘between the logic of exclusion and that of participation’.

Timaeus emphasises several times it is ‘a likely story’ that he relates, or ‘a seemly myth’, it beautifies the world making much use of mathematics and no use of dialectics, providing answers and not questions, a science remaining within the Platonic cave its world projected onto the wall. And the new beginnings, the account by nous or intellect of the making of the world and of human beings by nous or intellect, and a new beginning combining the two accounts and ending with a detailed description of the human body and its diseases, a new beginning in the first account of a divine intellect, the world created by a divine craftsman working from an eternal model or blueprint ,the cosmos as an divine animal with a soul constructed from the most perfect harmonies, human being as an animal within this animal whose goodness or badness all the other animals proceed from. And what of the body? What account explains how this particular cause and animals come to be and pass away, and so another new beginning, or restart, with a third cause, after the eternal model and divine craftsman, the receptacle is not a thing but a place that is formless but not void, pure potential waiting to receive form and Timaeus describes triangles giving the receptacle its most basic forms which then combine to make the four elements fire, earth, air, and water, which then combine to make various natural forms including the human body with its variant sensations, an attempts to account for the body and becoming while shining as much light as s he can on this mysterious cause the receptacle. And then the prior two accounts are combined, although much time is devoted to the human body which combines both intellect and necessity. The head houses the intellect while the neck keeps the intellect some distance from the raging of spiritness located in our heart and the demands of the desires which are located around our stomachs. Man the microcosm reflects the combination of disparate causes in the macrocosm. A combination that is not integration. A picture of the whole is thus presented that supports the view of the centrality of humankind and the providence of beneficent gods. A likely story confronting the puzzling nature of the body and soul, we are not merely two-dimensional cut-outs from an eternal model, the experience of human life is an experience of depth, and the language of the body, dark and light, rich or shallow, is used to describe our experience of being ensouled, and attending to Timaeus puzzling and in some ways beautiful account of the whole of things, we, along with the attentive Socrates, may find occasion to reflect upon the greatest of all puzzles:

What am I?

Plato (Leonardo da Vinci?) on the left holding the ‘Timaeus’, detail from Raphael, ‘The School of Athens’, 1511

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David Proud is a British philosopher currently pursuing a PhD at the Institute of Irish Studies, University of Liverpool, on Hegel and James Joyce.

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David Proud

David Proud

David Proud is a British philosopher currently pursuing a PhD at the Institute of Irish Studies, University of Liverpool, on Hegel and James Joyce.