Plato’s Timaeus and Critias are works of perennial philosophical and historical interest. Timaeus gives us an account of how the cosmos and everything in it—stars, earth, and living creatures—came into existence. It also gives an account of the origin of human beings, their place in the cosmos, and what they should aspire to. It is a complex and multifaceted work, offering important ideas in philosophy, theology, and the study of the natural world. The unfinished Critias gives us the beginnings of a fascinating account of the supposed ancient city of Atlantis.
Timaeus offers a pattern of explanation for all natural phenomena: they are to be explained teleologically, in terms of why it is best that they occur in the way that they do. Teleological explanation itself was not original to Timaeus, nor indeed to Plato. Anaxagoras (c. 500–c.428 B C) had previously proposed that a cosmic intelligence brought order to the universe. In his earlier work, Phaedo, Plato had criticized Anaxagoras for not employing this type of explanation fully enough. What Timaeus offers, then, is the first thoroughgoing, exhaustive teleological analysis of all natural phenomena. If we take the account literally, a craftsman god, the demiurge (the word literally means ‘craftsman’), imposes order on a pre-existing chaos because order is in all ways better than chaos. So the elements, the cosmos, and all living things are given a teleological ordering by a single god who acts only for the best. This makes Timaeus the first manifesto of teleology, and ever since, whenever explanations of natural phenomena based on matter, mechanism, and chance have been perceived to be implausible, the idea of a designer god has been an alternative. Another aspect of this design is that the craftsman god employs mathematics and geometry in the construction of the cosmos. Stars, sun, moon, and planets move with regular circular motions, the elements earth, water, air, and fire are conceived of as having specific, ideal shapes, and the ultimate building-blocks for the elements are two types of triangle.
The ideas of Timaeus were much discussed by Plato’s followers in the Academy, and by those who developed Plato’s thought into ancient neoplatonism. They influenced the Stoic philosophers, and had an important effect on the early Christian theologians, which is still felt in modern Christianity. Those who opposed the ideas of design and teleology felt the need to address and criticize Timaeus. Aristotle was both deeply influenced by Timaeus, in producing his own teleological account of the natural world, and highly critical of it. There were several Greek and Latin commentaries on Timaeus, seeking to interpret and explain its theories. The Renaissance also found Timaeus a fascinating and influential work, and Renaissance neoplatonism, an important movement in early modern philosophy and science, took it as its main text. Critias has been less influential, though some have seen in it evidence of an ancient tradition concerning a lost city of Atlantis, and so find support for the idea that there was a historical Atlantis of some form.
There are four characters in Timaeus and Critias. Socrates needs little introduction: a philosopher who lived in Athens, and the main character in many of Plato’s works, he lived from 469 to 399 BC, when he was prosecuted and executed by the people of Athens. Socrates, at least as Plato’s dialogues represent him, had no specific philosophical views of his own, but was very good at exposing the deficiencies in the views of others, and was particularly concerned with issues of ethics and knowledge. Socrates’ life, his manner of doing philosophy, and the manner of his death all seem to have had a significant effect on Plato. It must be said, though, that Socrates in Timaeus is very much more subdued than he is in Plato’s earlier works, After a brief and very friendly introduction, he drops out of the conversation entirely, leaving Timaeus to make a long, uninterrupted speech describing the origins of all natural phenomena. One odd aspect of this, relative to the Socrates of the early dialogues, is that Timaeus is introduced as an expert in astronomy. Elsewhere, this would be this would be a cue for Socrates to interrogate the expert and show the shortcomings of his supposed expertise. Why does Socrates not play a greater role here? One common suggestion is that Plato has portrayed Socrates as being uninterested in natural phenomena in earlier works, so it would look odd to have him knowledgeable about them here. At Apology 19b Socrates denies ever having had any interest in natural philosophy, while in Phaedo he says he became disenchanted with it. Aristotle reports that Socrates investigated ethics rather than nature (Metaphysics 987b).
Critias in Timaeus and Critias is very old, so old he finds it easier to recollect the events of long ago rather than those of yesterday (26b). This means that he cannot be the Critias who was one of the Thirty Tyrants in 404.1 If he is a representation of a real person, most likely he is Plato’s great-grandfather, who was grandfather of the Critias of Thirty Tyrants fame.
The Hermocrates of Timaeus and Critias may be the Hermocrates mentioned by Thucydides (IV. 58 and VI. 72). He lived in Syracuse in Sicily, and was a military leader, taking part in the defeat of the Athenian attack against Sicily in 415–413 BC. He was also a prominent oligarch in Syracuse.
It is unlikely that Timaeus himself was a real person. We are told quite a lot about him, that he was rich and well-born, that he was an excellent philosopher, that he was the best astronomer and had made a special study of the nature of the cosmos, and that he had held the highest political offices in Locri. There is no trace of any such person, which, given these attributes, would be surprising if he were real. Later in antiquity a work called Timaeus Locrus was produced. This was taken to be a genuine work of Plato’s Timaeus, but was in fact a forgery.
The dramatic setting for Timaeus is a meeting between Socrates and three of the four people he has been talking to the day before, Timaeus, Hermocrates, and Critias. The fourth person, who apparently has fallen ill, is not mentioned by name, and nothing is known of him. The occasion is a Panathenaea, a yearly festival in Athens celebrating the goddess Athena. Grand Panathenaeas were held every four years, but there is no indication whether this is an ordinary or grand Panathenaea. The speech which Socrates made on the previous day, and which he gives a summary of in Timaeus, has clear affinities to parts of Republic. Does Socrates summarize the actual speeches of Republic? If so, then the dramatic dates of Republic and Timaeus are only two days apart, as Republic gives an account of a conversation that happened the day before. This seems unlikely, however, as the action of Republic takes place on the festival of Bendis, and it is improbable that the Panathenaea would follow two days after this festival. Nor does Socrates give a summary of the whole of Republic, or even the whole of the political parts of Republic. It is probable, then, that the meeting of the day before Timaeus is some other day, real or imagined, when Socrates discussed his ideal city. After giving his summary, Socrates compares his description of the ideal state in yesterday’s speech with a painting depicting animals. In both cases, he says, one wants to see the subject in action. Critias then gives a brief summary of a tale he heard long ago, of a city with similarities to Socrates’ ideal city, a tale which he is to take up again in Critias.
Timaeus divides naturally into an introduction and three main sections. In the introduction, Timaeus is given the task of describing the birth of the world and the nature of mankind. Critias is then to give an account of how the ancient Athenians fought a war against the people of Atlantis. Before proceeding to the main part of his account, Timaeus gives us a philosophical preamble, making distinctions between being and becoming, and between knowledge and opinion. The main discourse of Timaeus then falls into three main parts, all well signposted. After the introductory niceties, Timaeus begins to give his account of the origins of the cosmos and its contents. These are the works of intelligence, and Timaeus tells us of the nature of the cosmos and the world-soul, of the nature of the stars, sun, moon, and planets and their orbits, and of the nature of human beings and their relation to the cosmos. Timaeus then shifts (47e) to what comes about of necessity. Here we are introduced to the receptacle, something in which everything occurs, though the exact nature of the receptacle is unclear. Timaeus also describes the nature of earth, water, air, and fire, and how they interact with one another. He then gives an account of the nature and function of the human senses. The final section of Timaeus, from 69a to the close, concerns the cooperation of reason and necessity. Essentially, this is an account of the anatomy and physiology of the human body, underpinned by the principles of intelligent design from the first section of Timaeus and given in terms of the theory of the elements developed in the second section. Critias begins to give an account of the lost city of Atlantis and its part in an ancient war with other city-states led by Athens. It does not get beyond a description of the city and island of Atlantis before it comes to an abrupt, unexpected, and inexplicable end.
Timaeus is the closest of Plato’s major works to being a monologue. There are other works where there are long individual speeches, but nothing on the same scale as Timaeus’ main speech here. There are passages in other works where the interlocutor has very little to contribute (for example, the latter part of Parmenides) but none where there is no interlocutor at all for such a long period. It is not known why this should be so. One might speculate that this has something to do with the subject-matter, but there are other works where Plato discusses the natural world and how we might explain it (Phaedo, Republic, and so on) where he uses dialogue rather then monologue. Similarly, Critias, after some opening niceties, settles down into a monologue from Critias.
The characters of Timaeus advertise it as part of a trilogy: Timaeus, Critias, and Hermocrates. Timaeus is complete, Critias abruptly ends after a few pages, and there is no record of Hermocrates having been written. We have no indication that Critias was actually finished but that the ending has subsequently been lost; what we have appears to be all there ever was of the work. It is a matter of speculation why Critias is unfinished, and why Hermocrates was never begun.
Plato’s works are usually divided into three groups: early, middle, and late. Timaeus and Critias are generally taken to be among Plato’s later works, along with Theaetetus, Statesman, Sophist, Philebus, and Laws. The actual date of composition of Timaeus and Critias is probably around 360 BC, but there is nothing to fix that with any great precision. Some of Plato’s works can be dated fairly accurately if they refer to datable historical events, but Timaeus and Critias have no such references. Depending on the order and manner in which Plato wrote his later works, the date of composition could even be later.2
The dramatic date of Timaeus partly depends on whether or not we believe that Socrates is summarizing Republic in the introduction. If he is, then the action takes place on the second day after the festival of Bendis, though we do not know which year, and there is the problem mentioned above of the relation of the festival of Bendis and the Panathenaea.
Timaeus offers the first thoroughgoing teleological account of the world, with order being imposed on chaos by an external deity. Timaeus is infamous for its teleological approach to the explanation of nature. A standard view from the history of science would have it that only with the revival of the views of the ancient atomists by seventeenth-century thinkers such as Descartes and Gassendi did science free itself from the restrictive tentacles of the teleology of Plato and Aristotle. Since then science has progressed rapidly, relying on a mechanistic conception of the world in which there is no place for teleology.
Why does Plato feel that he requires this teleology? There can be no doubt that Plato wants to link his account of the natural world to ethics and politics. In particular, the heavens stand as an exemplar of well-ordered motion. Just as the cosmos is well ordered, we, individually and collectively, should order our lives well. There is a good, that good exists independently of us, and we should aspire to that good. Timaeus 47a is a clear example of this, where we hear that we should try to bring the wanderings of our mind into order to match the unwandering motions of the heavens. Timaeus 90a ff., close to the end of the dialogue, ties up the preceding theme of ordering our minds along the same lines as the universe is organized, and exhorts us to be as much like god as possible. What else, though, does Plato get from his use of teleology in explaining natural phenomena?
First, he gains an important decision-making criterion. Where there is a multiplicity of possibilities, the demiurge selects what is best. The demiurge is faced with the problem of which triangles he should choose to be the basic elements of the geometrical atomism. There is a multitude to choose from. The demiurge is able to make a rational choice, on the grounds of selecting the two best types of triangles. We are able to develop an account of what the demiurge must have chosen if we assume that at all times he makes the best choice. Arguably, this begins an important tradition within the philosophy of science. In modern philosophy of science there is a problem known as underdetermination, describing a situation where the data (however good) are insufficient to allow us to determine which theory to adopt to explain them, and non-empirical criteria must be employed. It is always possible to generate a multiplicity of theories for a single set of data, all of which will account for that data. How can we have a rational choice between these theories, which are all empirically adequate? Plato develops a solution involving teleology, but one which nevertheless contains certain important affinities with modern realist attempts to solve the underdetermination problem by applying criteria such as beauty, simplicity, and unity. If the demiurge constructs the cosmos on the principles of beauty, simplicity, and unity, and does so employing mathematics and geometry, then we can understand that cosmos by applying the same principles. This is important for understanding how Plato goes about solving certain problems in astronomy and cosmology in Timaeus, especially those problems where he argues for a single solution from an indefinite field of possibilities.
The second advantage Plato is able to gain from his adoption of teleology is that he is able to oppose an important new explanatory trend in ancient natural philosophy, developed by Empedocles and by the atomists Leucippus and Democritus. Complex entities, such as the cosmos and living creatures, can be thought of as the result of a multiplicity of chance occurrences. So, for Leucippus and Democritus there is an unlimited void, in which there are an unlimited number of atoms of all shapes and sizes. When, by chance, some atoms form a vortex, the processes of cosmos formation begin.3 There is a sorting of ‘like to like’ which generates the earth and the heavens.4 Many of these worlds are generated, all different from one another, and our cosmos is just one of them. It is not in any way designed. It has its characteristics entirely by chance, but that is made plausible by its being one of an infinite array of accidental worlds.
For Empedocles, the types of living creatures we are now familiar with are the result of the chance meeting of their parts.5He envisions, in a somewhat nightmarish fashion, parts of the human body wandering about and joining up by chance, the two most gruesome passages being:
Here many heads sprang up without necks,
Mere arms were wandering around without shoulders,
And single eyes, lacking foreheads, roamed around.6
Many grew with faces and breasts on both sides,
And man-headed bull-natured creatures, and again there arose
Bull-headed man-natured creatures, and mixtures of male
And female, equipped with shade-giving limbs.7
Many chance meetings of parts produced creatures which were not able to survive, or were not able to reproduce and quickly died out. Ultimately, though, creatures which were able to reproduce came about purely by chance. So living things too can be seen as the result of a multiplicity of accidents.
Plato’s alternative is clear. There is one and only one cosmos, which has been designed. We can explain the complex features of that cosmos by the use of teleology. There are single, fixed species which have been designed and, again, we can explain their complex features in teleological terms. It is also significant that instead of having an unlimited multiplicity of atoms of all shapes and sizes as the basic constituents of the physical world, as Leucippus and Democritus believed, Plato opts for a small number (two) of geometrically well-defined basic entities, which are chosen specifically by the demiurge as being best for their purpose.
One might object to the multiplicity-of-accidents view either on philosophical grounds or on the grounds of plausibility. Is it possible for the cosmos to come together accidentally? According to Plato, it is not. As we have seen, Leucippus and Democritus make use of a like-to-like principle; according to Plato at Laws 889b, though, a cosmos is a ‘fitting and harmonious’ blend of opposites, such as hot and cold, dry and moist, soft and hard. How do these come together by chance when the sorting is like to like? In the absence of any ordering by the demiurge, but in the presence of a like-to-like principle, wouldn’t there simply be a sorting out of the elements into areas of earth, water, air, and fire, rather than the coming together of a cosmos? It is significant in this context that Timaeus tells us that:
It’s like when things are shaken and sifted by sieves or other devices for cleaning grain: the heavy, dense material goes one way, while the light, flimsy material goes and settles elsewhere. Likewise, when these four were shaken at that time by the receptacle (which was itself in motion, like an implement for shaking stuff), the least similar among them ended up the furthest apart, and those that were most similar were pushed the closest together. (53a)
So a like-to-like principle will produce a sorting, but not interesting order and not a cosmos. Plato never mentions Leucippus or Democritus by name, but one can take this passage to be directly critical of anyone who supposes that a like-to-like principle is sufficient in cosmogony, the account of how the cosmos comes into being. Plato similarly refers tacitly to Empedocles, when he says: ‘Not wanting the head to roll around on the ground without the ability to climb over the various rises and out of the various dips, they gave it the body to be its vehicle and means of transport’ (44c). Empedocles needs the parts of the body to move around and associate with each other accidentally for his account of zoogony to work. But, Plato implies, if heads, and possibly many other body parts as well, are going to get stuck in every rut, the account is not going to work, or at the very least is going to become much less plausible. There are philosophical objections to the multiplicity-of-accidents view as well. Timaeus 30a presents an argument for there being a single cosmos. In Philebus Plato says: ‘The indefinite plurality of things and in things makes you in each case indefinite of thought and someone of neither status nor account, since you have never yet examined the number in anything.’8
A third possible advantage of teleology is this. In the Socrates’ dream passage of Theaetetus 201e ff., Socrates argues that composite entities can be analysed into their parts, and so we can have accounts of them. However, that which is incomposite cannot be given the same sort of analysis or account, and on this conception of knowledge the incomposite is unknowable. Employing one of his favourite analogies, Plato argues that we might have an account of syllables (in terms of the letters which constitute them) but not of letters. One problem for natural philosophy here is what sort of account we can have of the ultimate parts of the physical world. We cannot account for them or analyse them in terms of further physical parts. Plato in Theaetetus is happy just to present the problems. In Timaeus, however, we are given a theory of geometrical atomism, couched in the same terminology of letters and syllables; and after the elements of earth, water, air, and fire have been analysed into planes and then into the basic triangles, we have further teleological accounts of the nature of the basic triangles. This is not to say that a switch to teleology is a general answer to all the philosophical problems raised by the Socrates’ dream passage in Theaetetus. It is significant, though, that Timaeus does give a teleological account of incomposite entities in his natural philosophy.
Plato has reasons, then, for wanting teleology in his natural philosophy, independent of the demands of his ethical programme. We ought also to place Plato’s teleology in context. In Greece of the fourth century BC, how plausible were the accounts of Empedocles, Leucippus, and Democritus? That their accounts have affinities with modern material and mechanical explanation ought not to lead us into overestimating the plausibility of their theories. They lacked many of the tools and discoveries that have made modern theories acceptable, and to many ancients the notion that a cosmos or living beings could come about solely by chance would have seemed radically implausible. Add in Plato’s criticisms, that a like-to-like principle on its own cannot produce the requisite order, and that body parts on their own are going to be immobile, and these theories look even more unlikely.
It is also easy to look back and be critical of Plato’s teleological programme; but it should be remembered that here is an idea that had yet to be put to any sort of test. With it, Plato is able to give a comprehensive account of physical phenomena, one that is at least as plausible as its rivals. The theory of combinations of regular circular motions produces a better model of the motions of the sun, moon, and planets than anything previously, and arguably produces one of the most important and progressive research programmes in antiquity. In the context of fourth-century Greece, Plato’s teleological approach was a plausible and viable project.
Subsequently, the debate between the multiplicity-of-accidents view and the unique-entities view took an interesting course. In zoogony, the multiplicity-of-accidents view has won out in the form of the theory of evolution. It is significant, though, that this did not happen until the nineteenth and twentieth centuries, with the development of Darwin’s theory and the discovery of DNA, and until then design theories of various types flourished whenever new phenomena were discovered which the mechanical approach had difficulty explaining.
More controversially, in modern atomism we think in terms of a relatively small number of mathematically well-defined ultimate particles rather than an indefinite multiplicity of shapes and sizes. So too, we believe that these particles form well-defined structures in specific manners, rather than that they come together in an accidental fashion. It is not necessary to think of the ultimate particles as being designed, but there are ways in which they have more in common with Plato’s atomism than that of Leucippus and Democritus.
It would be wrong to see the seventeenth century as solely reviving atomism to the exclusion of Plato’s geometrical atomism. This is historically important, as one of the great claims for the atomism of Democritus, Leucippus, Epicurus, and Lucretius is that it inspired this revival, and that this was important in the fight against scholasticism, the combination of Christian and Aristotelian thought which dominated the Middle Ages. But in fact seventeenth-century thinkers also felt the need to cure atomism of atheism, and this was not merely a religious predilection, but a borrowing from Plato. The philosophical problems with presocratic atomism, of why atoms should have certain shapes and combine in certain ways, which Plato addressed with teleology and the demiurge, were now addressed with a Christian deity. So we can find Robert Boyle saying that: ‘The provident demiourgos wisely suited the fabric of the parts to the uses that were to be made of them.’9
So too, there was a considerable debate between those who advocated a universe consisting of a plenum of particles and those who favoured atoms and void. It is notable that those who favoured the plenum and rejected the idea of action at a distance, such as Descartes, adopted a similar solution to Plato for the awkward cases of gravity and magnetism. Timaeus 80c argues that the attractive powers of static electricity and magnetism are not due to any action at a distance, but can be explained by the fact that there is no void and the atoms jostle each other and move to their own region. Descartes, while using vortices to explain gravitational effects, did without a void, and used screw-shaped particles moving among smaller particles to explain magnetism.10
In cosmogony, there is still very much a live debate about whether or not we should consider our universe to be one of a multiplicity of accidental universes. The modern question is slightly different from the ancient one, in that it asks why the values of certain fundamental constants (such as the speed of light, or the value of the gravitational constant) have values set within the extremely tight limits which allow for the generation of planets and life. One type of answer to this is the descendant of the view of the ancient atomists. It is that there is an infinite number of universes and that the fundamental constants have different values in other universes. Our universe is one of an infinite array, and that is all we need to explain the (apparently fortuitous) values of the fundamental constants in our universe. Another type of answer descends from Plato: there is one universe, and the values of the fundamental constants are part of the design of that universe.
Finally, it is worth drawing some comparisons between Plato’s and Aristotle’s teleology. For Plato, order is imposed on the cosmos rather than being inherent in it. For Aristotle, the cosmos has always existed (it has no beginning) and it has always had its order inherently. Plato requires something to impose order upon the cosmos, the demiurge. Aristotle’s god may be important as an object of love, and has an important explanatory function in his scheme, but this god does not order anything. For Plato, it is the demiurge who acts purposively, not nature.
The cosmology of Timaeus marks both an important development in Greek thinking about the nature of the cosmos and some important developments in Plato’s own thinking. Timaeus attempts to integrate mathematics into thinking about cosmology in a new way; it contains an essentially animate conception of cosmology, where the cosmos and the heavenly bodies are alive, but have regular behaviour; it offers a more stable conception of the cosmos than in Plato’s earlier works; finally, it gives us the first argument that there is one, and only one, cosmos, possibly in reply to those presocratic thinkers who believed there to be more than one.
At Phaedo 108e ff. Plato had conceived of the earth as free-floating and immobile. The Myth of Er in Republic 616c ff. then made a significant conceptual leap, and began to talk of the integrity of the cosmos and how the cosmos might be supported. Here the cosmos needs bonds or braces (which may be internal or external to the cosmos; Plato uses a technical term from shipping, which we do not now fully understand) to hold it together. It is notable that here the cosmos is not referred to as a living entity and requires bracing, while in Statesman, Timaeus, and later works the cosmos is a living entity (mortal in Statesman, immortal in Timaeus) and needs no such bracing.11
Further important contrasts are that, while in previous works the cosmos turns on a pivot (Republic 616b ff., Statesman 270a), the Timaeus cosmos is entirely free-floating (33d and 34a), and that while in previous works the cosmos does not have an immortal soul (no soul in Republic, a mortal soul in Statesman), in Timaeus it does. In Timaeus the cosmos is all there is, so it can have no external bracing nor can it rest on a pivot. This move to an unsupported cosmos is the culmination of a strand of presocratic thought. According to Aristotle, Thales proposed that the earth did not fall because it floated on water.12 Then came theories of the earth not falling by being supported by air, or being in equilibrium. Plato, then, asked similar questions of the cosmos itself.
The integrity of the cosmos (and indeed of all the celestial bodies) is explained by their having souls, so no bracing is required, and as these souls are immortal, there is no degeneration. So too, the motions of the cosmos and the celestial bodies are generated by their souls. While there is a sense in which we can easily think of the cosmos in the Myth of Er as having a top and bottom (as it is supported by a sitting goddess), Timaeus 62c ff. makes it very clear that terms such as ‘above’ and ‘below’ are not suitable. One must make due allowance for the highly metaphorical language of the Myth of Er and the fact that cosmology is not Plato’s primary concern there, but still there are important differences in the structure of the cosmos between Republic and Timaeus.
There are further contrasts to be made, concerning the regularity of circular motion and the stability of the cosmos. In Republic and Statesman, where there is a pivot for the cosmos to turn on, celestial motion is not entirely regular and degenerates, while with the free-floating Timaeus cosmos it is regular and stable. In Timaeus the cosmos is unageing and free from any disease, and indissoluble unless the demiurge wills otherwise, which he will not. There is an indication of a degenerating cosmos at Phaedo 110a, where the world is said to have been ‘corrupted and eaten away’. At Republic 530b Socrates, talking about the motions of the heavens, says that it would be ‘ludicrous to suppose that these things are constant and unvarying, and never change in the slightest’. In the Statesman we have something more forthright:
At first, it carried out the commands of its father-maker quite exactly, but later—due to the fact that at least some of its components were material—some precision was lost, because before attaining its current ordered form as the cosmos, materiality (which is a primordial and inherent aspect of the universe) was steeped in a great deal of disorder . . . While the universe was under the helmsman’s guidance, then, it used to engender little bad and plenty of good in the creatures it maintained within its boundaries. But then the helmsman departs. In the period immediately following this release, the universe continues to keep everything going excellently, but as time goes by it forgets his injunctions more and more. Then that primeval disharmony gains the upper hand and, towards the end of this period, the universe runs riot and implants a blend of little good and plenty of the opposite, until it comes close to destroying itself and everything in it. (Statesman 273b ff.)
That this change affects the heavenly bodies is confirmed at Statesman 269a. We might also infer this from Plato’s general conviction that the stars have physical bodies and the myth’s statement that all physical bodies degenerate. If the cosmos is continually degenerating towards chaos—and as Statesman 273b makes clear, this will be a radical and fundamental chaos (unless god intervenes, the cosmos will be ‘storm-driven by confusion and broken up into an endless sea of unlikeness’, Statesman 273de)—then clearly the periods of the planets will be subject to deviation. In the Statesman, though, either god must perpetually guide the cosmos or it degenerates of its own inherent nature, and is saved from sinking into ‘an endless sea of unlikeness’ only by the active intervention of god (Statesman 273b ff.). The cosmos of Timaeus, then, is more stable in its nature and more sophisticated in its conception.
One of the criticisms of Plato’s natural philosophy is that he had an essentially animate conception of the cosmos. Plato indeed considers the heavenly bodies to be gods, to be animate, to be intelligent, and to have souls, and so too for the cosmos as a whole. Coming after the materialism of the atomists, is this not a regressive move in Greek cosmology? After all, Plato is well aware of the views of the atomists and Anaxagoras’ theory that the celestial bodies are hot stones.13 For Plato, regular and orderly behaviour requires further explanation. Matter, on its own, will not, by chance and necessity alone, exhibit the sort of regularity we see in the heavens. Laws 967b says in relation to astronomy: ‘Those who studied these matters accurately would not have been able to make such wonderfully accurate calculations if these entities did not have souls.’14
Timaeus states that the cosmos does not have many of the things we would usually associate with an animal (or even, within either a pagan or a Christian tradition, with a god). From Timaeus 33b onwards we are told that this ‘animal’ is perfectly spherical; has neither eyes nor ears, as there is nothing external to see or hear; nor does it have any need of organs to receive food or to excrete the remains, as it is entirely self-sufficient and nothing comes in or goes out. As it needs neither hands to defend itself nor feet to stand on, and has no need of legs or feet to propel itself, it has no limbs, and at 34b we are told it is a god. To say the least, this is a somewhat strange animal, and certainly could not be considered anthropomorphic, even if it does have intelligence and soul. Plato’s claim in Timaeus that the cosmos is like an animal is a claim for the integrity and the internal organization of the cosmos, and the ongoing order of the cosmos, even though there are properties that animals have but inanimate matter does not.
What does this god do, though? All it does is revolve uniformly in one place (34a). The stars are spherical and intelligent like the cosmos (40a), and are divine and living creatures (40b). As with the cosmos, they have motions befitting their intelligence, and so we are told that:
He endowed each of the gods with two kinds of motion: even rotation in the same place, to enable them always to think the same thoughts about the same things; and forward motion, under the sovereignty of the revolution of identity and sameness. But with respect to the other five kinds of motion, they were to be stable and unmoving, so that each of them might be, to the fullest extent, as perfect as possible. And so all the fixed stars were created as divine, ever-living beings, spinning evenly and unerringly for ever. (40a)
The essential point here, then, is that the celestial bodies have no freedom of action (or no desire to deviate from regular circular motion). They have the intelligence to carry out their assigned duties, and not to do anything else. It is their intelligence which explains their regular and orderly behaviour. That they move, and do so without any external compulsion, is explained by their having souls. For Plato, the soul is a principle of motion.15
Although the cosmos and the heavenly bodies have life, soul, divinity, and intelligence, they have these in a highly circumscribed and attenuated manner, from a modern point of view. If this is describable as vitalism, it is a highly depersonalized version, where the attributes of animate beings that are required for the description of the cosmos have been carefully sorted from those that are not. This allows us to distinguish quite sharply between Plato and the mythological and magical traditions. The key issue here is that these souls/gods are not capricious. They always act for the best, and so will always act in the same manner. There is nothing unpredictable or irregular about their behaviour.
As we now express physical laws in terms of equations, we slip very easily into a mathematical model of physical law. That is, we consider physical laws to be unbreakable in a manner analogous to mathematical or geometrical laws. It is very easy to assume that physical law has always been modelled on mathematical law, but this is not so, the scientific revolution of the seventeenth century being the watershed. Prior to the seventeenth century, in the Western tradition and in other cultures, it is common to find physical law modelled on civil law instead. So while physical law ought to be upheld, it is conceivable that it will not be, and then there may even be a punishment for a breach of the law. So we find Heraclitus saying that: ‘The sun will not overstep its measures, or else the Furies, the allies of Justice, will find it out.’16
Plato’s conception of physical law in Timaeus is based on a civil rather than a mathematical model. The heavenly bodies have intelligence, understand what they ought to do for the best, and, being good souls, carry that out. While it is conceivable that the heavenly bodies will deviate from the intelligent course, due to their nature they will not in fact do so. We might compare here the fate of the cosmos in Timaeus. As the cosmos was generated, it is dissoluble, but as the demiurge is good, this will not in fact happen, and the cosmos will continue indefinitely.
There is also a question of resources here. The Greeks had no conception of gravity, so that what we take to be gravitational phenomena had to be explained in different terms. Hence we get like-to-like theories of why heavy objects fall to the ground, or Aristotle’s theories of natural place and natural motion. What ancient physical explanation could be given of the heavens? The atomist notion of a vortex sweeping the heavens around may account for the simple motion of the stars, but as becomes evident in the astronomy of Timaeus, it cannot account for the more complex motions of sun, moon, and planets. Once one employs more than one circular motion to explain the motion of a celestial body, it becomes difficult to see how the motion of that body can be explained in terms of a single force. As the Greeks held that the earth is central and stable, they had to treat all the movements of the heavens as real motions. We understand many of these to be apparent, due to the motion of the earth. We think in terms of a force emanating from the sun controlling geometrically relatively simple, elliptical orbits, but this was not an option for the Greeks, as they had to explain the highly complex motions of the heavens (as seen from the earth) as if they were real. No force emanating from the earth could explain these, which meant they had to seek different types of explanation.
Plato was not alone, then, in the history of scientific thought in using divine entities to explain regular behaviour—there has been a long tradition within Christian thought, right down to the current day, of asserting that God ensures the regularity of the universe. The key question is whether these entities are law-abiding or not, and for Plato they most certainly are. In the sense that teleology is imposed on the world by the demiurge and so is not an original feature of the world, Plato’s teleology is unnatural. It is also important to recognize, however, that Plato’s demiurge is a god subject to natural law and regular behaviour, as are his demigods, and so there is a sharp contrast with the caprice of the gods of Greek myth. Nor is Plato alone in the ancient world in using biological analogues for physical processes. Aristotle is perhaps a good example of how biological analogues can intrude into physics in a more subtle manner, and this is something which is continued by the Stoics. With modern science having moved away from the use of biological analogues, the essential question is: is it evident, in the context of fourth-century Greece, that one should be using mechanical rather than biological analogues? The answer to that is quite clearly no. There are several reasons for this. If one wishes to explain order and regularity, mechanisms are not a good option for the Greeks. While mechanisms, and particularly clockwork, are paradigms of regularity and predictability to us, the mechanisms available to the Greeks, such as the cart and the winch, cannot serve as such models. It is not surprising, then, that even where the Greeks might be described as materialists, they are not mechanists.
Timaeus is one of the first attempts to bring together mathematics and cosmology. Indeed, the demiurge can reasonably be described as a geometer god. One of the odd aspects of this from a modern point of view is that Plato employs a theory of harmony in cosmology: the spacing of the orbits of the planets is related to the musical scale. Musical notes can be expressed as the ratio between two numbers, as can the size of the planetary orbits. Why does Plato do this? First, when we express physical laws now, we often write them as equations, but has it always been evident that we should express physical laws in this manner? The answer to that is a definite no, and in fact physical laws have only been systematically written in this form since around the seventeenth century. Prior to that, many possibilities of how mathematics in general might relate to the world were open. The relationship might be arithmetical, the world itself consisting of numbers, as the Pythagoreans suggested; or it might be based on harmony, as there is clearly some relation between harmony and number (string-lengths for musical instruments, and so on); or the relation might be geometrical, the world being constituted from shapes, or shapes playing an important role in the ordering of the world. The idea that physical laws should be expressed in equations was not intuitively obvious, and had to be hard fought for; indeed, even over the last century science has refined its use of mathematics, with the introduction of the theory of probability. One reason why Plato does not express the motions of the heavens as equations, then, is that this is not really a resource that is open to him. Another is an extension of the idea of civil law being applied to the intelligences that guide the celestial bodies. There is no question here, for instance, of there being a force impressed and there being a resulting action in proportion to the size of that force, nor any question of an expenditure of energy or fuel. The heavenly bodies simply manage their own motions.
In order to illustrate what Plato may be doing here, let us take a short digression via Johannes Kepler (1571–1630), the great astronomer famous for his three laws of planetary motion. Kepler was an ardent Platonist, and an avid reader of Timaeus. Two millennia after Plato, was the modern relationship between mathematics and cosmology clear to one of the most important figures in the history of astronomy? Or did he struggle with problems similar to Plato’s, and if he did, how did he propose to resolve them? Kepler attempted to derive the size and number of the planetary orbits from the Platonic solids17—the cube, tetrahedron, octahedron, icosahedron, and dodecahedron. The precise details need not concern us here, but in outline Kepler’s thinking is this: for each of these solids, we can imagine a sphere touching each of the surfaces on the inside, and another touching each of the vertices on the outside. It is then possible to calculate a ratio, r : R, of the radius of the inner sphere and the radius of the outer sphere. This is most easily illustrated in two dimensions for a square face of a cube of earth and a triangular face of a tetrahedron:
It is then possible, given some assumptions about how planetary orbits nest together, to generate ratios for the relative spacings of the orbits of the planets visible to the naked eye. In one of the most remarkable phenomena of the history of science, this process can be made to give very good results, certainly by the standards of seventeenth-century observation.
Once he had discovered that planetary orbits were elliptical, Kepler needed a reason why they have their specific eccentricities and why the planets had their specific velocities. 18 It is possible to express many of the properties of a planetary orbit as ratios, such as the ratio of the lengths of the axes of the ellipse or the ratio of the speeds of a planet as it crosses the axes. With some mathematical processing, Kepler could then produce the harmonies expressed by the planets. The more pronounced the ellipse (as with Mercury), the more notes a planet produces; the more nearly circular (as with Venus), the more monotonous it is.
Why do Plato and Kepler approach cosmology in this manner? If we ask modern science why there are eight planets in the solar system, with specific spacings of the orbits and specific orbital speeds, the answer is likely to be that this is largely a matter of chance. Kepler, though, has an explanation of why there are only a specific number of planets (there are only a determinate number of Platonic solids to space their orbits with), and why the planets have specific eccentricities and velocities (to produce a celestial harmony). In a cosmos generated by a benevolent demiurge there is nothing which is produced arbitrarily, and the demiurge has a reason for all that he does. Or, to put this another way: what sufficient reason is there for the demiurge to use one set of orbit sizes for the planets rather than any other? Plato and Kepler recognize the need for criteria here. Possibilities open to them, but closed by the developments of the seventeenth century, are forms of geometrical or harmonic ordering.
Kepler’s work illustrates that the Renaissance was still struggling with the relation of mathematics and cosmology. Kepler asked a slightly different question from modern science, but a perfectly rational and reasonable one within his historical context, and one that many others of his time were asking. Kepler himself is adamant that there is nothing mystical in his work, and I would agree with him. At no stage does he say that anything is inexplicable; rather, he is always seeking some form of mathematical explanation. So if a major figure in the history of science was still struggling with the relation between mathematics and cosmology nearly 2,000 years later than Plato, we can perhaps be a little more sympathetic to Plato’s plight. He too wished to know why the demiurge had formed the cosmos in this specific manner, and pursued what to him would have been open possibilities for the mathematical structure of the cosmos without any recourse to numerology or mysticism.
The demiurge, the primary god, plays an important role in Timaeus, though we are told frustratingly little about him. He is a craftsman god, which is not how one would describe the gods of Greek myth. Since manual labour was looked down upon in cultured circles in Plato’s time, this conception of the demiurge is very radical.19 Plato’s god needs to be skilled, as the production of the cosmos and everything in it is something which requires skill, but Plato does not tell us exactly how the demiurge is supposed to exercise that skill.
It is significant, relative to previous Greek mythology, that Plato’s demiurge wishes everything to be in the best possible state of order and has no jealousy. In previous mythology the gods often begrudge any gift to mankind, and disagree among themselves about such gifts, and sometimes the gifts turn out to be double-edged; but the demiurge freely gives his gifts, and they are of undoubted benefit to mankind. The relation between humans and god is also significant. Where previously humans had sought to become gods, or sought to be physically like gods, and had suffered for their hubris, Plato attempts to channel human aspirations towards being intellectually like god. There is no sense in Timaeus that it is an act of hubris to try to become intellectually as like god as possible.
Relative to earlier Greek cosmogony, this is the first time that we have an independent god imposing order on a pre-existing chaos. In other cosmogonies there is often a principle of ‘steering’ by which the cosmos is formed, but that which does the steering does not seem to be separate from that which is steered.
Alternatively, there were the chance-dominated cosmogonies of the early atomists and Empedocles, or the rejection of cosmogony in Heraclitus or Parmenides’ ‘Way of Truth’. Plato’s demiurge is the first god to impose order explicitly by using mathematics, geometry, and harmony.
That Plato’s demiurge is entirely good and free from jealousy, and is unlike humankind, can be seen as a development away from Greek mythological conceptions of god, a trend that was begun in the sixth century by Xenophanes, who tells us that:
Homer and Hesiod have attributed to the gods
Everything that men find shameful and reprehensible—
Stealing, adultery, and deceiving one another.
But mortals think that the gods are born,
Wear their own clothes, have voices and bodies.
If cows and horses or lions had hands,
Or could draw with their hands and make things as men can,
Horses would have drawn horse-like gods, cows cow-like gods,
And each species would have made their gods’ bodies just like their own.
Ethiopians say that the gods are flat-nosed and black,
And Thracians that theirs have blue eyes and red hair.20
That god is entirely good and behaves in a predictable and invariant manner, and imposes that sort of order on the cosmos, is of considerable importance for the philosophical and scientific ideas of believers from Plato onwards. In Timaeus the demiurge is not one god among many, or even the first among equals as we find in myth. He is the only god of his type, and prior to his ordering of the cosmos he is the only god at all, although then he produces demigods to aid him in ordering the cosmos and, in particular, in forming mankind.
There is still some distance, though, between Plato and a Christian conception of God, and we must be careful not to attribute later theological ideas to Plato. While Plato’s god is omni-benevolent, he is not omnipotent, in that he cannot do the physically or the logically impossible. It is an important theme in Timaeus that the demiurge does as well as he can with the materials available to him, but that reason can only persuade necessity so far and no further. In early Christianity there was considerable debate about whether god created the universe from nothing, or from some pre-existing matter, the former view eventually winning.
Timaeus is not really a religious work, at least in the sense that it does not say that we should worship god, nor does it lay down how god should be worshipped, nor give any structure for the organization of a religion. Rather, it tells us how we can embark on a programme of intellectual improvement, based on an analysis of the relation between the cosmos and god. We should strive to become like god.
Timaeus was much discussed in antiquity in relation to two related theological issues, both stemming from the idea of the creation of the universe by a benevolent deity. First, there is the question of divine providence. If god has created a good world, as far as possible, and continues to care for that world, how exactly does that work? How do we understand the nature of the world as the product of providence? How do we understand our own actions, goals, and fate in relation to god’s providence?21 Secondly, there is the question of evil. Why is it, if god is entirely good, that human beings do bad things and there is evil in the world?
The narrative which Timaeus gives is described as an eikos logos, a ‘likely account’ (29d, 30b), but it would be misleading to consider it a myth in the orthodox sense. Timaeus does not just assert the existence of a god, a world-soul, and so on, but assigns important function to each of these things. In other words, he can justify the existence of everything he supposes to exist, whereas myths are more profligate in what they suppose to exist (many gods, monsters, titans, and so on). Plato’s god also behaves in an entirely rational manner, unlike the gods of myth. Plato does use the Greek word muthos in Timaeus (29d, 68d), but this need not be translated as ‘myth’. It can mean any oral account, or any tale, story, or narrative. As Timaeus’ account is also referred to as a logos (30b), which in philosophical contexts has strong connotations of explanation, it is probably best to think of Timaeus’ narrative as a likely account.
The ‘likely’ part of this description stems from a word-play in the Greek, between eikones ‘likenesses’ and eikos ‘likely’. One of the important metaphysical themes of Timaeus is that the cosmos is in some sense a copy or a likeness. The demiurge looks to an unchanging original, and makes our changeable cosmos as much like that original as possible. Timaeus offers us the principle that explanations have to be of the same order as what they explain. So an account of the forms,22 which are stable, secure, and manifest to the intellect, should itself be stable and reliable. An account of what is a likeness, on the other hand, can only be likely. But it is difficult to determine the degree of likelihood the account can aspire to. Certainly this is not just one story among many, as several times we are told that this account is second to none in its likelihood. While there are passages where Timaeus is quite tentative in his claims, there are others where he is considerably more confident. We can, for instance, make entirely correct calculations about the motions of the heavenly bodies. Or again, Timaeus seems quite confident about his choice of the two basic sorts of triangle for geometrical atomism, but goes on to say if anyone can think of better triangles than these he will be welcomed as a friend (54a). That the account is currently second to none does not preclude its being improved, though whether it could ever be a definitive account would be open to question. What the ‘likely account’ cannot do and could never do is produce knowledge, in the sense that Plato believes we can have knowledge of the forms.
What does this mean for Plato’s attitude towards natural philosophy and the investigation of nature? In Plato’s sense of the word, we cannot have knowledge of the physical world. Plato’s use of the word ‘knowledge’ is very strong, however, and there are differing degrees of opinion we can have concerning the physical world; we may even hold true opinions about it. Plato was highly critical of the physiologoi, the presocratic natural philosophers, particularly in his earlier work Phaedo. This should not be taken to indicate that he was hostile to natural philosophy, but rather that he had his own conception of how natural philosophy should be done. That, of course, involves the sort of teleology that Timaeus supplies. Phaedo does not argue that the shape and position of the earth or the constitution of the body are matters of no interest, but rather that purely material explanations of these phenomena are inadequate. Timaeus delivers, it can be argued, Plato’s more fully worked-out riposte to the physiologoi, offering teleological explanations for all phenomena. In Phaedo, Socrates says this about causes:
It would be quite true to say that without possessing such things as bones and sinews, and whatever else I possess, I shouldn’t be able to do what I judged best; but to call these things the reasons for my actions, rather than my choice of what is best, and that too though I act with intelligence, would be a thoroughly loose way of talking. Fancy being unable to distinguish two different things: the reason proper, and that without which the reason could never be a reason! (Phaedo 99a)
Timaeus has a slightly different view: ‘we should discuss both kinds of causes, but keep those which fashion good and beautiful products with the help of intelligent craftsmanship separate from those which produce random and disorderly results, with no part played by intelligence’ (46e). Plato still talks of two sorts of causes, but no longer is one a real cause and the other not. Plato has the reputation of being rather anti-empirical. In part this is deserved, as he often emphasizes that forms are intelligible entities and not the subject of sense-perception. This attitude is easy to exaggerate, though, and the best antidote is perhaps to quote Timaeus on the benefits of eyesight: sight is enormously beneficial for us, in the sense that, if we couldn’t see the stars and the sun and the sky, an account such as I’ve been giving of the universe would be completely impossible. As things are, however, the visibility of day and night, of months and the circling years, of equinoxes and solstices, resulted in the invention of number, gave us the concept of time, and made it possible for us to enquire into the nature of the universe. These in their turn have enabled us to equip ourselves with philosophy in general, and humankind never has been nor ever will be granted by the gods a greater good than philosophy. (47a)
Timaeus gives us a model for the motions of the heavenly bodies: the earth is central and unmoving, and there are the fixed stars, which rotate around the earth once every day. Typically for the ancient world, these stars are all presumed to be equidistant from the earth and to undergo no change of position relative to one another. Unlike Aristotle, where the stars are fixed in a sphere, Plato’s stars are free-moving and hold their pattern due to the intelligences that guide them. Each of the other seven heavenly bodies visible to the naked eye (the sun, the moon, Mercury, Venus, Mars, Jupiter, and Saturn) has a second circular motion, in addition to the first, with a different axis. So each time the fixed stars complete a revolution, the sun, moon and five planets will be in slightly different positions (see figure).
We do not know what angle Plato supposed there to be between the axis of revolution for the fixed stars and that of the sun, moon, and planets, though he does describe the relation between the two as like the Greek letter chi, Χ (36bc). The angle required is around 23.5 degrees, which is the difference between the plane of the earth’s motion around the sun and the axis of earth’s rotation (see figure).
If one plots where the sun sets through the year, it sets due west at equinox (when day and night are of equal length) and at 23.5 degrees north or south at the solstices (when either the day is longest and the night shortest, or vice versa):
If you observe which stars rise at the point where the sun sets, you get a line called the ecliptic. The sun changes position relative to the stars by about 1 degree a day (the earth completes an orbit of 360 degrees in around 365 days). In Plato’s model, it is the sun which moves, and completes its second circular motion in one year, so it will move by around 1 degree a day relative to the fixed stars and will move along the ecliptic, assuming the correct angle has been chosen. The planets also appear close to the ecliptic. The reason for this is that, if we draw a line from the sun through the earth, the orbits of the other planets are relatively close to this line. So, in the following diagram, the figures indicate the angle between the planets’ orbit around the sun and that of the earth: The planets deviate slightly from the ecliptic, and the band of sky they move in is known as the zodiac. Plato also has Timaeus tell us that the moon completes its second revolution in a month, the sun in a year, but that few have taken note of the other celestial bodies (39c). The second circular motion will produce motion along the ecliptic, moving the planets relative to the fixed stars, but it will not produce any deviation from the ecliptic.
In Timaeus, all the celestial bodies move in a perfectly regular manner. At 34a Timaeus tells us that the universe itself revolves uniformly and has no trace of any other motion. If the universe as a whole and the fixed stars have regular motion, there cannot be any metaphysical reason why the rest of the heavenly bodies cannot move in a regular manner as well. Timaeus tells us that the motions of the planets constitute time (39c). If so, their motion must be regular or time will be irregular. But Plato mentions no irregularity in relation to time, nor is there any need for time to be irregular in Timaeus. All that is needed for a distinction between time and eternity is that time flows while eternity stands still. At 39d Timaeus tells us of the ‘great year’, the time taken for all the heavenly bodies to repeat their positions relative to each other and to the fixed stars. This is a calculable amount of time, so the motions of the planets must be regular. The general idea that the visible heavens are amenable to calculation proliferates throughout the Timaeus (e.g. 40d and 47c). The motions of the heavens are also the visible manifestations of the movements of the world-soul, and these motions are entirely regular (47c).
That the heavens move in a perfectly regular fashion is very important. It marks a significant change from Republic, where Socrates asks:
Don’t you think that a genuine astronomer feels the same when he looks at the movements of the heavenly bodies? He’ll certainly think that the artist of the heavens has constructed them and all they contain to be as beautiful as such works could ever possibly be, but what about the ratio between night and day, between them and a month, between a month and a year? And what about the relations of the heavenly bodies in general to these phenomena or to one another? Don’t you think he’d regard it as ludicrous to suppose that these things are constant and unvarying, and never change in the slightest, when they’re material and visible, and to devote all one’s energy to discovering the truth about these things? (Republic 530a–b)
At Laws 822a, however, Plato adopts a similar position to that of Timaeus: ‘The usual opinion concerning the sun, moon, and other planets, that they occasionally wander, is not the case; precisely the opposite is true. For each of these bodies always travels on one path, and not many, although this may not seem so.’ This is important for the history of astronomy; previously, the Babylonians had called the planets bibbu, ‘sheep’, and our own word planet derives from the Greek planetes, meaning something that wanders, or a vagabond. There is a tradition that Plato set problems in astronomy for others to solve. Simplicius reports that: ‘Plato assigned circular, regular, and ordered motions to the heavens, and offered this problem to the mathematicians: which hypotheses of regular, circular, and ordered motion are capable of saving the phenomena of the planets? And first Eudoxus of Cnidus produced the hypothesis of the so-called unrolling spheres.’23 Plato recognized that there are no irregular motions in the heavens and, in supposing that all the motions of the heavenly bodies are either simple regular circular motions or combinations of regular circular motions, he set the parameters for one of the longest and most fruitful research programmes in the history of science. The concentric-sphere astronomies of Eudoxus, Callippus, and Aristotle all developed from this, as did the epicyclic astronomies of Ptolemy and his followers. Even as late as 1543, Copernicus, supposing the earth to be in motion around the sun, stayed with combinations of regular circular motion. It was not until 1609 that Kepler suggested that planetary orbits are simple ellipses about the sun.
There are, of course, problems with the astronomy of Timaeus. As it is one of the earliest models of the cosmos that makes a serious attempt at accommodating the phenomena, it would be very surprising if there were not. Plato was aware of at least some of these.
We are told that Venus and Mercury are placed in circles with speeds equal to that of the sun, but that due to having a tendency that opposes the sun (38d), these two planets overtake and are overtaken by each other. This overtaking and being overtaken cannot be generated by a combination of two regular circular motions, so the tendency opposing the sun must involve some other motion. That may be some further regular motion that Plato leaves out of the account for simplicity, or it may be that he has no answer for this problem as yet. Two further major difficulties are that Plato cannot account for the retrograde motion of the planets, and his account of eclipses is seriously astray.
The planets appear to do a little dance (see figure).24 They move relative to the fixed stars, stop, move backwards, stop again, and then move forwards again. The backward movement is known as retrograde motion, and though Plato is aware of it, he cannot account for it, as on his model the planets move with a uniform speed along the ecliptic. If the sun, moon, and planets were all permanently in the same plane, along with the earth, there would be a lunar eclipse every full moon, and a solar eclipse every new moon. These eclipses would always be of the same type, both in the sense of the linear alignment of the sun, moon, and earth giving identical total/partial eclipses and in the sense of the relative distances of sun and moon giving either a complete or an annular eclipse each time (see figure). 25
It is wrong to assume that ancient thinkers believed that their models could solve all the problems of astronomy. Simplicius tells us that: ‘The unrolling spheres of Eudoxus’ school do not save the phenomena, not only those that were found later, but also those known before and recognized by them.’26 The three phenomena Simplicius cites are that (1) Venus and Mars appear at times much brighter than at others; (2) there is variation in the apparent size of the moon; (3) there are variations in the type of solar eclipses relating to the apparent size of the moon.
Plato’s model is best viewed as a prototype. It is strong on philosophical and cosmological principle (all the motions of the heavenly bodies are either simple regular circular motions or combinations of regular circular motions), but weaker in its application to specific problems in astronomy. It is an advance on previous theories, including the model put forward in the Myth of Er in Republic, but it is not as good as later theories. We might reasonably suppose, given Plato’s philosophical predilections, that he was more concerned with generating a teleological cosmology than with astronomy. Clearly, for such a cosmology to be plausible it has to be able to give a reasonable account of the phenomena, but Plato’s priorities are surely with cosmological principles.
Timaeus gives us an account of the origins of the cosmos. Prior to the intervention of the demiurge, there is a chaos. There is no order to the constituents of the cosmos, in two senses: what there is in this chaos is not distributed through space in any orderly fashion, and it is not properly formed into orderly elements. Plato subscribes to the usual Greek view that there are four elements: earth, water, air, and fire. Prior to the ordering of the cosmos, there are only accidental traces of these. So Plato’s vision of chaos is quite radical. Matter itself has no order, as well as being randomly distributed. There is also, in an important sense, no time prior to the ordering of the cosmos. There is no measurable time because time is bound up with the movements of the sun, moon, and planets. It is their regular motions which constitute measurable time, and this sort of time comes into existence with the establishment of the heavens.
The pre-cosmic chaos is non-progressive, a dead end. This is different from modern cosmogony, and is critical to Plato’s view. In modern cosmogony there is the chaos of the Big Bang, then gravity does the work. Small areas of greater density (the ‘wrinkles in space-time’) act as attractors and pull matter towards them, eventually forming stars and so on. We can then give an account of the formation of stars, the sun, earth, and the solar system without recourse to a designer. For Plato, though, the pre-cosmic chaos is non-progressive and will remain a chaos unless there is an intervention to generate order, and that is the task of the demiurge. That order will not come about by chance. Timaeus does give us a like-to-like principle, but it would be wrong to think of it as a principle of attraction, as with gravity. Rather, when many things are agitated, like things aggregate together. This like-to-like principle will not produce a cosmos from a chaos, however. It will merely sort like things together, and that is not sufficient. There is an important passage in Laws where Plato says:
Let me put it more clearly. Fire, water, earth, and air all exist due to nature and chance, they say, and none to skill, and the bodies which come after these, earth, sun, moon, and stars, came into being because of these entirely soulless entities. Each being moved by chance, according to the power it has, they somehow fell together in a fitting and harmonious manner, hot with cold or dry with moist or hard with soft, all of the forced blendings happening by the mixing of opposites according to chance. In this way and by these means the heavens and all that pertains to them have come into being and all of the animals and plants, all of the seasons having been created from these things, not by intelligence, they say, nor by some god nor some skill, but as we say, through nature and chance.27
A cosmos, then, has a ‘fitting and harmonious’ blending of opposites, something that will not be generated by a like-to-like principle. There is a need for the demiurge to intervene in order to establish a cosmos, and the demiurge has considerable work to do. Not only must he create an orderly distribution of the elements; he must form those elements themselves.
There is another aspect to Plato’s cosmogony, which is that the cosmos has to have a soul as well as a body. The creation of the soul takes place on a more metaphysical level. The soul is compounded from sameness, being, and difference. This is in order that the world-soul will be able to make judgements of existence, sameness, or difference (the primary characteristics of the world), and so will be able to live an intelligent life. This mix is then split up according to harmonic principles and bound together to form the cosmos and the paths of the sun, moon, and planets. This is not something that can come about by chance either, as there must be precise proportion in the mixing, precise division to form the world-soul, and the different is described as ‘difficult to mix’.
The key to Plato’s cosmogony is that the cosmos cannot have come about by chance. The demiurge must act on a non-progressive chaos. He has to generate the elements, the cosmos, and the soul of the cosmos, as well as humans and animals.
Timaeus develops an analogy between the nature of the world-soul and the nature of our own soul. Our own souls, the microcosms, have very strong similarities to the world-soul, the macrocosm. The world-soul is constituted from sameness, being, and difference. It consists of two revolutions, the same and the different, which move with perfect regularity. The world-soul is intelligent, and all the judgements it makes about sameness (or identity), being, and difference in relation to the objects it encounters are correct. The human soul is constituted in a similar manner, though the mix of sameness, being, and difference is not as good as it was for the world-soul. We too have a pair of mental revolutions. Ours, though, do not move in a perfectly regular manner. When our souls are bound into our bodies, the revolutions of our minds are disrupted by the sudden influx of sensations. Because of this, our judgements of sameness, being, and difference in the objects we encounter is flawed, especially in our early years before the revolutions have had a chance to settle down again (43d).
Plato may not mean all of this quite literally, but it is of great importance for what we should be doing with our lives. Our goal should be to correct our mental revolutions and try to bring them as far as possible to resemble those of the world-soul. If we are able to control our sensations and to bring our mental revolutions under control, we will live justly; if we do not, we will live unjustly. While we should not neglect the health of the body, it is the health of our minds that is really important. Our goal should be to become as much like god as possible, in having perfect mental revolutions. The study of astronomy has a key part in this: ‘the gods wanted us to make a close study of the circular motions of the heavens, gain the ability to calculate them correctly in accordance with their nature, assimilate ours to the perfect evenness of the god’s, and so stabilize the wandering revolutions within us’ (47c). What happens if we do not lead a good life? A good life is an end in itself for Plato, but there are consequences in subsequent incarnations for wrongdoers. The highest part of the soul is immortal and undergoes incarnations, first in the body of a man. If a man should lead a poor life, on the next incarnation he will have the body of a woman. Men who are light-witted and make only a superficial study of astronomy come back as birds. Men who take no part in either philosophy or astronomy become land animals, and the most stupid of these become snakes, or even sea creatures (90e–92c). If this seems harsh, remember that in Timaeus humans are responsible for their own mental condition. Everyone is capable of improving his or her condition by study, or of allowing his or her mind to deteriorate through laziness or folly. It is an important principle of Timaeus that god is blameless and man generates his own evil.
It is up to us, then, to correct the revolutions in our heads that are so badly disrupted when we are given bodies. These revolutions do settle down of their own accord, to a certain extent, but we must do all we can to encourage this. The housing of the soul in the body has its own problems. The higher part of the soul is placed in the head, in order to keep it as far away as possible from the baser passions of other parts of the body. There is a skull to protect it, but this skull cannot be so thick that it seriously hinders perception. The demiurge favours a short, intelligent, well-lived life over a longer life lived at a lower level, and this informs the disposition of the body around the soul when the demiurge generates humans.
The macrocosm/microcosm analogy also features in the strictures on the health of the body (88d). The receptacle shakes what is in it, and this shaking helps to keep the elements in their order. Similarly, we should keep our bodies in motion, that is, we should take some exercise, in order that the movement of our bodies keeps the elements in their proper places.
The macrocosm/microcosm analogy inspired at least one important scientific breakthrough. Giordano Bruno, in the latter part of the sixteenth century, associated soul with the blood, and speculated that as the soul of the macrocosm had a circular motion, so the blood of the microcosm (that is, humans) must circulate around the body. William Harvey, who discovered the circulation of the blood around 1619, supported his view largely with argument and experiment, though a macrocosm/microcosm relation was an important part of his thinking too.
After he has described what he calls the works of intelligent craftsmanship, at 47e Timaeus switches to discussing what comes about by necessity. Timaeus tells us that intelligence persuaded necessity for the most part to produce good results. What does Plato mean by necessity, and how is it that necessity can be ‘persuaded’ by anything? As reason scores only a partial victory over necessity, there is some residual chance and disorder. Now, it seems strange that necessity should be associated with these things. However, one might take both chance and disorder in two separate senses, depending on what they are contrasted with:
(1) An event might be said to occur by chance because there is no causal chain that leads to its occurrence, contrasting chance with causal determinism.
(2) An event might be said to occur by chance in the absence of design. If we were to blindly throw paint at a canvas, in an attempt to generate a portrait, it would be mere chance if anything good were the result, though no causal chain need be broken if such an event were to occur.
We can take the same sort of approach with disorder. The order that it is contrasted with might be that of physical law, or that of a teleological arrangement of phenomena. The ordinary emission of light, for instance, might be law-like but disorderly (with no order to wavelength or direction), relative to a stimulated emission of light and its ordering into a laser beam (ordered in wavelength and direction). An ancient analogue here might be that the principles of military strategy apply to all groups of men, but some groups are well-ordered formations while others are disordered rabbles. Plato often uses the word taxis and its cognates for ‘order’ (e.g. 30a), and it is also the regular word for good military formations.
There are, then, a number of possibilities for how intelligence persuades necessity:
(1) There is only a partial imposition of causal determinism. So there will be ‘turbulence’, in the sense that there will be unpredictable behaviour by matter.
(2) There is causal determinism, but there is an ordering of the elements by the demiurge such that they produce good results.
(3) The demiurge generates the best bodies for earth, water, air, and fire. Although these are the best possible bodies, they still have limitations for instantiating the best possible world.
(4) It may be that the attempt to completely instantiate the good produces a set of conflicting demands which cannot all be jointly met. A good example of this might be the question of the human skull, discussed at Timaeus 75bc. In order for us to have acute perception, the skull ought to be as thin as possible; in order for it to protect our brains and ensure a long life, it should be as thick as possible. Similarly, at 75e there must be some flesh around the skull for the purpose of temperature control, but as little as possible so as not to obstruct perception. If we think of necessity in this manner, then reason can only persuade it as far as logical possibility will allow.
(5) According to Timaeus, it is necessary that the human soul is housed in a body. As the mortal appetites will have bad effects on the soul, these are housed as far away from the head, the seat of the immortal soul, as possible. So while mortal appetite and immortal soul cannot be completely separated, the action of intelligence is to separate them as far as is possible, given that they are to be housed in one body.
Of these possibilities, we can rule out only the first one, as there is no need in Timaeus’ account for unpredictable behaviour in this sense, and there is no evidence that he recognizes any such unpredictable behaviour, at least after the demiurge has ordered the cosmos. There are examples of the other four possibilities for intelligence persuading necessity.
How is necessity persuaded by intelligence? Primarily this must be down to the actions of the demiurge, who is able to order the pre-cosmic chaos into the elements and sort those elements into a good order. The demigods and the world-soul must also play a part, though, as their souls direct the motions of the heavens and it is the demigods who produce human beings.
The receptacle is probably the hardest and most philosophically challenging concept in Timaeus. Plato introduces a third thing, apart from the forms and whatever participates in forms. The receptacle is that in which phenomena occur, and out of which they are formed. So the receptacle seems to be space and also to be matter: it provides the space in which perceptible phenomena can occur, and also is the substrate from which phenomena are generated.
The problem which introduces the receptacle is how we refer to changing phenomena. It appears that all four elements can change into one another. If we identify something as water, and it changes into air, should we now identify the same stuff as air? If we do, what happens to any distinction between the elements—what name, rather than ‘all four names, one after another’ (49b), ought to be applied to each? One target Plato has in mind here is the presocratic view that one substance—such as water or air or fire—is primary, but transmutes into the other elements. Why should we consider one element out of the four to be primary? Why should we take, say, water to be primary if it changes into air, fire, and earth, losing all its characteristics as water? A related question is: what stays the same when something changes? If all the perceptible characteristics change, can we say that the thing we started with is the same thing we end up with? So perhaps there is some substrate, something that underlies the perceptible changes, that does not itself change. Another related question is how we refer to things that are changing. Ought we to give names that imply stability to things that change? Perhaps we should not call perceptible fire ‘fire’ at all, but some other name that reflects its transient nature. Only things that do not change can have names which imply stability.
There are several difficulties with the receptacle, and Timaeus is aware that he is talking about something difficult to describe. One difficulty is what we can know of it: the receptacle has to be characterless, so as not to distort what comes to be in it: if something is so characterless, what can be said about it? Timaeus struggles to say anything positive about the receptacle, and of course there will be serious epistemological problems with anything so utterly characterless. At Timaeus 49a it is something difficult and obscure, at 52b it is grasped without sensation by ‘a kind of bastard reasoning’ and is the subject of a dream. Something that cannot be explained in terms of anything more basic and has no character seems in itself inexplicable.
Is the receptacle supposed to be space, or matter, or some combination of the two? Plato uses a range of metaphors to describe it, without being entirely clear. The evidence for the receptacle as matter is that, in the gold analogy, the receptacle is that out of which shapes are formed (specifically ‘out of gold’, 50a). So too it is referred to as a plastic base (50c) or soft material (50e), and as mother (50d, 51a) and nurse (49a, 52d). It is like an odourless base for perfumes (50e). The receptacle is also that which is partly ignified and liquefied (51b; cf. 52d) to produce phenomenal fire and water, and so would seem to be a material constituent. A further question here is whether this collection of material metaphors can be made to yield a consistent account of a material receptacle.
On the other hand, the evidence for the receptacle as space is that the receptacle is specifically or implicitly referred to as space (52b, 52d, 53a; cf. 58a) and as a seat or place (52b, 53a) and as that ‘in which’ things occur (49e, 50d, 50e, 52a, 52b). It is also referred to as a winnowing-basket (52e; cf. 57c, 88de), the motion of which sorts the particles it contains. This is a particularly strong spatial metaphor, as it would suggest that the particles are independent of, but contained by, the winnowing-basket.
Whether all the descriptions that Plato uses for the receptacle are compatible with one another is an open question. It is possible to fuse matter and space together in this way, as Descartes did in the seventeenth century when he argued for an equivalence of matter and extension. Whether Plato manages an entirely coherent account here is debatable, though in relation to this difficult topic we must remember that Timaeus is giving us a likely tale, has warned us that his account may not be entirely consistent, and has issued special warnings about the difficult nature of the receptacle. That something beyond forms and their likenesses is required is relatively easy to argue for. The nature of what is required, whether it is space, matter, or some combination of the two is a rather more difficult issue.
Timaeus provides us with a new take on atomism. The atomism of Leucippus and Democritus supposed that atoms had an infinite variety of shapes, and an infinite variety of sizes too. Plato offers a much more definite, structured, and geometrical approach. Each of the four elements of earth, water, air, and fire is assigned a three-dimensional shape. Earth consists of cubes, water of octahedra, air of icosahedra, fire of tetrahedra. These are a special set of solids, often known as the ‘Platonic solids’. They are constructed from two-dimensional figures of the same shape and size. So the cubes of earth are made from six identical squares, and the tetrahedra of fire from four identical triangles. Plato is aware of a fifth ‘Platonic’ solid, the dodecahedron, but this does not come into his atomic theory, though there is a vague mention of its being used by the demiurge for the cosmos (55c). The individual solids are too small to be seen by the naked eye, so what we see as fire are many tetrahedra of fire together.
Why does Plato choose these solids, and these triangles to make them up? The claim is that they are the best solids and triangles (53e), so Plato’s atomism is, not surprisingly, a teleological one. The size and shape of the basic particles is not accidental, as it was for the early atomists, Leucippus and Democritus. It is a matter of intelligent choice and design by the demiurge. He imposes order on chaotic matter by generating shapes and number (53b).
The elements water, air, and fire can transmute into each other. The solids which constitute them can come apart, as can the planes which constitute the solids. So an octahedron of water can come apart into eight triangular planes, and each of these too can come apart into six basic triangles. These can reform as tetrahedra, and so we have a transmutation of water to fire. Only earth cannot take part in these transmutations, as its faces are squares and its basic particles are of a different type. Plato seeks to explain the characteristic of an element in terms of the properties of its particles. So fire burns because its particles have sharp edges and are good at cutting, and they also move quickly as they are small. Hence the phenomenon of burning is due to the cutting action of sharp, rapidly moving particles. The idea that there is a micro-world beyond our perception, which while it underpins our sense-perceptions can be radically different in its nature from the macro-world, is an enormously significant step forward in the history of science. The idea was not original to Plato, though he developed it in interesting ways.
It is worth considering some of the ways in which Plato’s geometrical atomism is rather more like modern atomism than that of Leucippus and Democritus. Plato insists that there is a small number of types of ultimate particle, which are mathematically well defined, as opposed to the indefinite number of shapes and sizes of the atomists. Plato’s discussion of geometrical atomism stresses that matter has deep structure, in the sense of ultimate particles forming structures which in turn themselves form further structures, and so on. That is an idea which is absent from Leucippus and Democritus. Although Plato is not specific about how bonding between particles occurs, and indeed this is the major theoretical flaw in the scheme, he is right that this is not an accidental matter based on mechanical interaction but happens in a specific and well-defined manner.
A further important aspect of Plato’s thinking on geometrical atomism is the question of irrational numbers and measurement. The Pythagoreans treated geometry arithmetically, by attempting to treat geometrical problems as part of the theory of natural numbers; that is, as numbers composed of indivisible monads. Thus every geometrical length ought to be expressible as the ratio of two natural numbers. If these numbers represent a length, then if we ask how long something is, rather than measure the distance we count the number of monadic lengths involved. So too, according to Aristotle, the Pythagoreans treated physical entities as in some way constituted out of number.28 The great problem for these projects came with the discovery of the irrationality of the square root of two, for here we have a number/length that cannot be expressed as a ratio of two natural numbers, or as a multiple of a monadic length.29 That Plato was aware of this not only for lengths but for areas and volumes too is made clear by the Athenian’s explicit comments at Laws 819d ff.30 In response to the difficulties of the Pythagorean programme Plato advocated geometrical rather than arithmetical means for the description and explanation of the world. As if to emphasize the overcoming of the difficulties dogging the Pythagoreans, the most basic triangles have sides of root two and root three.
There are some difficulties with Plato’s geometrical atomism, as Aristotle was quick to point out.31 When the solid figures of the elements undergo transmutation, and break up into their two-dimensional components, surely there is then empty space, an impossibility in Aristotle’s view. When two-dimensional figures come together, why do they do so in a precise manner, to form perfect three-dimensional figures? Why do they join edge to edge, rather than edge to surface, or surface to surface like a pile of sheets of paper?
Critias follows directly on from Timaeus, with Timaeus beginning the work by commenting on the account he has just given in the previous work. Critias then begins to tell the full tale which he had given in outline in the introduction to Timaeus. He tells us something of the political order of the city of Atlantis, and gives a description of the city. Critias then breaks off abruptly.
There are two sorts of question that we can ask about the origins of the Atlantis myth. First, is it true that Atlantis once existed, or is there at least a basis of fact which Plato has embellished for his own purposes? As far as Atlantis itself is concerned, there is no basis in fact. There is no sunken city in the place he indicates, nor is there any geological remnant (volcanoes, shallow muddy part of the Atlantic), although there are shoals just beyond the Strait of Gibraltar. There are of course undulations in the Atlantic sea floor, but these are caused by tectonic plate movements which force the floor up, rather than by islands having sunk down.
Secondly, is Plato’s Atlantis tale based on or derived from some earlier mythological tradition? As far as we are aware, it is not. There is no source for this legend prior to Plato, and no later source that is independent of Plato. Given the ubiquity of the Atlantis story, this may come as a surprise, but it is nevertheless true: Plato is our sole source for the Atlantis myth. It is significant that Plato’s tale was believed by many in antiquity who came after him, but they failed to refer to any other source for the myth.
A variation on these possibilities is that Plato was aware of some other disaster affecting an island, and transformed this into the Atlantis myth. The civilization of Minoan Crete, at its height in the fifteenth century BC, has been the focus of attention here. There are some interesting parallels between Minoan Crete and Plato’s Atlantis in terms of culture, but nothing compelling. There was a massive volcanic eruption on Thera, 115 km north of Crete, but this has now been accurately dated to around 1640 BC and cannot have anything to do with the decline of Minoan Crete some 200 years later. Should we take the account given by Plato at face value? Was there a record of the demise of Minoan Crete in the written Egyptian records, which somehow came down to Plato? There is nothing in the extant Egyptian records to support this, though it is always possible that the relevant material has been lost. More of a concern is why this information should come to Plato and only to him. One would expect some trace of it in other Greek sources before, during, and after his lifetime, but there is none.
It is likely, then, that Plato’s account of Atlantis is largely fictional, though we should take care with the term ‘fiction’. This is a modern category, covering a huge diversity of literature, and the distinction between fiction and other forms is by no means sharp, especially with the rise of ‘faction’. Even within modern fiction, there is a genre where fictional characters take part in historical events.
If Critias is not history as it claims to be, and is not based on any historical event, what is it about? It may be some form of political allegory, with Plato expressing opinions about recent and current politics. The description of ancient Athens can be read as referring to contemporary Sparta rather than to any real ancient Athens. The description of Atlantis can be read as referring to Athens and its recent history. The war between Atlantis and ancient Athens then represents the Peloponnesian war between Sparta and contemporary Athens.32 The moral of the tale is that Athens should shun extreme democracy, the growth of the navy, and naval imperialism, and return to the political structures that had served her well in the past, notably in the Persian war. Such a message would be in accord with Plato’s known political views. This theory does have the advantage that we can now explain why Plato chooses these particular characters to express this tale: Hermocrates was instrumental in the defeat of the Athenian naval expedition to Sicily, while Solon was the author of the ‘ancestral constitution’ that the rule of the Thirty Tyrants was supposed to restore.
The fit between Atlantis/ancient Athens and contemporary Athens/contemporary Sparta is interesting, though far from perfect. As Critias tells us relatively little, and Athens had a rich political past, it would be surprising if we could not fit some events to the Atlantis myth reasonably well, allowing a Platonic political moral to be drawn. So it cannot be taken as proved that Critias ought to be read as a political allegory. Such a reading would also need to explain how such a political allegory fits into Timaeus/Critias as a whole. If there is a unified project in Timaeus/Critias, how does a political allegory contribute to that? Why, after Timaeus has given us an extended account of the origins of the cosmos and mankind, should a political allegory be the next part of the project?
Alternatively, we can take the view that Timaeus and Critias together have a very strong compositional unity, at least in the sense that Critias does precisely what is asked in the introduction to Timaeus. Johansen also links Critias quite closely with Republic,33as providing an example of how virtue, construed along the lines of the account in Republic, would prevail even under adverse conditions. Critias delivers the encomium of virtuous men in action allowed for in Republic X 607a and asked for at Timaeus 19de. A further link to Republic is the allusion to painting in the introduction to Timaeus; a similar remark can be found at Republic 472d–e in relation to the ideal city. Critias also provides something very important for Plato, which Timaeus leaves out. While Timaeus gives us an account of cosmic order, of the origins of mankind, of how individual men should strive to live, and what can go wrong with their bodies and minds, within this context Critias shows us how men should live together in civil society, how civil society was formed, and what can go wrong with such a society. However, since Critias is incomplete, no theory about the purpose of the dialogue can be demonstrated to be true.