Plato’s Cosmic Manual:
Introduction, Reader’s Guide, and Acknowledgements
Introduction
This collection of essays brings together physicists, philosophers, classicists, and architects to assess the meaning and impact of one of the most profound and influential works of Western letters—Plato’s Timaeus, a work which comes as close as any to giving a comprehensive account of life, the universe, and everything, and does so in a startlingly narrow compass. Its core is but sixty-five pages long.
This core gives an account of the nature of god and creation, a theory of knowledge that explains various grades of cognition, a comprehensive taxonomy of the soul and perception, and an account of the objects that gods and souls might know or encounter, call them collectively, in John Wesley’s phrase, the furniture of the universe. The analytical inventory of this furniture includes theories of what is and is not eternal, of the basic constituents of material objects, of how material objects compound into large scale, even cosmic, structures, of time and of space. There are elaborate accounts of both physical processes and life processes, the nature of making, morality, sickness and health. There are even accounts of accounts, of what can and cannot be said. We have then, in a single book the length of a modest novella, a comprehensive theology, metaphysics, physics, epistemology, and psychology, with significant excursions into logic, biology, astronomy, medicine, and ethics.
Hovering over all of this is the notion that the objects and structures in the world around us—both sub-atomic and cosmic—are, at some deep level, perhaps the deepest level, mathematical constructs. Building on a cosmic scale consists of adjusting ratios and measures found in the materials that confront the builder. Structures at the largest scale are numerical progressions, while the sub-atomic components of the primary bodies, earth, air, fire, and water, are not granules or other bits of stuff, but triangles and squares. When, in Douglas Adams’ Hitchhiker’s Guide to the Galaxy, the answer to the ultimate question of life, the universe, and everything turns out to be the number forty-two, we are meant to chuckle at both the incongruity and the banality of the answer, but we have in fact wandered deep into Platonic turf. What is basic is quantitative, not qualitative. The basic constituents of material reality are going to be things like number, proportion, and the regular polyhedrons, not properties like yellow, blue, warm-blooded, feathered, hot, cold, dry, wet. Hardly any historians of thought now believe that Plato personally made any significant contributions to mathematics, but his basic vision that the intelligibility of physical reality is fundamentally mathematical has turned out to be right, at least as things now stand in science. Those who view various elements of Plato’s theology and metaphysics as at best bloated, should remember that he held out the correct model for science unheralded for over two thousand years until Kepler used regular polyhedrons, the Platonic solids, to get astronomy and, by analogy, all of science back operating on a mathematical paradigm.
It is not surprising then that physicists remain fascinated by the Timaeus, even when they reject what many see as its metaphysical excesses. In this volume, we have two contrasting physicists. Sir Anthony Leggett, 2003 Nobel Laureate for Physics, gives a sympathetic account of the Timaeus’ general bearings, while astrophysicist Sean Carroll, the New York Times’ go-to guy for all things cosmological, thinks we can get along just fine without the Timaeus as an intellectual antecedent. Two additional contrasting essays explore the extent to which Plato’s geometrizing of the universe is a coherent project. Thomas Johansen argues that Plato overreaches in this project, while Alan Code argues that the geometrizing project has been misunderstood.
So we have gods, some eternal objects, material objects, space, time, and numbers. But wait, there’s more. In addition to the Timaeus’ synoptic presentation of life, the universe, and everything, the dialogue and its companion fragment, the Critias, present one thing more, myth. They contain one of the West’s most enduring myths, the legend of Atlantis. As disappointing as the news may be to some New Age-ers and mystics, it appears that the myth is wholly an invention of Plato’s imagination. Near the start of the Timaeus, Critias gives a short version of the myth, which he holds to be an account of actual history, but which no critics now think Plato believed to be actual history. Critias begins to give the full version of the myth as the dialogue named after him, but this ‘dialogue’ breaks off in mid-sentence after only a dozen pages of what is mostly geographical description. The body of the Timaeus, that is, Timaeus’ account of life, the universe, and everything, is wedged in between the short version and the severely truncated, long version of the myth.
The myth recounts events said to have occurred nine thousand years in the past. At that time, the evil island empire of Atlantis has a world-historical battle with a wholly just Athens, an Athens that realizes the principles of the paradigmatically just society laid out in Plato’s Republic or in the close approximation of it that Socrates has spun out to Timaeus, Critias, and two others just the day before. Critias recounts the myth in answer to a request by Socrates to be shown his ideal state realized in action. Athens wins the battle, but then, just as in a hurricane that sinks pirates and admirals alike, a terraqueous disaster of cosmic proportion befalls the Mediterranean catchment. The island of Atlantis sinks below the ocean and earthquakes and floods level Athens, killing all its soldiers and virtually all of its inhabitants. As in a gangland massacre, somebody has to be left standing to tell the tale.
The Atlantis myth has provided the West with the concept of the lost world, the displaced world, the other world, and the world of the other. From these points of departure, the myth has enchanted the Western mind and launched a thousand variants in utopias, novels, movies, and resorts. But as much as it has enchanted the storyteller, it has puzzled the critic. In particular, the two dialogues leave maddeningly unclear what the relationship is between the cosmology of the Timaeus and the content of the myth. With literary explorations of Plato on the rise, this problem has become an important topic and is addressed by a number of the essays in this collection, as is the reception of the myth into the West. See especially the contributions of Barbara Sattler, Kathryn A. Morgan, and Jon Solomon. In addition, two essays address the nature and status of myths and stories within the epistemological framing of the dialogue—those by Gábor Betegh and Alexander Mourelatos.
Even the metaphysics of the Timaeus is spun out in the manner of a story. But virtually all critics now think that Timaeus’ story about the universe, unlike Critias’ about Atlantis, is one in which Plato advances his own views—to the extent, that is, that Plato’s own views can be found in his dialogues. A lot of critics deny this latter position. For them, Plato’s writings are ‘just’ literature or rhetoric or prods to thought, but not a body of thought. Pursuing this debate would take us well beyond the four corners of this book. For the sake of full disclosure, though, let it be known that all of the contributors here who write on the content of Timaeus’ speech work on the unstated presumption that the speech represents Plato’s views.
But given that the thoughts of Timaeus are spun out in narrative form, it comes as no surprise that lively debates rage over what in the speech is to be taken literally, at face value, and what figuratively, ‘merely’ as an aid for exposition. These debates go as far back as Plato’s Academy itself, where there was a debate over whether Timaeus’ account of creation was meant to be read literally when it says that the organized universe at some point had a beginning and that before that beginning every sensible thing was in a chaotic flux or whether this “In the beginning” trope—it’s a fixed formula in Greek—was just a highly effective literary device for Plato to sort out for the reader conflicting strands that have always jointly existed in the universe—order and disorder—and that there actually was no first moment at which God intervened into the world around us.
The last few decades have seen a general, though not universal, shift toward literal readings of the Timaeus, especially surrounding the creation story. Perhaps part of this shift is the result of the theory of the Big Bang having made talk of origins in physics respectable again. And perhaps another part of the shift is a consequence of there being less pressure now to see Plato’s views as invariant across his career. The non-literal reading of the creation story, going clear back to the Academy, was driven in large part by an effort to make the Timaeus consistent with two other dialogues—the earlier Phaedrus and Plato’s last work, the Laws—both of which view each soul as a self-moving motion that has always existed, while the Timaeus, when read literally, views at least most souls as creations in time with external sources of motion. Critics worry less about this sort of inconsistency now than they did through most of the twentieth century.
But one thing is certain: not everything in the Timaeus can be read literally. At one point, Timaeus reports that a soul that extends through the whole universe (more on this later) was whipped up by God in a kratêr, the Greek word from which we get “crater” and which refers to a large footed and handled ceramic bowl in which the Greeks diluted their muddy, sweet wines with water to make them palatable. No one thinks that Plato believes that out there in the universe somewhere there is floating around a giant ceramic vessel at least the size of California. And what sense does it make to speak of mixing up a non-material thing in a material thing to begin with? Literal readings of the Timaeus may generally be correct, but they are not universal access badges.
So how does the creation story go? In the beginning, . . . or rather even before the beginning, there is a supreme God, who exists outside the world and is chiefly viewed as a craftsman or demiurge—dêmiourgos—a Greek notion that can apply to any type and rank of craftsmanship from lowly potting, a job fit for a slave, on up to the marble-carving of Phidias, the sculptor of the Parthenon statuary. Such a supreme craftsman god first appears in Plato’s Republic, in the seventh book’s discussion of astronomy, where, as in the late Timaeus, he creates the heavenly bodies and establishes their function as temporal markers—for days, months, years. A craftsman god also appears in each of the rest of the late group of Platonic dialogues—the Sophist, Statesman, Philebus, and Laws. In the Timaeus, the Craftsman or Demiurge is further characterized as being a father and a maker, and as a builder, carpenter, and timber framer, a person who makes things hang together. He is eternal. He is rational in his agency and is himself an object of reason. He has a personality: he isn’t jealous, he harbors no grudges, he wants things to be as good as they can be. He is providential: he intervenes in the world. He creates the heaven and the earth. So far at least, this Platonic God is quite similar to the Judeo-Christian God, but surprisingly new when set against earlier Greek literature and philosophy. Indeed we would be shocked by his newness if we were not familiar with the Judeo-Christian God.
But he also differs in a number of significant ways from the Christian God. First, the Christian God draws not just his agency from within himself—his will and motive powers flow from himself—but the content of his mind, his ideas, his plans, have their origin internally to himself as well. This is not so for Plato’s God or for Greek craftsmen more generally. They create with an eye to models or paradigms that are external to them and which they aim to realize or instantiate perfectly in the things upon which they work. We might say that while the Demiurge’s motives are (largely) internal to him, his intentions, the things and conditions that he wants to realize, are not.
The models, which the Demiurge uses for his creation of the orderly world, are another Platonic first. They are what Plato calls Forms or Ideas, capitalized here to distinguish them from both forms that are the mere shapes of material objects and ideas that are thoughts in the mind. Forms or Ideas are mind-independent, eternal, non-material objects of knowledge. They are what guarantee that knowledge is knowledge and not some lesser grade of cognition. They serve as paradigms or standards for our moral and productive activities. They allow us to accurately identify things in this world and, in some sense, are the cause of them as well. They are said to be the things that really are, in contrast to the objects around us that are said sort of to be and sort of not to be. Forms exist in themselves, not in relation to other things. The rule seems to be that there is exactly one Form for each general concept that we have. But as with nearly every feature of Forms, their exact range is contested by critics. Still, the traditional list of Forms include moral and aesthetic notions (Justice Itself, Goodness Itself, Beauty Itself), mathematical concepts (Three, Oddness, Even, Square, Sphere), Relations (Double, Half, Large, Small, Octave, Speed), notions that range widely over other notions (Being, Sameness, Difference, Motion, Rest), and in the Timaeus at least, there is a clear commitment to Forms of natural kinds—the species and genera of living things and the primary bodies (Earth, Air, Fire, and Water). These Forms of natural kinds are said in particular to provide the eternal paradigms after which the Demiurge crafts the world.
A plurality of twentieth-century Platonic scholarship was devoted to a war over the nature and status of Platonic Forms. Critics disputed over what Forms are, whether they have any merit, when Plato came to believe in them, and whether Plato changed his mind about them over the course of his fifty-year philosophical and literary career. These debates have tended to wane of late, as critics have found other things of interest in Plato, and too, perhaps, this vein has been somewhat mined out. After five-hundred articles on whether the Form of good is good, there may not be much more to be said on the subject. In any case, the theory of Forms is not the exclusive or even primary focus of any of the contributions to this collection, even though traditionally the Timaeus has been a major site in the debates about Forms. By contrast, there is rising critical interest in theological matters in Plato, and five of the essays in the volume take the Demiurge as their central focus or at least point of departure—the essays by Anthony Long, Allan Silverman, Charles Kahn, Matthias Vorwerk, and Thomas Robinson.
So far we have the Craftsman and his model. But on what does he work? Another major way in which the Demiurge differs from the Christian God relates to the materials that he crafts. In Christian theology, God is omnipotent—there is nothing he can’t do—and spectacularly, with such power he makes the world from nothing. Neither of these conditions—omnipotence and creation ex nihilo—holds of the Platonic Demiurge. He desires everything to be orderly because he believes that order is everywhere better than disorder, but he is confronted with a blooming buzzing confusion, a chaotic flux, over which he has limited control and of which, at least on a literal reading of the dialogue, he is not the cause. The pre-cosmic world is like a flooding river that turns back upon itself, leaps its banks, and sweeps everything along with it, tossing things to and fro, flipping them about, and doing so again. The Demiurge can do a pretty good job at controlling the flux. He is even able to use some of the same forces that in some contexts are so destructive and disordering (e.g., fire) to enable him to produce good things (like, sunlight and vision). These enabling capacities adapted from the pre-cosmos into the orderly world are called auxiliary or accompanying causes. But even after the Demiurge’s best efforts, there remains a certain cussedness in things, a recalcitrance to good. The world’s permanent undertow is called Necessity, the thing that trips up the best laid plans and intentions, even God’s: “The Lord says, ‘Go out and have fun,’/ But the landlord says, ‘Your rent ain’t paid!’ / Necessity, it’s plain to see / What a lovely old world this silly old world could be, / But man, it’s all in a mess, account of Necessity.”
In consequence of his view that God’s capacities for good deeds are limited, Plato does not have to, as his Christian counterparts must, work through the tangles and trammels of the problem of evil. Plato does not frame tornados as tests of belief in God, mass slaughter as the product of valuable free-wills. That children come down with incurable cancers is not something about which Plato must wring his hands or expend cleverness of mind. The Timaeus does not and need not offer a theodicy—a justification for the presence of evil in a world where Providence is all powerful and all good.
The Timaeus says next to nothing, even metaphorically, about the instrumentalities of God, the means he uses when he confronts the world as given to him. In Christian iconography, the instruments of God standardly are his fingers and hands: In Exodus, God writes the Ten Commandments with his forefinger, the same one with which on the ceiling of the Sistine Chapel he gives Adam the spark of life, and according to folk song, “He has the whole wide world in his hands.” The Demiurge has no such iconography. This aspect of his nature is left vague, passed over in silence. By contrast, in the Timaeus we learn a great deal more of the manners or respects of the Demiurge’s creation than Bible or tradition reports of the Christian God’s. The Demiurge creates by introducing, or maybe more accurately, adjusting the conditions of, unity, order, harmony, proportion, measure, and number in the world.
Until quite recently, the overwhelming majority of critics have taken these properties of unity, order, and the like, not as manners or respects of creation, but as the very ends or goals of the Demiurge’s creation, and so traditionally, though often tacitly, it has been assumed that the chief aims of the Demiurge are aesthetic: the goodness with which he invests the world is primarily to be understood as beauty; his primary aim is to make the world a more beautiful place, as beautiful as it can be. The cosmos is a work of art. But of late, some critics have begun viewing the Demiurge less as a producer of beauty than as a producer of rationality. In this collection, versions of this newer view are reflected in Anthony Long’s and Barbara Sattler’s contributions. Here, the aim of the Demiurge is not so much to make the world look good as to make it intelligible and have intelligence. Rationality is the supreme good of which this world is capable. Proportionality, number, and the like are vehicles for this end, not the project’s end itself. Understood in this way, Timaeus’ creation story at least stands some chance of linking up with the ethical and political concerns found in his speech, in the literary frame of the dialogue, and in other late dialogues that combine moral and cosmological concerns—notably the Statesman and Philebus.
The rationality project has three prongs. First, there will need to be creatures who have the developed capacity to be rational. Those would be creatures like you and me in good circumstances. But too frequently circumstance is not good. Our souls’ very encounter with the cussedness of the material world causes us to fall far away from being able to develop our rational capacities. One of the most dramatic passages of the dialogue is the description of the newly incarnate infant soul maddened and deranged by its contact with the flux of the phenomena. As a result of our naturally deranged nature, if we are to have a capacity for rationality, we will need to have a model of it present to mind, so that we can begin to set aright our ability to think by reference to it. So second, there will need to be a fully, properly rational soul available to serve as a paradigm after which we can model our mental processes. And finally, even with our rational capacities in order and developed to the point of proper use, we will still need to have objects about which to think correctly. For Plato, rationality is not just a matter of method and process; it’s a matter of taking in the right sorts of things. For the vast majority of humans, the things that finalize rationality by giving it proper objects will not be Platonic Forms, rather most of us will have to find rational objects in the world present to hand. The Demiurge leaves the creation of potentially rational creatures—humans—to the lesser gods. And takes on for himself the two larger projects that will make potential rationality actual rationality for humans. Along the way, he makes the world as thoroughly rational and as full of intelligence as is possible, a project to which, at our best, we humans contribute.
The two Demiurgically engendered parts of the complex that results in human rationality are the two chief projects that the Demiurge performs in the Timaeus. They are exemplary of his other formative activities. In each case, the Demiurge introduces a standard or paradigm into the phenomenal realm; he introduces some of the ideality of the Ideas into the phenomenal realm. His aim is not just to copy Forms correctly, but to replicate some of their function as Forms as well.
The Demiurge’s making of a model or standard for our rational capacities turns out, for our modern minds, to be the strangest bit in the Platonic cosmology: The supreme God, who may or may not be a soul himself, creates a giant, thoroughly rational soul and stretches it through the entirety of the organized material realm, making the universe into a single rational living creature, a World Animal—a World Soul in the World Body. Plato gives a complicated, much debated argument for why there is only one world and how its singularity is tied up with its animality. But his overall point is as clear as it is odd to us. We will only be able to get rid of the vestiges of our gyrating discombobulated and discombobulating infant souls, if we have a model or standard for rational capacities. Having a single model eliminates possible confusions that might arise if there were more than one ‘model’. So if there can be just one true model, that is a good thing. In the case of a model soul, it is possible for there to be just one, and so God makes just one. We come to have the developed capacity for reason when we model the circuits of our souls after the perfectly circular circuits of the rational World Soul. It is only then that we are capable of making true judgments about the most important matters and lead our lives correctly. As contributor Anthony Long puts it, “Plato’s World Soul, so far as we can determine, was a largely original concept, intended by him as a major scientific break-through.”
What of the required content of our rationality? One can’t think about nothing. And as we will see later, we cannot think rightly or even at all about the blooming buzzing confusion. And for most of us, access to Forms is not in the cards. Yet we are, if stumblingly, rational. How so? The Demiurge comes to the rescue with the invention of . . . time. Time? Time provides us both a general model or standard for our understanding of the world and a specific mode of access to the higher reaches of intellectual content. The Demiurge makes time by setting, to the extent possible, the heavenly bodies in regularly repeating circuits. We are able to use these circuits as clocks, as standards or measures of time. At one point, Plato simply equates the regular circuits with time, which elsewhere he defines as motion that moves according to number. With clocks or standards more generally, we are able to make precise numerical judgments (“The train arrived at 6:01pm”), not merely relative comparisons that one thing is more or less or even the same as another (“The baby was born before the train arrived, but at the same time the news report started, whatever time that was”). It is in this capacity—to be able to make precise numerical judgments—that time provides us the highest grade of true opinion of which we are capable while staying within the heavens—that is, without access to either the intelligence of the Demiurge or the intelligibility of the Forms.
More particularly, it is from time that we learn number. It is for this reason that time is said to have been created. By learning number, we are set on the way up the path of higher education as laid out in Republic VII, where the orderly progression through the study of arithmetic, geometry, stereometry, astronomy, and harmonics is the course to reach dialectics and unhypothetical knowledge.
The core project of the Demiurge is to create two earthly standards—the rational World Soul as conveyed by the World Body and time viewed as a cluster of clocks.
The first movement of the Timaeus draws to a close with an elaborate account of vision, the very means by which we lowly but potentially rational creatures access these reason-generating standards—the heavens, their numbered motions, and their collective rationality.
The second movement of the Timaeus is cued by a problem left over in the furniture of the universe as it stood before the Demiurge began intervening into the world. The problem has something to do with the blooming buzzing confusion of the phenomenal realm. If the phenomena are in a universal flux, if, that is as Plato holds, earth, air, fire, and water are not eternal, inalterable, indivisible Democritean atoms, but transform into each other ceaselessly and in every moment, then how can we identify something as being any one of these rather than some other type of thing? It, whatever it is, say, water, may as well be and be called fire or air as water. Put generally, if each thing is transforming at every moment into every sort of thing, then we are not capable of saying what type of thing anything is.
The flux, which engines the resistance that the world presents to the Demiurge’s projects here, draws into doubt its intelligibility for everyone. In order to solve this problem, Timaeus says that he has to invoke an additional stick of cosmic furniture, which like the Demiurge, Forms, and flux, existed before the orderly heavens were formed. This additional thing is called the Receptacle of all becoming. It is something in which or across which the flux of the phenomena takes place. Indeed it is also called “place” or “space”—the single Greek word for both is chôra. The Receptacle is chiefly characterized through a series of metaphors. It provides a place for sitting. It is a nurse, foster-mother, or (simply) mother—in contrast to the Forms, which are analogized to a Father, and to the phenomena, which, to complete the extended nuclear-family metaphor, are analogized to offspring. It is like a waxy substance that can receive impressions or a perfume base. In both of these cases, the relevant salient feature of the analogy is made explicit by Plato—the base or substrate must be perfectly characterless, lest it impose its properties onto the things it receives. One would not use as a base for a rose scent an unguent that smells of musk. The efficient perfumer would want to have on hand a base, like case, that would take on and then release any scent while contributing nothing of itself to the odor of the product. It is a vehicle for scent, but does not enter into the scent. Each phenomenon is necessarily in the Receptacle, but then it is necessarily not in them, since “in” is an asymmetrical relation. The receptacle is all receiving, receives all characteristics, and so must itself be characterless. It facilitates the presence of the phenomena, but is not part of that presence.
That said, there have been critical storms going clear back to the Academy over what metaphysical function or functions the Receptacle has. But of late, a consensus of critics, including several writing on the Receptacle in this volume, is forming up around the view that Plato hypothesizes the Receptacle of all becoming in order to explain the status of phenomena as (insubstantial) images of the Forms. Phenomenal objects in the Timaeus have the same metaphysical status as phenomenal objects in the central books of the Republic, where they are famously analogized to shadows on the wall of a cave and to reflections on water or in mirrors. In all these cases of images, but unlike photographic images or marble statues, the image, in order to exist, requires both the persistence of its original and a medium across which it can flicker.
The problem that was left over from the first part of Timaeus’ speech was that flux draws the intelligibility, even existence, of the phenomena into doubt. Flux makes the phenomena self-contradictory. At one and the same time and in the same respect, a thing in flux is both fire and not-fire. But now, with the phenomena understood as images appearing in a medium, the phenomena can be ‘saved’ and the problem solved. For now in their second aspect as images, the phenomena can be accurately described by reference to the Forms of which they are instances. They are saved from utter unintelligibility—and from utter non-existence as well.
As images, they do not fully exist; they are not freestanding beings. Their existence is dependent on both the persistence of Forms and the existence of space. And yet they are there to be pointed at; they are not bottomless void, emptiness, nothingness. In the Timaeus at least, Plato’s understanding of existence is basically locative. To exist is to be somewhere on pain of being nothing at all. The Forms and space fully exist because neither of them is dependent upon anything else. They are freestanding, there to be pointed at independently of anything else. Still, since what we see of the Receptacle is not the Receptacle itself, but the dream-like images in it, it is not fully knowable in the way the Forms are. If we see Forms head on, as it were, we see them as they are. They are self-revealing and incapable of deception. In contrast, we are said to know the Receptacle by a sort of bastard reasoning. In our cognition, the Receptacle is a product of hypothetical inference, not direct acquaintance. These dream-like images must be somewhere, what that somewhere is is the Receptacle of space.
Still, lots of controversy continues, including in the pages of this collection, over the nature and status of the Receptacle, especially over whether it makes sense to think of the Receptacle, in the way Aristotle did, as a material cause, as that out of which the phenomena are (made) and which persists through the changes of a phenomenon. An additional metaphor given for the Receptacle is that it is like gold out of which geometrical shapes can be ceaselessly remolded. What is the salient detail here? The out-of-which claim? Or the ceaseless-remolding claim?
Finally, there is controversy over the last metaphor that Timaeus gives for the Receptacle. He says that it shakes like a winnowing basket that separates kernels of grain. More particularly, the Receptacle is said to be shaken by the phenomena in it and, in turn, to shake them. Is this shaking to be read literally? Nearly all critics now, including all the contributors to this collection who weigh in on the subject, take the claim that the Receptacle shakes at face value, even though this seems to collide directly with the repeated claims that the Receptacle contributes no content to its contents. Motions characterize, even define, many things in the Receptacle. In the Sophist, there is a Form of motion. Its instances are in the Receptacle. How can all these claims be squared? To address these sorts of worries, God invented scholars.
Another consensus that is forming and that registers in this volume has to do with the characterization of the primary bodies (earth, air, fire, and water) in the pre-cosmic Receptacle. The background: In the Demiurgically ruled world, each primary body is equated with one of the five possible Platonic solids, that is, the five types of stereometric bodies that have both regular faces and regular vertices. So, for instance, the octahedron is a Platonic solid, but the double tetrahedron (or triangular hexahedron) is not, because some of its vertices have three sides coming together, others four. Plato views the regular ‘solids’ as made up of just their depthless faces. A particle of earth is an empty cube with sides that can and sometimes do come totally unhinged. Fire is an empty tetrahedron, whose sides of equilateral triangles can and do come totally unhinged. And so on with the icosahedron of water and octahedron of air. Primary bodies come unhinged as the result of their crushing and cutting each other in the rough and tumble of the phenomenal flux.
Since instances of the last three (fire, air, water) are all made of equilateral triangles, when their triangles come unhinged, they can recombine either as the type of particle they formed before (fire recombines as fire) or as one of the other two primary bodies with triangular faces (fire recombines, with additional unhinged triangles, to form air or water). This recombinant geometry is how Plato explains the resolution of the primary bodies into each other, a phenomenon that Plato thinks needs to be saved on any explanatory model of the physical world. The endless resolution of the four primary particles into each other essentially characterizes the flux of the phenomena. But how can all these claims be compatible with the theo-physics of the first part of the discourse, even if we acknowledge, as Plato does, that the atomic account is inadequate because it necessarily leaves earth, with its square sides, outside the primary bodies’ cycle of resolutions.
Here is the puzzle more precisely: if order is the exclusive product of the Demiurge and the geometrical orderings of the Platonic solids are necessary to explain the pre-cosmic flux of the world before the Demiurge’s interventions into it, then we seem to have a contradiction. The contradiction can be avoided if the primary bodies are viewed as existing in less than fully geometrized forms in the pre-cosmos: they are geometrical enough to produce the inter-body resolutions of the flux, but not so perfect that they can’t be improved upon. And indeed later in the dialogue, we hear of the weak and warped triangles from which some primary bodies are constituted. Further, even at their introduction, the primary bodies are said to have “traces” of their natures prior to the interventions of the Demiurge. What these traces are are foreshadowings of the fully geometrical natures that they will have when the Demiurge does intervene; they are approximations to perfect instantiations of their Ideal geometries (the Form of fire, of earth, etc). That phenomenal earth, air, fire, and water exist as mathematical entities is a direct result of their Forms casting images of themselves across the medium of space. But they are imperfect tetrahedrons, octahedrons, etc. The dispersion of the geometrical, though imperfect, images of the primary bodies occurs without help from the Demiurge.
The emerging critical consensus is that the primary bodies do indeed exist in their geometrized form in the pre-cosmos. See the essays by Alan Code and Verity Harte. That the primary bodies are geometrized in the pre-cosmos has two important consequences. First, it turns out paradoxically that some order is a precondition of disorder. Underlying the flux of the phenomena is the geometry of the primary bodies. Their basic geometry is not dependent upon the Demiurge. This, in turn, explains why the Timaeus is not framed as a teleological argument for the existence of god. It gives no argument from design. God is simply presumed, not argued for. Depending on one’s metaphysical sympathies, one might argue from geometrical order to Forms, holding that orderly mathematical objects can only exist if there are Forms of them, but in the Timaeus’ view, one can legitimately claim that there is quite a lot of order in the world, necessarily so, independently of the Demiurge—even though that world is also properly called chaotic.
Second, from the geometric status of the primary bodies in the pre-cosmos, we learn more clearly about the manner in which the Demiurge goes about improving things. It is not by imposing order where there was none before, but rather it is the sort of ordering that takes something that falls away from a standard and brings it (more) fully into accord with it, a bit like straightening out a knife blade that has become bent. The Demiurge does not impose form on characterless matter. He improves things by tinkering and adjusting proportions and measures that already exist. If the World Body is running a fever, he lowers its temperature. But at each and every moment of the Body, whether fevered, chilled, or hale, it has a determinate temperature. At any moment, it is as ‘formed’ as it is at any other moment. If, as seems to be entertained in the cosmological myth of the Statesman, the World Soul eventually begins gradually to gyrate off center, the Demiurge brings it back on course, makes its rotations perfect again.
The Receptacle of space and the geometrized bodies of the Timaeus have fascinated Platonic scholarship. Six contributions to this collection have these topics as their points of departure—those of Donald Zeyl, Verity Harte, Alan Code, Stephen Menn, Ian Mueller, and Zina Giannopoulou. These topics have fascinated still others, not just physicists, classicists, and philosophers, but literary theorists and architects as well. In 1974, the literary theorist and litterateur Julia Kristeva wrote a germinal essay on Plato’s Receptacle of space in her book Revolution in Poetic Language. The essay takes the shaking of the Receptacle literally and links it to Plato’s many female metaphors for space—nurse, foster-mother, mother. The resulting position views the shaking not as a part of the workings of chaos, but as a distinctive generative principle, a source of creativity, a particularly female form of creativity, one which on the plane of meaning communicates by showing rather than telling, one that operates by signs and indicators rather than symbols, and which has certain parallels to the Freudian subconscious.
This cluster of Platonically inspired ideas has had a widespread and abiding afterlife especially within the Continental tradition—in linguistics, literary theory, psychiatry, and, as it turns out, architecture. The architect Peter Eisenman and the philosopher Jacques Derrida jointly created an architectural design, based on their understanding of Platonic space, for a garden within Paris’ Parc de la Villette (general architect, Bernard Tschumi, 1982–1993) and produced an important testamentary book on the project, Chora L Works (1997). Architectural historian Anthony Vidler made the project a core of his 2005 memorial to Derrida, while architect and classicist Ann Bergren condemned the project as hopelessly confused, degrading to women, and having entirely missed the Timaeus’ potentials. Both authors are represented in this volume with new essays tracking the positive influences of the Timaeus on modern architectural theory and practice. Additionally, Zina Giannopoulou’s essay directly addresses Derrida’s views on Platonic space.
The later reaches of the Timaeus have drawn far less attention than its opening two sections, those on the works of reason and the effects of necessity. The official program of the last third of the Timaeus sounds grand enough: it is to present a synthesis of reason and necessity operating cooperatively. But its content is deflationary when compared to what has gone before. The objects of the grand synthesis are largely just the bodily structures and processes of humans and other animals: the formation of the abdomen, marrow, hair, and sinews; the mechanisms of respiration and digestion; diseases involving air, phlegm, and bile—topics like that. Admittedly, this is not sexy stuff compared to god, time, and space. But all of the biology is built off of the chemistry of the primary particles, and so even when the text seems playful or wacky in its details—it is, after all, based on an atomic story that Plato knows will, at the end of the scientific day, not remain on the table of possibly true theories—it contains a suggestive reductionist account of biology, the model that predominates in contemporary science: if we remove talk of both souls and values from the discourses of nature, then biological properties (cell division, leaves turning red in the Fall, etc.) can be exhaustively analyzed into chemical properties, which are exhaustively reducible to properties of physics. Plato will not let us get strongly emergent or supervenient properties, like consciousness, mind, and free will, on the cheap. These things will not easily percolate up from Democritean atoms and the void, and they certainly will not bubble up from Plato’s geometrized particles and the Receptacle. For Plato, it is physics and God that do the explaining in the realm animate beings with functions and goals. If a sum is greater than its parts in the physical realm, that is God’s doing. There are things still to think about in the third part of the Timaeus, but, not surprisingly, none of the contributors to this volume focus on it.