The new starting point in my account of the universe needs to be more complex than the earlier one. Then we distinguished two kinds, but now we must specify a third, one of a different sort. The earlier two sufficed for our previous account: one was proposed as a model, intelligible and always changeless, a second as an imitation of the model, something that [49] possesses becoming and is visible. We did not distinguish a third kind at the time, because we thought that we could make do with the two of them. Now, however, it appears that our account compels us to attempt to illuminate in words a kind that is difficult and vague. What must we suppose it to do and to be? This above all: it is a receptacle of all becoming—its wetnurse, as it were.
However true that statement may be, we must nevertheless describe it more clearly. This is a difficult task, particularly because it requires us to [b] raise a preliminary problem about fire and the other three:
It is difficult to say of each of them—in a way that employs a reliable and stable account—which one is the sort of thing one should really call water rather than fire, or which one one should call some one of these rather than just any and every one of them. What problem, then, do they present for us to work through in likely fashion? And then how and in what manner are we to go on to speak about this third kind?
First, we see (or think we see) the thing that we have just now been [c] calling water condensing and turning to stones and earth. Next, we see this same thing dissolving and dispersing, turning to wind and air, and air, when ignited, turning to fire. And then we see fire being condensed and extinguished and turning back to the form of air, and air coalescing and thickening and turning back into cloud and mist. When these are compressed still more we see them turning into flowing water, which we see turning to earth and stones once again. In this way, then, they transmit their coming to be one to the other in a cycle, or so it seems. Now then, [d] since none of these appears ever to remain the same, which one of them can one categorically assert, without embarrassment, to be some particular thing, this one, and not something else? One can’t. Rather, the safest course by far is to propose that we speak about these things in the following way: what we invariably observe becoming different at different times—fire for example—to characterize that, i.e., fire, not as “this,” but each time as “what is such,” and speak of water not as “this,” but always as “what is such.” And never to speak of anything else as “this,” as though it has [e] some stability, of all the things at which we point and use the expressions “that” and “this” and so think we are designating something. For it gets away without abiding the charge of “that” and “this,” or any other expression that indicts them of being stable. It is in fact safest not to refer to it by any of these expressions. Rather, “what is such”—coming around like what it was, again and again—that’s the thing to call it in each and every case. So fire—and generally everything that has becoming—it is safest to call “what is altogether such.” But that in which they each appear to keep coming into being and from which they subsequently pass out of being, [50] that’s the only thing to refer to by means of the expressions “that” and “this.” A thing that is some “such” or other, however,—hot or white, say, or any one of the opposites, and all things constituted by these—should be called none of these things [i.e., “this” or “that”].27
I must make one more effort to describe it, more clearly still. Suppose you were molding gold into every shape there is, going on non-stop remolding one shape into the next. If someone then were to point at one of them and ask you, “What is it?,” your safest answer by far, with respect [b] to truth, would be to say, “gold,” but never “triangle” or any of the other shapes that come to be in the gold, as though it is these, because they change even while you’re making the statement. However, that answer, too, should be satisfactory, as long as the shapes are willing to accept “what is such” as someone’s designation. This has a degree of safety.
Now the same account, in fact, holds also for that nature which receives all the bodies. We must always refer to it by the same term, for it does not depart from its own character in any way. Not only does it always receive all things, it has never in any way whatever taken on any characteristic [c] similar to any of the things that enter it. Its nature is to be available for anything to make its impression upon, and it is modified, shaped and reshaped by the things that enter it. These are the things that make it appear different at different times. The things that enter and leave it are imitations of those things that always are, imprinted after their likeness in a marvellous way that is hard to describe. This is something we shall pursue at another time. For the moment, we need to keep in mind three types of things: that which comes to be, that in which it comes to be, and [d] that after which the thing coming to be is modeled, and which is the source of its coming to be. It is in fact appropriate to compare the receiving thing to a mother, the source to a father, and the nature between them to their offspring. We also must understand that if the imprints are to be varied, with all the varieties there to see, this thing upon which the imprints are to be formed could not be well prepared for that role if it were not itself devoid of any of those characters that it is to receive from elsewhere. For [e] if it resembled any of the things that enter it, it could not successfully copy their opposites or things of a totally different nature whenever it were to receive them. It would be showing its own face as well. This is why the thing that is to receive in itself all the elemental kinds must be totally devoid of any characteristics. Think of people who make fragrant ointments. They expend skill and ingenuity to come up with something just like this [i.e., a neutral base], to have on hand to start with. The liquids that are to receive the fragrances they make as odorless as possible. Or think of people who work at impressing shapes upon soft materials. They emphatically refuse to allow any such material to already have some definite shape. Instead, they’ll even it out and make it as smooth as it can be. In the same [51] way, then, if the thing that is to receive repeatedly throughout its whole self the likenesses of the intelligible objects, the things which always are28—if it is to do so successfully, then it ought to be devoid of any inherent characteristics of its own. This, of course, is the reason why we shouldn’t call the mother or receptacle of what has come to be, of what is visible or perceivable in every other way, either earth or air, fire or water, or any of their compounds or their constituents. But if we speak of it as an invisible [b] and characterless sort of thing, one that receives all things and shares in a most perplexing way in what is intelligible, a thing extremely difficult to comprehend, we shall not be misled. And in so far as it is possible to arrive at its nature on the basis of what we’ve said so far, the most correct way to speak of it may well be this: the part of it that gets ignited appears on each occasion as fire, the dampened part as water, and parts as earth or air in so far as it receives the imitations of these.
But we must prefer to conduct our inquiry by means of rational argument. Hence we should make a distinction like the following: Is there such a thing as a Fire by itself? Do all these things of which we always say that [c] each of them is something “by itself” really exist? Or are the things we see, and whatever else we perceive through the body, the only things that possess this kind of actuality, so that there is absolutely nothing else besides them at all? Is our perpetual claim that there exists an intelligible Form for each thing a vacuous gesture, in the end nothing but mere talk? Now we certainly will not do justice to the question before us if we dismiss it, leaving it undecided and unadjudicated, and just insist that such things [d] exist, but neither must we append a further lengthy digression to a discourse already quite long. If, however, a significant distinction formulated in few words were to present itself, that would suit our present needs best of all. So here’s how I cast my own vote: If understanding and true opinion are distinct, then these “by themselves” things definitely exist—these Forms, the objects not of our sense perception, but of our understa
nding only. But if—as some people think—true opinion does not differ in any way from understanding, then all the things we perceive through our [e] bodily senses must be assumed to be the most stable things there are. But we do have to speak of understanding and true opinion as distinct, of course, because we can come to have one without the other, and the one is not like the other. It is through instruction that we come to have understanding, and through persuasion that we come to have true belief. Understanding always involves a true account while true belief lacks any account. And while understanding remains unmoved by persuasion, true belief gives in to persuasion. And of true belief, it must be said, all men have a share, but of understanding, only the gods and a small group of people do.
[52] Since these things are so, we must agree that that which keeps its own form unchangingly, which has not been brought into being and is not destroyed, which neither receives into itself anything else from anywhere else, nor itself enters into anything else anywhere, is one thing. It is invisible—it cannot be perceived by the senses at all—and it is the role of understanding to study it. The second thing is that which shares the other’s name and resembles it. This thing can be perceived by the senses, and it has been begotten. It is constantly borne along, now coming to be in a certain place and then perishing out of it. It is apprehended by opinion, which involves sense perception. And the third type is space, which exists always and cannot be destroyed. It provides a fixed state for all things [b] that come to be. It is itself apprehended by a kind of bastard reasoning that does not involve sense perception, and it is hardly even an object of conviction. We look at it as in a dream when we say that everything that exists must of necessity be somewhere, in some place and occupying some space, and that that which doesn’t exist somewhere, whether on earth or in heaven, doesn’t exist at all.
We prove unable to draw all these distinctions and others related to them—even in the case of that unsleeping, truly existing reality—because our dreaming state renders us incapable of waking up and stating the [c] truth, which is this: Since that for which an image has come to be is not at all intrinsic to the image, which is invariably borne along to picture something else, it stands to reason that the image should therefore come to be in something else, somehow clinging to being, or else be nothing at all. But that which really is receives support from the accurate, true account—that as long as the one is distinct from the other, neither of them ever comes to be in the other in such a way that they at the same time [d] become one and the same, and also two.
Let this, then, be a summary of the account I would offer, as computed by my “vote.” There are being, space, and becoming, three distinct things which existed even before the universe came to be.
Now as the wetnurse of becoming turns watery and fiery and receives [e] the character of earth and air, and as it acquires all the properties that come with these characters, it takes on a variety of visible aspects, but because it is filled with powers that are neither similar nor evenly balanced, no part of it is in balance. It sways irregularly in every direction as it is shaken by those things, and being set in motion it in turn shakes them. And as they are moved, they drift continually, some in one direction and others in others, separating from one another. They are winnowed out, as it were, like grain that is sifted by winnowing sieves or other such implements. They are carried off and settle down, the dense and heavy ones in [53] one direction, and the rare and light ones to another place.
That is how at that time the four kinds were being shaken by the receiver, which was itself agitating like a shaking machine, separating the kinds most unlike each other furthest apart and pushing those most like each other closest together into the same region. This, of course, explains how these different kinds came to occupy different regions of space, even before the universe was set in order and constituted from them at its coming to be. Indeed, it is a fact that before this took place the four kinds all lacked [b] proportion and measure, and at the time the ordering of the universe was undertaken, fire, water, earth and air initially possessed certain traces of what they are now. They were indeed in the condition one would expect thoroughly god-forsaken things to be in. So, finding them in this natural condition, the first thing the god then did was to give them their distinctive shapes, using forms and numbers.
Here is a proposition we shall always affirm above all else: The god fashioned these four kinds to be as perfect and excellent as possible, when they were not so before. It will now be my task to explain to you what [c] structure each of them acquired, and how each came to be. My account will be an unusual one, but since you are well schooled in the fields of learning in terms of which I must of necessity proceed with my exposition, I’m sure you’ll follow me.
First of all, everyone knows, I’m sure, that fire, earth, water and air are bodies. Now everything that has bodily form also has depth. Depth, moreover, is of necessity comprehended within surface, and any surface bounded by straight lines is composed of triangles. Every triangle, moreover, [d] derives from two triangles, each of which has one right angle and two acute angles. Of these two triangles, one [the isosceles right-angled triangle] has at each of the other two vertices an equal part of a right angle, determined by its division by equal sides; while the other [the scalene right-angled triangle] has unequal parts of a right angle at its other two vertices, determined by the division of the right angle by unequal sides. This, then, we presume to be the originating principle of fire and of the other bodies, as we pursue our likely account in terms of Necessity. Principles yet more ultimate than these are known only to the god, and to any man he may hold dear.
[e] We should now say which are the most excellent four bodies that can come to be. They are quite unlike each other, though some of them are capable of breaking up and turning into others and vice-versa. If our account is on the mark, we shall have the truth about how earth and fire and their proportionate intermediates [water and air] came to be. For we shall never concede to anyone that there are any visible bodies more excellent than these, each conforming to a single kind. So we must wholeheartedly proceed to fit together the four kinds of bodies of surpassing excellence, and to declare that we have come to grasp their natures well enough.
[54] Of the two [right-angled] triangles, the isosceles has but one nature, while the scalene has infinitely many. Now we have to select the most excellent one from among the infinitely many, if we are to get a proper start. So if anyone can say that he has picked out another one that is more excellent for the construction of these bodies, his victory will be that of a friend, not an enemy. Of the many [scalene right-angled] triangles, then, we posit as the one most excellent, surpassing the others, that one from [a pair of] which the equilateral triangle is constructed as a third figure. Why this is so is too long a story to tell now. But if anyone puts this [b] claim to the test and discovers that it isn’t so, his be the prize, with our congratulations. So much, then, for the selection of the two triangles out of which the bodies of fire and the other bodies are constructed—the [right-angled] isosceles, and [the right-angled] scalene whose longer side squared is always triple its shorter side squared [i.e., the half-equilateral].
At this point we need to formulate more precisely something that was not stated clearly earlier. For then it appeared that all four kinds of bodies could turn into one another by successive stages.29 But the appearance is wrong. While there are indeed four kinds of bodies that come to be from [c] the [right-angled] triangles we have selected, three of them come from triangles that have unequal sides, whereas the fourth alone is fashioned out of isosceles triangles. Thus not all of them have the capacity of breaking up and turning into one another, with a large number of small bodies turning into a small number of large ones and vice-versa. There are three that can do this. For all three are made up of a single type of triangle, so that when once the larger bodies are broken up, the same triangles can go to make up a large number of small bodies, assuming shapes appropriate to them. And likewis
e, when numerous small bodies are fragmented into [d] their triangles, these triangles may well combine to make up some single massive body belonging to another kind.
So much, then, for our account of how these bodies turn into one another. Let us next discuss the form that each of them has come to have, and the various numbers that have combined to make them up.
Leading the way will be the primary form [the tetrahedron], the tiniest structure, whose elementary triangle is the one whose hypotenuse is twice the length of its shorter side. Now when a pair of such triangles are juxtaposed along the diagonal [i.e., their hypotenuses] and this is done three times, and their diagonals and short sides converge upon a single [e] point as center, the result is a single equilateral triangle, composed of six such triangles. When four of these equilateral triangles are combined, a single solid angle is produced at the junction of three plane angles. This, [55] it turns out, is the angle which comes right after the most obtuse of the plane angles.30 And once four such solid angles have been completed, we get the primary solid form, which is one that divides the entire circumference [sc. of the sphere in which it is inscribed] into equal and similar parts.
Complete Works Page 190
