Complete Works

by Plato, Cooper, John M. , Hutchinson, D. S.

  The second solid form [the octahedron] is constructed out of the same triangles which, however, are now arranged in eight equilateral triangles and produce a single solid angle out of four plane angles. And when six such solid angles have been produced, the second body has reached its completion.

  Now the third body [the icosahedron] is made up of a combination of one hundred and twenty of the elementary triangles, and of twelve solid [b] angles, each enclosed by five plane equilateral triangles. This body turns out to have twenty equilateral triangular faces. And let us take our leave of this one of the elementary triangles, the one that has begotten the above three kinds of bodies and turn to the other one, the isosceles [right-angled] triangle, which has begotten the fourth [the cube]. Arranged in sets of four whose right angles come together at the center, the isosceles triangle produced a single equilateral quadrangle [i.e., a square]. And when six of [c] these quadrangles were combined together, they produced eight solid angles, each of which was constituted by three plane right angles. The shape of the resulting body so constructed is a cube, and it has six quadrangular equilateral faces.

  One other construction, a fifth, still remained, and this one the god used for the whole universe, embroidering figures on it.31

  Anyone following this whole line of reasoning might very well be puzzled about whether we should say that there are infinitely many worlds [d] or a finite number of them. If so, he would have to conclude that to answer, “infinitely many,” is to take the view of one who is really “unfinished” in things he ought to be “finished” in. He would do better to stop with the question whether we should say that there’s really just one world or five and be puzzled about that. Well, our “probable account” answer declares there to be but one world, a god—though someone else, taking other things into consideration, will come to a different opinion. We must set him aside, however.

  Let us now assign to fire, earth, water and air the structures which have just been given their formations in our speech. To earth let us give the [e] cube, because of the four kinds of bodies earth is the most immobile and the most pliable—which is what the solid whose faces are the most secure must of necessity turn out to be, more so than the others. Now of the [right-angled] triangles we originally postulated, the face belonging to those that have equal sides has a greater natural stability than that belonging to triangles that have unequal sides, and the surface that is composed of the two triangles, the equilateral quadrangle [the square], holds its position with greater stability than does the equilateral triangle, both in [56] their parts and as wholes. Hence, if we assign this solid figure to earth, we are preserving our “likely account.” And of the solid figures that are left, we shall next assign the least mobile of them to water, to fire the most mobile, and to air the one in between. This means that the tiniest body belongs to fire, the largest to water, and the intermediate one to air—and also that the body with the sharpest edges belongs to fire, the next sharpest to air, and the third sharpest to water. Now in all these cases the body that has the fewest faces is of necessity the most mobile, in that it, more [b] than any other, has edges that are the sharpest and best fit for cutting in every direction. It is also the lightest, in that it is made up of the least number of identical parts. The second body ranks second in having these same properties, and the third ranks third. So let us follow our account, which is not only likely but also correct, and take the solid form of the pyramid that we saw constructed as the element or the seed of fire. And let us say that the second form in order of generation is that of air, and the third that of water.

  Now we must think of all these bodies as being so small that due to their small size none of them, whatever their kind, is visible to us individually. [c] When, however, a large number of them are clustered together, we do see them in bulk. And in particular, as to the proportions among their numbers, their motions and their other properties, we must think that when the god had brought them to complete and exact perfection (to the degree that Necessity was willing to comply obediently), he arranged them together proportionately.

  Given all we have said so far about the kinds of elemental bodies, the following account [of their transformations] is the most likely: When earth [d] encounters fire and is broken up by fire’s sharpness, it will drift about—whether the breaking up occurred within fire itself, or within a mass of air or water—until its parts meet again somewhere, refit themselves together and become earth again. The reason is that the parts of earth will never pass into another form. But when water is broken up into parts by fire or even by air, it could happen that the parts recombine to form one corpuscle of fire and two of air. And the fragments of air could produce, [e] from any single particle that is broken up, two fire corpuscles. And conversely, whenever a small amount of fire is enveloped by a large quantity of air or water or perhaps earth and is agitated inside them as they move, and in spite of its resistance is beaten and shattered to bits, then any two fire corpuscles may combine to constitute a single form of air. And when air is overpowered and broken down, then two and one half entire forms of air will be consolidated into a single, entire form of water.

  Let us recapitulate and formulate our account of these transformations as follows: Whenever one of the other kinds is caught inside fire and gets [57] cut up by the sharpness of fire’s angles and edges, then if it is reconstituted as fire, it will stop getting cut. The reason is that a thing of any kind that is alike and uniform is incapable of effecting any change in, or being affected by, anything that is similar to it. But as long as something involved in a transformation has something stronger than it to contend with, the process of its dissolution will continue non-stop. And likewise, when a few of the smaller corpuscles are surrounded by a greater number of bigger [b] ones, they will be shattered and quenched. The quenching will stop when these smaller bodies are willing to be reconstituted into the form of the kind that prevailed over them, and so from fire will come air, and from air, water. But if these smaller corpuscles are in process of turning into these and one of the other kinds encounters them and engages them in battle, their dissolution will go on non-stop until they are either completely squeezed and broken apart and escape to their own likes, or else are defeated, and, melding from many into one, they are assimilated to the kind that prevailed over them, and come to share its abode from then on. [c] And, what is more, as they undergo these processes, they all exchange their territories: for as a result of the Receptacle’s agitation the masses of each of the kinds are separated from one another, with each occupying its own region, but because some parts of a particular kind do from time to time become unlike their former selves and like the other kinds, they are carried by the shaking towards the region occupied by whatever masses they are becoming like to.

  These, then, are the sorts of causes by which the unalloyed primary bodies have come to be. Now the fact that different varieties are found within their respective forms is to be attributed to the constructions of [d] each of the elementary triangles. Each of these two constructions did not originally yield a triangle that had just one size, but triangles that were both smaller and larger, numerically as many as there are varieties within a given form. That is why when they are mixed with themselves and with each other they display an infinite variety, which those who are to employ a likely account in their study of nature ought to take note of.

  Now as for motion and rest, unless there is agreement on the manner and the conditions in which these two come to be, we will have many [e] obstacles to face in our subsequent course of reasoning. Although we have already said something about them, we need to say this as well: there will be no motion in a state of uniformity. For it is difficult, or rather impossible, for something to be moved without something to set it in motion, or something to set a thing in motion without something to be moved by it. When either is absent, there is no motion, but [when they are present] it is quite impossible for them to be uniform. And so let us always presume that rest is found in a state
of uniformity and to attribute motion to non-uniformity. 58 The latter, moreover, is caused by inequality, the origin of which we have already discussed.32 We have not explained, however, how it is that the various corpuscles have not reached the point of being thoroughly separated from each other kind by kind, so that their transformations into each other and their movement [toward their own regions] would have come to a halt. So let us return to say this about it: Once the circumference of the universe has comprehended the [four] kinds, then, because it is round and has a natural tendency to gather in upon itself, it constricts them all and allows no empty [b] space to be left over. This is why fire, more than the other three, has come to infiltrate all of the others, with air in second place, since it is second in degree of subtlety, and so on for the rest. For the bodies that are generated from the largest parts will have the largest gaps left over in their construction, whereas the smallest bodies will have the tiniest. Now this gathering, contracting process squeezes the small parts into the gaps inside the big ones. So now, as the small parts are placed among the large ones and the smaller ones tend to break up the larger ones while the larger tend to cause the smaller to coalesce, they all shift, up and down, into their own respective regions. For as each changes in quantity, it also changes the [c] position of its region. This, then, is how and why the occurrence of non-uniformity is perpetually preserved, and so sets these bodies in perpetual motion, both now and in the future without interruption.

  Next, we should note that there are many varieties of fire that have come to be. For example, there is both flame and the effluence from flame which, while it doesn’t burn, gives light to the eyes. And then there is the residue of flame which is left in the embers when the flame has gone out. [d] The same goes for air. There is the brightest kind that we call “aether,” and also the murkiest, “mist” and “darkness.” Then there are other, nameless sorts which result from inequality among the triangles. The varieties of water can first of all be divided into two groups, the liquid and the liquifiable. Because the former possesses water parts that are not only unequal but also small, it turns out to be mobile, both in itself and when acted upon by something else. This is due to its non-uniformity and the configuration of its shape. The other type of water, composed of large and [e] uniform kinds, is rather more immobile and heavy, compacted as it is by its uniformity. But when fire penetrates it and begins to break it up, it loses its uniformity, and once that is lost it is more susceptible to motion. When it has become quite mobile it is spread out upon the ground under pressure from the air surrounding it. Each of these changes has its own name: “melting” for the disintegration of its bulk and “flowing” for the spreading on the ground. But when, conversely, the fire is expelled from [59] it, then, since the fire does not pass into a void, pressure is exerted upon the surrounding air, which in turn compresses the still mobile liquid mass into the places previously occupied by the fire and mixes it with itself. As it is being compressed, the mass regains its uniformity now that fire, the agent of non-uniformity, has left the scene, and it resettles into its own former state. The departure of the fire is called “cooling,” and the compression that occurs when the fire is gone is called “jelling.” Of all these types of water that we have called liquifiable, the one that consists of the finest, [b] the most uniform parts and has proved to be the most dense, one that is unique in its kind and tinged with brilliant yellow, is gold, our most precious possession, filtered through rocks and thereby compacted. And gold’s offshoot, which because of its density is extremely hard and has a black color, is called adamant. Another has parts that approximate gold and comes in more than one variety. In terms of density, it is in one way denser than gold and includes a small, fine part of earth, so that it is harder. But it is actually lighter than gold, because it has large gaps inside [c] of it. This, it turns out, is copper, one variety of the bright, jelled kinds of water. Whenever the earth part of the mixture separates off again from the rest in the passage of time, this part, called verdigris, becomes visible by itself.

  As for going further and giving an account of other stuffs of this sort along the lines of the likely stories we have been following, that is no complicated matter. And should one take a break and lay aside accounts [d] about the things that always are, deriving instead a carefree pleasure from surveying the likely accounts about becoming, he would provide his life with a moderate and sensible diversion. So shall we, then, at this time give free rein to such a diversion and go right on to set out the next likelihoods on these subjects, as follows:

  Take now the water that is mixed with fire. It is fine and liquid and on account of its mobility and the way it rolls over the ground it is called “liquid.” It is soft, moreover, in that its faces, being less firm than those [e] of earth, give way to it. When this water is separated from its fire and air and is isolated, it becomes more uniform, and it is pressed together into itself by the things that leave it. So compacted, the water above the earth which is most affected by this change turns to hail, while that on earth turns to ice. Some water is not affected quite so much, being still only half compacted. Such water above the earth becomes snow while that on the earth becomes what is called “frost,” from dew that is congealed.

  Now most of the varieties of water which are mixed with one another [60] are collectively called “saps,” because they have been filtered through plants that grow out of the earth. Because they are mixed, each of them has its own degree of non-uniformity. Many of these varieties are nameless, though four of them, all with fire in them, are particularly conspicuous and so have been given names. First, there is wine, which warms not only the body but the soul as well. Second, there are the various oils, which are smooth and divide the ray of sight and for that reason glisten, appearing bright and shiny to the eye: these include resin, castor oil, olive oil and [b] others that share their properties. And third, there is what is most commonly called honey, which includes all that relaxes the taste passages of the mouth back to their natural state, and which by virtue of this property conveys a sense of sweetness. Fourth, there is what has been named tart juice, quite distinct from all the other saps. It is a foamy stuff, and is caustic and hence hazardous to the flesh.

  As for the varieties of earth, first, such earth as has been filtered through water turns into a stony body in something like the following way: When the water that is mixed with it disintegrates in the mixing process, it is [c] transformed into the form of air, and, once it has turned into air, it thrusts its way upwards toward its own region. And since there is no void above it, it pushes aside the air next to it. And when this air, heavy as it is, is pressed and poured around the mass of earth, it squeezes it hard and compresses it to fill the places vacated by the recently formed air. When so compressed by air, earth is insoluble in water and constitutes itself as stone. The more beautiful kind of stone is stone that is transparent and made up of equal and uniform parts; the uglier kind is just the opposite. [d] Second, there is the kind of earth from which moisture has been completely expelled by a swiftly burning fire and which thus comes to have a rather more brittle constitution than the first kind of earth. This is a kind to which the name “pottery” has been given. Sometimes, however, moisture gets left in and we get earth that is made liquifiable by fire. When it has cooled it turns to stone that is black in color (i.e., lava). Then, thirdly, there are the two varieties of earth that both alike are the residue of a mixture of a great quantity of water. They are briny, made up of the finest parts of earth, and turn out to be semi-solid and water soluble again. One of these is soda, a cleansing agent against oil and dirt; the other is salt, which is well suited to enhance various blends of flavor and has, not unreasonably, [e] proven itself to be a stuff pleasing to the gods.

  There are also compounds of earth and water which are soluble by fire but not by water.33 These are compacted in this way for the following sort of reason: Neither air nor fire will dissolve masses of earth, because air and fire consist of parts that by na
ture are smaller than are the gaps within earth. They thus pass without constraint through the wide gaps of a mass of earth, leaving it intact and undissolved. But since the parts of water are naturally bigger, they must force their way through, and in so doing they undo and dissolve the earth. For water alone can in this way dissolve [61] earth that isn’t forcibly compressed, but when earth is compressed nothing but fire can dissolve it. That is because fire is the only thing left that can penetrate it. So also, only fire can disperse water that has been compressed with the greatest force, whereas both fire and air can disperse water that is in a looser state. Air does it by entering the gaps, and fire by breaking up the triangles. The only way in which air that has been condensed under force can be broken up is into its elemental triangles, and even when it is not forcibly compressed only fire can dissolve it.

  So as for these bodies that are mixtures of earth and water, as long as the gaps within a given mass of earth are occupied by its own water which [b] is tightly packed within the gaps, the water parts that come charging upon it from the outside have no way of getting into the mass and so flow around the whole of it, leaving it undissolved. The fire parts, however, do penetrate the gaps within the water parts and hence as fire they do to water34 what water did to earth. They alone, it turns out, cause this body, this partnership of earth and water to come apart and become fluid. These compounds of earth and water include not only bodies that have less water in them than earth, such as glass and generally all stone formations that can be called liquifiable, but also bodies that have more water than earth, namely all those that have the consistency of wax or of incense. [c]