Tuesday, June 13, 2006

Selections from Plato's Timaeus
Translated by Benjamin Jowett from
The Collected Works of Plato, Huntington and Cairns (ed.), Princeton U. Press, 1980, p.1176-1181.
Thus far in what we have been saying, with small exceptions, the works of intelligence have been set forth, and now we must place by the side of them in our discourse the things which come into being through necessity--for the creation of this world is the combined work of necessity and mind. Mind, the ruling power, persuaded necessity to bring the greater part of created things to perfection, and thus and after this manner in the beginning, through necessity made subject to reason, this universe was created. But if a person will truly tell of the way in which the work was accomplished, he must include the variable cause as well, and explain its influence. Wherefore, we must return again and find another suitable beginning--as about the former matters, so also about these. To which end we must consider the nature of fire and water and air and earth, such as they were prior to the creation of the heaven, and what was happening to them in this previous state, for no one has as yet explained the manner of their generation, but we speak of fire and the rest of them, as though men knew their natures, and we maintain them to be the first principles and letters or elements of the whole, when they cannot reasonably be compared by a man of any sense even to syllables or first compounds. And let me say thus much. I will not now speak of the first principle or principles of all things, or by whatever name they are to be called, for this reason-- because it is difficult to set forth my opinion according to the method of discussion which we are at present employing. Do not imagine, any more than I can bring myself to imagine, that I should be right in undertaking so great and difficult a task. Remembering what I said at first about probability, I will do my best to give as probable an explanation as any other--or rather, more probable--and I will first go back to the beginning and try to speak of each thing and of all. Once more, then, at the commencement of my discourse, I call upon God and beg him to be our savior out of a strange and unwonted inquiry, and to bring us to the haven of probability. So now let us begin again.
Plato: Timaeus (48e-49b) p 1176
This new beginning of our discussion of the universe requires a fuller division than the former, for then we made two classes; now a third must be revealed. The two sufficed for the former discussion. One, which we assumed, was a pattern intelligible and always the same, and the second was only the imitation of the pattern, generated and visible. There is also a third kind which we did not distinguish at the time, conceiving that the two would be enough. But now the argument seems to require that we should set forth in words another kind, which is difficult of explanation and dimly seen. What nature are we to attribute to this new kind of being? We reply that it is the receptacle, and in a manner the nurse, of all generation. I have spoken the truth, but I must express myself in clearer language, and this will be an arduous task for many reasons, and in particular because I must first raise questions concerning fire and the other elements, and determine what each of them is, for to say, with any probability or certitude, which of them should be called water rather than fire, and which should be called any of them rather than all or some one of them, is a difficult matter. How, then, shall we settle this point, and what questions about the elements may be fairly raised?
Plato: Timaeus (49b-51c) p 1176
In the first place, we see that what we just now called water, by condensation, I suppose, becomes stone and earth, and this same element, when melted and dispersed, passes into vapor and air. Air, again, when inflamed, becomes fire, and, again, fire, when condensed and extinguished, passes once more into the form of air, and once more, air, when collected and condensed, produces cloud and mist--and from these, when still more compressed, comes flowing water, and from water comes earth and stones once more--and thus generation appears to be transmitted from one to the other in a circle. Thus, then, as the several elements never present themselves in the same form, how can anyone have the assurance to assert positively that any of them, whatever it may be, is one thing rather than another? No one can. But much the safest plan is to speak of them as follows. Anything which we see to be continually changing, as, for example, fire, we must not call 'this' or 'that,' but rather say that it is 'of such a nature,' nor let us speak of water as 'this,' but always as 'such,' nor must we imply that there is any stability in any of those things which we indicate by the use of the words 'this' and 'that,' supposing ourselves to signify something thereby, for they are too volatile to be detained in any such expressions as 'this,' or 'that,' or 'relative to this,' or any other mode of speaking which represents them as permanent. We ought not to apply 'this' to any of them, but rather the word 'such,' which expresses the similar principle circulating in each and all of them; for example, that should be called 'fire' which is of such a nature always, and so of everything that has generation. That in which the elements severally grow up, and appear, and decay, is alone to be called by the name 'this' or 'that,' but that which is of a certain nature, hot or white, or anything which admits of opposite qualities, and all things that are compounded of them, ought not to be so denominated. Let me make another attempt to explain my meaning more clearly. Suppose a person to make all kinds of figures of gold and to be always remodeling each form into all the rest; somebody points to one of them and asks what it is. By far the safest and truest answer is, 'That is gold,' and not to call the triangle or any other figures which are formed in the gold 'these,' as though they had existence, since they are in process of change while he is making the assertion, but if the questioner be willing to take the safe and indefinite expression, 'such,' we should be satisfied. And the same argument applies to the universal nature which receives all bodies--that must be always called the same, for, inasmuch as she always receives all things, she never departs at all from her own nature and never, in any way or at any time, assumes a form like that of any of the things which enter into her; she is the natural recipient of all impressions, and is stirred and informed by them, and appears different from time to time by reason of them. But the forms which enter into and go out of her are the likenesses of eternal realities modeled after their patterns in a wonderful and mysterious manner, which we will hereafter investigate. For the present we have only to conceive of three natures: first, that which is in process of generation; secondly, that in which the generation takes place; and thirdly, that of which the thing generated is a resemblance naturally produced. And we may liken the receiving principle to a mother, and the source or spring to a father, and the intermediate nature to a child, and may remark further that if the model is to take every variety of form, then the matter in which the model is fashioned will not be duly prepared unless it is formless and free from the impress of any of those shapes which it is hereafter to receive from without. For if the matter were like any of the supervening forms, then whenever any opposite or entirely different nature was stamped upon its surface, it would take the impression badly, because it would intrude its own shape. Wherefore that which is to receive all forms should have no form, as in making perfumes they first contrive that the liquid substance which is to receive the scent shall be as inodorous as possible, or as those who wish to impress figures on soft substances do not allow any previous impression to remain, but begin by making the surface as even and smooth as possible. In the same way that which is to receive perpetually and through its whole extent the resemblances of all eternal beings ought to be devoid of any particular form. Wherefore the mother and receptacle of all created and visible and in any way sensible things is not to be termed earth or air or fire or water, or any of their compounds, or any of the elements from which these are derived, but is an invisible and formless being which receives all things and in some mysterious way partakes of the intelligible, and is most incomprehensible. In saying this we shall not be far wrong; as far, however, as we can attain to a knowledge of her from the previous considerations, we may truly say that fire is that part of her nature which from time to time is inflamed, and water that which is moistened, and that the mother substance becomes earth and air, in so far as she receives the impressions of them.
Plato: Timaeus (51c-51d) p 1178
Let us consider this question more precisely. Is there any self- existent fire, and do all those things which we call self-existent exist, or are only those things which we see or in some way perceive through the bodily organs truly existent, and nothing whatever besides them? And are those intelligible forms, of which we are accustomed to speak, nothing at all, and only a name? Here is a question which we must not leave unexamined or undetermined, nor must we affirm too confidently that there can be no decision; neither must we interpolate in our present long discourse a digression equally long, but if it is possible to set forth a great principle in a few words, that is just what we want.
Plato: Timaeus (51d-52d) p 1178
Thus I state my view. If mind and true opinion are two distinct classes, then I say that there certainly are these self-existent ideas unperceived by sense, and apprehended only by the mind; if, however, as some say, true opinion differs in no respect from mind, then everything that we perceive through the body is to be regarded as most real and certain. But we must affirm them to be distinct, for they have a distinct origin and are of a different nature; the one is implanted in us by instruction, the other by persuasion; the one is always accompanied by true reason, the other is without reason; the one cannot be overcome by persuasion, but the other can; and lastly, every man may be said to share in true opinion, but mind is the attribute of the gods and of very few men. Wherefore also we must acknowledge that one kind of being is the form which is always the same, uncreated and indestructible, never receiving anything into itself from without, nor itself going out to any other, but invisible and imperceptible by any sense, and of which the contemplation is granted to intelligence only. And there is another nature of the same name with it, and like to it, perceived by sense, created, always in motion, becoming in place and again vanishing out of place, which is apprehended by opinion jointly with sense. And there is a third nature, which is space and is eternal, and admits not of destruction and provides a home for all created things, and is apprehended, when all sense is absent, by a kind of spurious reason, and is hardly real--which we, beholding as in a dream, say of all existence that it must of necessity be in some place and occupy a space, but that what is neither in heaven nor in earth has no existence. Of these and other things of the same kind, relating to the true and waking reality of nature, we have only this dreamlike sense, and we are unable to cast off sleep and determine the truth about them. For an image, since the reality after which it is modeled does not belong to it, and it exists ever as the fleeting shadow of some other, must be inferred to be in another [that is, in space], grasping existence in some way or other, or it could not be at all. But true and exact reason, vindicating the nature of true being, maintains that while two things [that is, the image and space] are different they cannot exist one of them in the other and so be one and also two at the same time.
Plato: Timaeus (52d-53c) p 1179
Thus have I concisely given the result of my thoughts, and my verdict is that being and space and generation, these three, existed in their three ways before the heaven, and that the nurse of generation, moistened by water and inflamed by fire, and receiving the forms of earth and air, and experiencing all the affections which accompany these, presented a strange variety of appearances, and being full of powers which were neither similar nor equally balanced, was never in any part in a state of equipoise, but swaying unevenly hither and thither, was shaken by them, and by its motion again shook them, and the elements when moved were separated and carried continually, some one way, some another. As, when grain is shaken and winnowed by fans and other instruments used in the threshing of corn, the close and heavy particles are borne away and settle in one direction, and the loose and light particles in another. In this manner, the four kinds or elements were then shaken by the receiving vessel, which, moving like a winnowing machine, scattered far away from one another the elements most unlike, and forced the most similar elements into close contact. Wherefore the various elements had distinct places also before they were arranged so as to form the universe. At first, however, they were all without reason and measure. But when the world began to get into order, fire and water and earth and air did indeed show faint traces of themselves, but were altogether in such a condition as one may expect to find wherever God is absent. Such, I say, being their nature, God now fashioned them by form and number. Let it be consistently maintained by us in all that we say that God made them as far as possible the fairest and best, out of things which were not fair and good. And now I will endeavor to show you the disposition and generation of them by an unaccustomed argument which I am compelled to use. But I believe that you will be able to follow me, for your education has made you familiar with the methods of science.
Plato: Timaeus (53c-54b) p 1179
In the first place, then, as is evident to all, fire and earth and water and air are bodies. And every sort of body possesses volume, and every volume must necessarily be bounded by surfaces, and every rectilinear surface is composed of triangles, and all triangles are originally of two kinds, both of which are made up of one right and two acute angles; one of them has at either end of the base the half of a divided right angle, having equal sides, while in the other the right angle is divided into unequal parts, having unequal sides. These, then, proceeding by a combination of probability with demonstration, we assume to be the original elements of fire and the other bodies, but the principles which are prior to these God only knows, and he of men who is the friend of God. And next we have to determine what are the four most beautiful bodies which could be formed, unlike one another, yet in some instances capable of resolution into one another, for having discovered thus much, we shall know the true origin of earth and fire and of the proportionate and intermediate elements. For we shall not be willing to allow that there are any distinct kinds of visible bodies fairer than these. Wherefore we must endeavor to construct the four forms of bodies which excel in beauty, and secure the right to say that we have sufficiently apprehended their nature. Now of the two triangles, the isosceles has one form only; the scalene or unequal-sided has an infinite number. Of the infinite forms we must again select the most beautiful, if we are to proceed in due order, and anyone who can point out a more beautiful form than ours for the construction of these bodies, shall carry off the palm, not as an enemy, but as a friend. Now, the one which we maintain to be the most beautiful of all the many triangles-- and we need not speak of the others--is that of which the double forms a third triangle which is equilateral. The reason of this would be long to tell; he who disproves what we are saying, and shows that we are mistaken, may claim a friendly victory. Then let us choose two triangles, out of which fire and the other elements have been constructed, one isosceles, the other having the square of the longer side equal to three times the square of the lesser side.
Plato: Timaeus (54b-55c) p 1180
Now is the time to explain what was before obscurely said. There was an error in imagining that all the four elements might be generated by and into one another; this, I say, was an erroneous supposition, for there are generated from the triangles which we have selected four kinds--three from the one which has the sides unequal, the fourth alone framed out of the isosceles triangle. Hence they cannot all be resolved into one another, a great number of small bodies being combined into a few large ones, or the converse. But three of them can be thus resolved and compounded, for they all spring from one, and when the greater bodies are broken up, many small bodies will spring up out of them and take their own proper figures. Or, again, when many small bodies are dissolved into their triangles, by their total number, they can form one large mass of another kind. So much for their passage into one another. I have now to speak of their several kinds, and show out of what combinations of numbers each of them was formed. The first will be the simplest and smallest construction, and its element is that triangle which has its hypotenuse twice the lesser side. When two such triangles are joined at the diagonal, and this is repeated three times, and the triangles rest their diagonals and shorter sides on the same point as a center, a single equilateral triangle is formed out of six triangles, and four equilateral triangles, if put together, make out of
every three plane angles one solid angle, being that which is nearest to the most obtuse of plane angles. And out of the combination of these four angles arises the first solid form which distributes into equal and similar parts the whole circle in which it is inscribed. The second species of solid is formed out of the same triangles, which unite as eight equilateral triangles and form one solid angle out of four plane angles, and out of six such angles the second body is completed. And the third body is made up of one hundred and twenty triangular elements, forming twelve solid angles, each of them included in five plane equilateral triangles, having altogether twenty bases, each of which is an equilateral triangle. The one element [that is, the triangle which has its hypotenuse twice the lesser side], having generated these figures, generated no more, but the isosceles triangle produced the fourth elementary figure, which is compounded of four such triangles, joining their right angles in a center, and forming one equilateral quadrangle. Six of these united form eight solid angles,
each of which is made by the combination of three plane right angles; the figure of the body thus composed is a cube, having six plane quadrangular equilateral bases. There was yet a fifth combination which God used in the delineation of the universe with figures of animals.
Plato: Timaeus (55c-55d) p 1181
Now he who, duly reflecting on all this, inquires whether the worlds are to be regarded as indefinite or definite in number will be of opinion that the notion of their indefiniteness is characteristic of a sadly indefinite and ignorant mind. He, however, who raises the question whether they are to be truly regarded as one or five, takes up a more reasonable position. Arguing from probabilities, I am of opinion that they are one; another, regarding the question from another point of view, will be of another mind. But, leaving this inquiry, let us proceed to distribute the elementary forms, which have now been created in idea, among the four elements.
Plato: Timaeus (55d-56c) p 1181
To earth, then, let us assign the cubic form, for earth is the most immovable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature. Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides, and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily a more stable basis than the equilateral triangle, both in the whole and in the parts. Wherefore, in assigning this figure to earth, we adhere to probability, and to water we assign that one of the remaining forms which is the least movable, and the most movable of them to fire, and to air that which is intermediate. Also we assign the smallest body to fire, and the greatest to water, and the intermediate in size to air, and, again, the acutest body to fire, and the next in acuteness to air, and the third to water. Of all these elements, that which has the fewest bases must necessarily be the most movable, for it must be the acutest and most penetrating in every way, and also the lightest as being composed of the smallest number of similar particles, and the second body has similar properties in a second degree, and the third body, in the third degree. Let it be agreed, then, both according to strict reason and according to probability, that the pyramid is the solid which is the original element and seed of fire, and let us assign the element which was next in the order of generation to air, and the third to water. We must imagine all these to be so small that no single particle of any of the four kinds is seen by us on account of their smallness, but when many of them are collected together, their aggregates are seen. And the ratios of their numbers, motions, and other properties, everywhere God, as far as necessity allowed or gave consent, has exactly perfected and harmonized in due proportion.

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