De animae procreatione in Timaeo
Plutarch
Plutarch. Plutarch's Morals, Vol. II. Goodwin, William W., editor; Philips, John, translator. Boston: Little, Brown, and Company; Cambridge: Press of John Wilson and Son, 1874.
Others, placing the two extremes of the diatessaron, the acute part in 288, and the lower sound in 216, in all the rest observe the same proportions, only that they take the remainder between the two middle intervals. For the base, being forced up a whole tone, makes 243; and the upper note, screwed downward a full tone, begets 256. Moreover 243 carries a sesquioctave proportion to 216, and 288 to 256; so that each of the intervals contains a full tone, and the residue is that which remains between 243 and 256, which is not a semitone, but something less. For 288 exceeds 256 by 32, and 243 exceeds 216 by 27; but 256 exceeds 243 by 13. Now this excess is less than half of the former. So it is plain that the diatessaron consists of two tones and the residue, not of two tones and a half. Let this suffice for the demonstration of these things. Nor is it a difficult thing to believe, by what has been already said, wherefore Plato, after he had asserted that the intervals of sesquialter, sesquiterce, and sesquioctave had arisen, when he comes to fill up the intervals of sesquiterces with sesquioctaves, makes not the least mention of sesquialters; for that the sesquialter is soon filled up, by adding the sesquiterce
to the sesquioctave, or the sesquioctave to the sesquiterce.Having therefore shown the manner how to fill up the intervals, and to place and dispose the medieties, had never any person taken the same pains before, I should have recommended the further consideration of it to the recreation of your fancies; but in regard that several most excellent musicians have made it their business to unfold these mysteries with a diligence more than usually exact,—more especially Crantor, Clearchus, and Theodorus, all born in Soli,—it shall suffice only to show how these men differed among themselves. For Theodorus, varying from the other two, and not observing two distinct files or rows of numbers, but placing the duples and triples in a direct line one before another, grounds himself upon that division of the substance which Plato calls the division in length, making two parts (as it were) out of one, not four out of two. Then he says, that the interposition of the mediums ought to take place in that manner, to avoid the trouble and confusion which must arise from transferring out of the first duple into the first triple the intervals which are ordained for the supplement of both. --- But as for those who take Crantor’s part, they so dispose their numbers as to place planes with planes, tetragons with tetragons, cubes with cubes, opposite to one another, not taking them in file, but alternatively odd to even. [Here is some great defect in the original.]
--- Which, being in themselves permanently the same, afford the form and species; but being subject to corporeal division, they become the matter and subject to receive the other’s impression, the common mixture being completed out of both. Now the indivisible substance, which is always one and the same, is not to be thought to be incapable of division by reason of its smallness, like the most minute of bodies, called atoms. But as it is unmixed,
and not to be any way affected, but pure and altogether of one sort, it is said not to consist of parts, but to be indivisible. By means of which purity, when it comes in any manner whatsoever to approach and gently touch compounded divisible and differing substances, all their variety ceases and they crowd together into one habit by sympathy and similitude. If now any one will call that substance which admits corporeal separation matter, as a nature subject to the former and partaking of it, the use of that equivocal term will nothing disadvantage our discourse. But they are under a mistake that believe the corporeal to be blended with the indivisible matter. First, for that Plato does not here make use of any one of its names; whereas in other places he calls it the receptacle and nurse, capable of both receiving and fostering the vast infinity of created beings; not divisible among bodies, but rather the body itself parted and divided into single individuals. Then again, what difference would there be between the creation of the world and that of the soul, if the composition of each proceeded from both matter and the intelligible essence? Certainly Plato, as endeavoring to separate the generation of the body from that of the soul, tells us that the corporeal part was by God seated and deposited within it, and that it was outwardly covered and enveloped by it; and after he had thus wrought the soul to its perfection out of proportion, he then proceeds to this argument concerning matter, of which he had no occasion to make mention before when he was producing the soul, as being that which had not its existence from matter.The same may be said against the followers of Posidonius. For they seem not altogether to separate the soul from matter; but imagining the essence of limitations to be divisible in reference to bodies, and intermixing it with the intelligible essence, they defined the soul to be an idea
(or essential form) of that which has extension in every direction, subsisting in an harmonical proportion of numbers. For (they say) all mathematical objects are disposed between the first intelligible and sensible beings; and since the soul contains the sempiternal nature of things intelligible and the pathetic nature of things subjected to sense, it seems but rational that it should consist of a substance between both. But they were ignorant that God, when the soul was already brought to perfection, afterwards making use of the limitations of bodies to form and shape the matter, confined and environed the dissipated and fleeting substance within the compass of certain surfaces composed of triangles adapted together. And it is even more absurd to make the soul an idea. For the soul is always in motion; the idea is incapable of motion; the one never to be mixed with that which is subjected to sense, the other wrought into the substance of the body. Moreover, God could be said only to imitate an idea, as his pattern; but he was the artificer of the soul, as of a work of perfection. Now enough has been already said to show that Plato does not assert number to be the substance of the soul, only that it is ordered and proportioned by number.However this is a common argument against both the former opinions, that neither in corporeal limits nor in numbers there is the least footstep or appearance of that power by which the soul assumes to itself to judge of what is subject to sense. For it was the participation of the intelligible principle that endued it with understanding and the perceiving faculty. But as for opinion, belief, imagination, and its being affected with qualities relating to the body, no man could ever dream that they proceeded simply either from units, or lines, or surfaces. For not only the souls of mortals have a power to judge of what is subject to sense; but the soul of the world also, says Plato, when it revolves upon itself, and happens once to touch upon any
fluid and roving substance or upon any thing indivisible, then being moved throughout its whole self, it gives notice with what this or that thing is identical, to what heterogeneal, and in what relations especially and in what manner it happens to be and to be affected towards each created thing. [*](Timaeus, p. 37 A.) Here he gives at the same time an intimation of the ten Categories or Predicaments; but afterwards he gives us a clearer manifestation of these things. For when true reason, says he, is fixed upon what is subject to sense, and the circle of the Other, observing a just and equal motion, conveys its intelligence to the whole soul, then both opinion and belief become steadfast and certain; on the other side, when it is settled upon ratiocination, and the circle of the Same. turning readily and easily, furnishes its intimations, then of necessity knowledge arrives to perfection. And indeed, whoever shall affirm that any thing in which these two operations take place is any thing besides a soul, may deservedly be thought to speak any thing rather than the truth.From whence then does the soul enjoy this motion whereby it comprehends what is subject to sense, different from that other intelligible motion which ends in knowledge? This is a difficult task to resolve, unless we steadfastly assert that Plato here did not compose the soul, so singly considered, but the soul of the world also, of the parts above mentioned,—of the more worthy indivisible substance, and of the less worthy divisible in reference to bodies. And this soul of the world is no other than that motion which gives heat and vigor to thought and fancy, and sympathizes with what is subject to sense, not created, but existing from eternity, like the other soul. For Nature, which had the power of understanding, had also the power of opining. But the intelligible power is subject neither to motion nor affection, being established upon
a substance that is still the same. The other is movable and fleeting, as being engaged to an unstable, fluctuating, and disunited matter. In regard the sensible substance was so far from any order, that it was without shape and boundless. So that the power which is fixed in this was capable of producing no clear and well-grounded notions and no certain or well-ordered movements, but only sleepy dreams and deliriums, which amuse and trouble corporeal stupidity; unless by accident they lighted upon the more worthy substance. For it was in the middle between the sensible and discerning faculty, and had a nature conformable and agreeable to both; from the sensible apprehending substance, and borrowing from judgment its power of discerning things intelligible.