WHAT IS PLATO'S MEANING, WHEN HE SAYS THAT GOD ALWAYS PLAYS THE GEOMETER?
DIOGENIANUS, TYNDARES, FLORUS, AUTOBULUS.
SILENCE following this discourse, Diogenianus began and said: Since our discourse is about the Gods, shall we, especially on his own birthday, admit Plato to the conference, and enquire upon what account he says (supposing it to be his sentence) that God always plays the geometer? I said that this sentence was not plainly set down in any of his books; yet there are good arguments that it is his, and it is very much like his expression. Tyndares presently subjoining said: Perhaps, Diogenianus, you imagine that this sentence intimates some curious and difficult speculation, and not that which he hath so often mentioned, when he praiseth geometry as a science that takes off men from sensible objects, and makes them apply themselves to the intelligible and eternal Nature, the contemplation of which is the end of philosophy, as a view of the mysteries of initiation into holy rites. For the nail of pain and pleasure, that fastens the soul to the body, seems to do us the greatest mischief, by making sensible things more powerful over us than intelligible, and by forcing the understanding [p. 403] to determine rather according to passion than reason. For the understanding, being accustomed by the vehemency of pain or pleasure to be intent on the mutable and uncertain body, as if it really and truly were, grows blind as to that which really is, and loses that instrument and light of the soul, which is worth a thousand bodies, and by which alone the Deity can be discovered. Now in all sciences, as in plain and smooth mirrors, some marks and images of the truth of intelligible objects appear, but in geometry chiefly; which, according to Philo, is the chief and principal of all, and doth bring back and turn the understanding, as it were, purged and gently loosened from sense. And therefore Plato himself dislikes Eudoxus, Archytas, and Menaechmus for endeavoring to bring down the doubling the cube to mechanical operations; for by this means all that was good in geometry would be lost and corrupted, it falling back again to sensible things, and not rising upward and considering immaterial and immortal images, in which God being versed is always God.
After Tyndares, Florus, a companion of his, who always jocosely pretended to be his admirer, said thus: Sir, we are obliged to you for making your discourse not proper to yourself, but common to us all; for you have made it possible to refute it by demonstrating that geometry is not necessary to the Gods, but to us. Now the Deity doth not stand in need of science, as an instrument to withdraw his intellect from things engendered and to turn it to the real things; for these are all in him, with him, and about him. But pray consider whether Plato, though you do not apprehend it, doth not intimate something that is proper and peculiar to you, mixing Lycurgus with Socrates, as much as Dicaearchus thought he did Pythagoras. For Lycurgus, I suppose you know, banished out of Sparta all arithmetical proportion, as being democratical and favoring the crowd; -but introduced the geometrical, as [p. 404] agreeable to an oligarchy and kingly government that rules by law; for the former gives an equal share to every one according to number, but the other gives according to the proportion of the deserts. It doth not huddle all things together, but in it there is a fair discretion of good and bad, every one having what is fit for him, not by lot or weight, but according as he is virtuous or vicious. The same proportion, my dear Tyndares, God introduceth, which is called δίκη and νέμεσις, and which teacheth us to account that which is just equal, and not that which is equal just. For that equality which many affect, being often the greatest injustice, God, as much as possible, takes away; and useth that proportion which respects every man's deserts, geometrically defining it according to law and reason.
This exposition we applauded; and Tyndares, saying he envied him, desired Autobulus to engage Florus and confute his discourse. That he refused to do, but produced another opinion of his own. Geometry, said he, considers nothing else but the accidents and properties of the extremities or limits of bodies; neither did God make the world any other way than by terminating matter, which was infinite before. Not that matter was really infinite as to either magnitude or multitude; but the ancients used to call that infinite which by reason of its confusion and disorder is undetermined and unconfined. Now the terms of every thing that is formed or figured are the form and figure of that thing, without which the thing would be formless and unfigured. Now numbers and proportions being applied to matter, it is circumscribed and as it were bound up by lines, and through lines by surfaces and profundities; and so were settled the first species and differences of bodies, as foundations from which to raise the four elements, fire, air, water, and earth. For it was impossible that, out of an unsteady and confused matter, the [p. 405] equality of the sides, the likeness of the angles, and the exact proportion of octahedrons, icosahedrons, pyramids, and cubes should be deduced, unless by some power that terminated and shaped every particle of matter. Therefore, terms being fixed to that which was undetermined or infinite before, the whole became and still continues agreeable in all parts, and excellently terminated and mixed; the matter indeed always affecting an indeterminate state, and flying all geometrical confinement, but proportion terminating and circumscribing it, and dividing it into several differences and forms, out of which all things that arise are generated and subsist.
When he had said this, he desired me to contribute something to the discourse; and I applauded their conceits as their own devices, and very probable. But lest you despise yourselves (I continued) and altogether look for some external explication, attend to an exposition upon this sentence, which your masters very much approve. Amongst the most geometrical theorems, or rather problems, this is one: Two figures being given, to construct a third, which shall be equal to one and similar to the other. And it is reported that Pythagoras, upon the discovery of this problem, offered a sacrifice to the Gods; for this is a much more exquisite theorem than that which lays down, that the square of the hypothenuse in a right-angled triangle is equal to the squares of the two sides. Right, said Diogenianus, but what is this to the present question? You will easily understand, I replied, if you call to mind how Timaeus divides that which gave the world its beginning into three parts. One of which is justly called God, the other matter, and the third form. That which is called matter is the most confused subject, the form the most beautiful pattern, and God the best of causes. Now this cause, as far as possible, would leave nothing infinite and indeterminate, but adorn Nature with number, measure, [p. 406] and proportion, making one thing of all the subjects together, equal to the matter, and similar to the form. Therefore proposing to himself this problem, he made and still makes a third, and always preserves it equal to the matter, and like the form; and that is the world. And this world, being in continual changes and alterations because of the natural necessity of body, is helped and preserved by the father and maker of all things, who by proportion terminates the substance according to the pattern. Wherefore in its measure and circuit this universal world is more beautiful than that which is merely similar to it....