него UNIVO FLOW? 161 THE ANCIENT QUESTION, DO ALL THINGS FLOW? 161 Tŵv övtwv), and when they were told that all things were moving, they greatly honoured those who taught them this," as being a most comforting and democratic doctrine. Theætetus, 180, A., B., &c. See In the Cratylus, which, although, in the main, a sportive jeu d'esprit, does yet abound in very many most important and serious views, Plato dwells at some length on two theories of language which may be derived from these two systems of philosophy, in one of which the idea of motion, and in the other that of rest, are made respectively the basis of an inquiry into the primitive etymological structure of words. After most ridiculously deriving ovoíav (woíav), or essence, from тò ¿lovv (pushing or impulse), because, on this hypothesis of Heraclitus, τὰ ὄντα ἰέναι τε πάντα καὶ μένειν οὐδὲν, “ all real existences were ever moving on, or pushing ahead, and nothing stood still" (401, C.), he comes to speak of Kronus and Rhea (pća), when Socrates, in his old ironical method, suddenly affects that in this name there is suggested to him this whole flowing philosophy. "Oh, my good sir (he exclaims), I have just discovered a whole hive of curious lore, σμήνος τι σοφίας Λέγει γάρ που Ἡράκλειτος ὅτι πάντα χωρεῖ καὶ οὐδὲν μέσ νει, καὶ ποταμοῦ ῥοῇ ἀπεικάζων τὰ ὄντα λέγει, ὡς δὶς ἐς τὸν αὐτὸν ποταμὸν οὐκ ἂν ἐμβαίης, κ. τ. λ.” "Heraclitus somehow says that all things are moving, &c., and, in his comparison of existences to the course of a stream, he even says that one could not twice enter into the same river.* Do you suppose, then, that he who originally gave names to Rhea and Kronus, the progenitors of the other Gods, had any other philosophy than this of Heraclitus? or do you * He would seem to mean something more here than a mere illustration. Since all being is compared to one ever-moving stream, the expression, that we cannot twice enter the same river, would signify, that neither our own personal identity, nor the identity of the universe, can remain for two consecutive moments. think that through mere accident he gave these flowing names to both? Just as Homer makes Oceanus and Tethys the original and mother of the Gods, and I think Hesiod also. But Orpheus surely says, Ὠκεανὸς πρώτιστα καλίῤῥους ἦρξε γάμοιο· ὅς ῥα κασιγνήτην ὁμομήτορα Τηθὺν ἔπυιεν. See how all these things accord with one another, and how they tend to these doctrines of Heraclitus." Cratylus, 402, A., B. At the conclusion of the first part of this etymological excursus, in which he sportively finds the origin of so many words in this ancient flowing theory, he assigns as the cause of it all the want of stability in their own brains (to adopt a modern phrase), which they mistook for the everlasting change of things and truths themselves. “I think (says Socrates, with grave irony) that I indulged in no bad surmise, when I just now supposed that the very ancient mеn (οi пáνν naλαιοí), who gave names to everything, just like many of our modern wits (T☎v vvv oopwv), in consequence of their getting frequently turned round in their search into the real nature of things, became dizzy, and then things themselves appeared to be whirling around, and to be borne in every direction. Wherefore they blame not the internal state of their own souls as the real cause, but say that this is the very nature of things, that there should be nothing firm or stable, but that all things flow (távta pɛiv), and are full of motion, change, and generation." Cratylus, 411, C., D. And again, 439, C., he thus characterizes the whole school under an ironical allusion to the old authors of language: "They seem to me to have thus thought (namely, that all things are in motion), but, in reality, it is not so. For the fact is, that they themselves are utterly confounded, like men who have fallen into a whirlpool, and would wish to drag us in after them. For con sider this, O most excellent Cratylus, of which I am often dreaming,* can we in truth affirm that there are such realities as the Beautiful, the Good,” &c. ? ὃ ἐγὼ πολλάκις ὀνειρώττω, πότερον φῶμέν τι εἶναι αὐτὸ ΤΟ ΚΑΛΟΝ καὶ ΑΓΑΘΟΝ καὶ ἓν ἕκαστον τῶν ὄντων ὅντως In this philosophy, too, he shows that there could be no true moral or political science, no law, no real State, no social or civil rights, with their corresponding obligations. See the Theætetus, 172, B., and the remarks thereupon, page 138. There could be no science, he affirms, of any kind, for it must necessarily be grounded on the eternal and immutable. Αἴσθησις would take the place of ἐπιστήμη, and nothing could be really known: ̓Αλλὰ μὴν οὐδ' ἂν γνωστ θείη γε ὑπ ̓ οὐδενὸς οὐδέν· ἅμα γὰρ ἂν ἐπιόντος τοῦ γνωσομένου ἄλλο καὶ ἀλλοῖον γίγνοιτο· καὶ ἐκ τούτου τοῦ λόγου οὔτε τὸ γνωσόμενον οὔτε τὸ γνωσθησόμενον ἂν εἴη. Hence he draws the sublime conclusion, that, since the very laws of our being compel us to affirm the real, and not merely relative existence of these ideas, therefore there is something which is eternal and immutable, or, in the language of the ancient schools, all things do not flow, but some things stand. Εἰ δὲ ἔστι μὲν ἀεὶ τὸ γιγνῶσκον, ἔστι δὲ τὸ ἀεὶ γιγνωσκόμενον, ἔστι δὲ τὸ ΚΑΛΟΝ, ἔστι δὲ τὸ ΑΓΑΘΟΝ, ἔστι δὲ ΤΟ ΔΙΚΑΙΟΝ, οὔ μοι φαίνεται ταῦτα ὅμοια ὄντα ῥοῇ οὐδὲν οὐδὲ φορᾷ. "But if there is something which eternally knows, and something which is eternally known—if there is THE BEAUTIFUL, and THE GOOD, and THE JUST, then things do not all seem to me to be similar to motion or a flowing stream." Cratylus, 440, B. * ὀνειρώττω. No word could better express that peculiar state of mind in which Socrates (or Plato) often contemplated his favourite doctrine of ideas. Sometimes he seems to be perfectly assured of the real existence of the καλὸν, &c., the Fair, the Just, and the Good. Again, he appears perplexed with doubt, and, at other times, seems to have but a glimpse, as in a dream, of some such bright reminiscences of a better state. XXI. Mathematical Use of the Word λόγος. PAGE 24, LINE 6. ȧvà λóyov. The common reading is áváλoyov; the other, however, is unquestionably to be preferred. It would signify here proportionally, certa quadam ratione. This is called in Latin ratio, and in Greek λóyos (especially in all mathematical writings), because a simple quantity or magnitude, irrespective of the relation it bears to another as a multiple or a divisor, cannot be an object of science, or be contemplated by the mind. It remains only an object of sense, aiolŋτóv, being, to the intellect, ἄλογον, and therefore ἄγνωστον. See the Theætetus, 202, B. It is this relation or ratio which becomes the true vonτòv, or real object of the mind, while the sensible figure serves only as the diagram by which it is exhibited. Hence it is styled the λóyoç, ratio, or reason. It is that which is predicated of its subject, and hence is its λóyos, or word, as well as reason; because, when viewed as simple quantity or magnitude, nothing can be said about it, no truth affirmed respecting it. This λóyos, or reason, ever implies a third thing or middle term, namely, the common measure or divisor to which both quantities must be referred, and by which we are enabled to predicate the one as a part, or multiple, or any certain ratio of the other. The λóyou or ratios are absolute and immutable verities of science, as all voŋtà must be, while the aioonrà by which they are suggested are muta. ble, flowing, and without anything which can be styled absolute. They likewise are capable of being compared among themselves, and thus give rise to others-ratios of ratios, ad infinitum. In modern works the simple radical meaning of the term is lost sight of, because we use the Latin ratio without any reference to its primary sense, as the same with the Greek λóyos, and hence the great vagueness which prevails in most minds respecting this plain mathematical idea. In some of our older mathematical works, such as the English editions of Euclid's Elements by Dee and Barrow respectively, our own word reason is everywhere properly employed instead of ratio. By this means the metaphysical notion of ratio is kept before the mind as the intelligible, by which what would otherwise be merely, as magnitude, an object of sense, becomes known to the intellect as an object of science. See Proclus, Commentary on Euclid's Elements, lib. i. All mathematical truths, and especially the geometrical, are ultimately to be resolved into a comparison of ratios. For even parallelism, and other properties which would seem to have no connexion with it, do, after all, depend upon certain equalities or correspondences, from which they derive their λóyoç, notion, or definition. So that all mathematical science is finally brought down to those innate ideas of the rò loov, &c,, which are discussed in the Phædon, and of which visible magnitude is only suggestive. Even a straight line involves this idea of the Tò loov, or simplest ratio. It is that which lies evenly, equally, or, as it is expressed by Euclid, ioov, between its extreme points; that is, having nothing capable of being predicated of the one side and not of the other. Playfair and others seem to have entirely misunderstood the expression, and to have greatly bungled in their efforts to amend, by substituting a far more complex idea for this old and perfect definition of Euclid. Any one who is capable of consulting his own consciousness, must acknowledge that the language of Euclid best expresses that innate idea of straightness, which we ever apply, as the perfect ideal exemplar, to the determination of visible figure. From this use of the word 2óyoç it is, that those magnitudes and numbers whose ratio cannot be expressed by |