Republic

Decide, then, on the spot, to which party you address yourself. Or are you speaking to neither, but chiefly carrying on the discussion for your own sake,[*](Cf. Charm. 166 D, Phaedo 64 C, Soph. 265 A, Apol. 33 A.) without however judging any other who may be able to profit by it?” “This is the alternative I choose,” he said, “that it is for my own sake chiefly that I speak and ask questions and reply.” “Fall back[*](ἄναγε is a military term. Cf. Aristoph. Birds 383, Xen. Cyr. vii. 1.45, iii. 3. 69.) a little, then,” said I; “for we just now did not rightly select the study that comes next[*](ἑξῆς Cf. Laches 182 B.) after geometry.” “What was our mistake?” he said. “After plane surfaces,” said I, “we went on to solids in revolution before studying them in themselves. The right way is next in order after the second dimension[*](Lit. increase Cf. Pearson, The Grammar of Science, p. 411: He proceeds from curves of frequency to surfaces of frequency, and then requiring to go beyond these he finds his problem lands him in space of many dimensions.) to take the third. This, I suppose, is the dimension of cubes and of everything that has depth.” “Why, yes, it is,” he said; “but this subject, Socrates, does not appear to have been investigated yet.[*](This is not to be pressed. Plato means only that the progress of solid geometry is unsatisfactory. Cf. 528 D. There may or may not be a reference here to the Delian problem of the duplication of the cube (cf. Wilamowitz, Platon, i. p. 503 for the story) and other specific problems which the historians of mathematics discuss in connection with this passage. Cf. Adam ad loc. To understand Plato we need only remember that the extension of geometry to solids was being worked out in his day, perhaps partly at his suggestion, e.g. by Theaetetus for whom a Platonic dialogue is named, and that Plato makes use of the discovery of the five regular solids in his theory of the elements in the Timaeus. Cf. also Laws 819 E ff. for those who wish to know more of the ancient traditions and modern conjectures I add references: Eva Sachs, De Theaeteto Ath. Mathematico, Diss. Berlin, 1914, and Die fünf platonischen Körper (Philolog. Untersuch. Heft 24), Berlin, 1917; E. Hoppe, Mathematik und Astronomie im klass. Altertum, pp. 133 ff.; Rudolf Eberling, Mathematik und Philosophie bei Plato, Münden, 1909, with my review in Class. Phil. v. (1910) p. 114; Seth Demel, Platons Verhältnis zur Mathematik, Leipzig, with my review, Class. Phil. xxiv. (1929) pp. 312-313; and, for further bibliography on Plato and mathematics, Budé, Rep. Introd. pp. lxx-lxxi.)” “There are two causes of that,” said I: “first, inasmuch as no city holds them in honor, these inquiries are languidly pursued owing to their difficulty. And secondly, the investigators need a director,[*](Plato is perhaps speaking from personal experience as director of the Academy. Cf. the hint in Euthydem. 290 C.) who is indispensable for success and who, to begin with, is not easy to find, and then, if he could be found, as things are now, seekers in this field would be too arrogant[*](i.e. the mathematicians already feel themselves to be independent specialists.) to submit to his guidance. But if the state as a whole should join in superintending these studies and honor them, these specialists would accept advice, and continuous and strenuous investigation would bring out the truth. Since even now, lightly esteemed as they are by the multitude and hampered by the ignorance of their students[*](This interpretation is, I think, correct. For the construction of this sentence cf. Isoc. xv. 84. The text is disputed; see crit. note.) as to the true reasons for pursuing them,[*](Lit. in what respect they are useful. Plato is fond of the half legal καθ’ ὅ τι. Cf. Lysis 210 C, Polit. 298 C.) they nevertheless in the face of all these obstacles force their way by their inherent charm[*](An eminent modern psychologist innocently writes: The problem of why geometry gives pleasure is therefore a deeper problem than the mere assertion of the fact. Furthermore, there are many known cases where the study of geometry does not give pleasure to the student. Adam seems to think it may refer to the personality of Eudoxus.) and it would not surprise us if the truth about them were made apparent.” “It is true,” he said, “that they do possess an extraordinary attractiveness and charm. But explain more clearly what you were just speaking of. The investigation[*](πραγματείαν: interesting is the development of this word from its use in Phaedo 63 A (interest, zeal, inquiring spirit. Cf. Aristot. Top. 100 a 18, Eth. Nic. 1103 b 26, Polyb. i. 1. 4, etc.) of plane surfaces, I presume, you took to be geometry?” Yes, said I. “And then,” he said, “at first you took astronomy next and then you drew back.” Yes, I said, “for in my haste to be done I was making less speed.[*](An obvious allusion to the proverb found in many forms in many languages. Cf. also Polit. 277 A-B, 264 B, Soph. Antig. 231 σχολῇ ταχύς, Theognis 335, 401 μηδὲν ἄγαν σπεύδειν, Suetonius, Augustus 25, Aulus Gellius x. 11. 4, Macrob. Sat. vi. 8. 9, festina lente, hâtez-vous lentement (Boileau, Art poétique, i. 171), Chi va piano va sano e va lontano (Goldoni, I volponi,I. ii.), Eile mit Weile and similar expressions; Franklin’s Great haste makes great waste, etc.) For, while the next thing in order is the study[*](μέθοδον: this word, like πραγματεία came to mean treatise.) of the third dimension or solids, I passed it over because of our absurd neglect[*](This is the meaning. Neither Stallbaum’s explanation, quia ita est comparata, ut de ea quaerere ridiculum sit,” nor that accepted by Adam, quia ridicule tractatur, is correct, and 529 E and 521 A are not in point. Cf. 528 B p. 176, note a.) to investigate it, and mentioned next after geometry astronomy,[*](Cf. Laws 822 A ff.) which deals with the movements of solids.” “That is right,” he said. “Then, as our fourth study,” said I, “let us set down astronomy, assuming that this science, the discussion of which has been passed over, is available,[*](i.e. assuming this to exist, vorhanden sein, which is the usual meaning of ὑπάρχειν in classical Greek. The science, of course, is solid geometry, which is still undeveloped, but in Plato’s state will be constituted as a regular science through endowed research.) provided, that is, that the state pursues it.”

“That is likely,” said he; “and instead of the vulgar utilitarian[*](Cf. Vol. I. p. 410, note c, on 442 E, Gorg. 482 E, Rep. 581 D, Cratyl. 400 A, Apol. 32 A, Aristot. Pol. 1333 b 9.) commendation of astronomy, for which you just now rebuked me, Socrates, I now will praise it on your principles. For it is obvious to everybody, I think, that this study certainly compels the soul to look upward[*](Cf. my review if Warburg, Class. Phil. xxiv. (1929) p. 319. The dramatic misunderstanding forestalls a possible understanding by the reader. Cf. on 523 B. The misapprehension is typical of modern misunderstandings. Glaucon is here the prototype of all sentimental Platonists or anti-Platonists. The meaning of higher things in Plato’s allegory is obvious. But Glaucon takes it literally. Similarly, modern critics, taking Plato’s imagery literally and pressing single expressions apart from the total context, have inferred that Plato would be hostile to all the applications of modern science to experience. They refuse to make allowance for his special and avowed educational purpose, and overlook the fact that he is prophesying the mathematical astronomy and science of the future. The half-serious exaggeration of his rhetoric can easily be matched by similar utterances of modern thinkers of the most various schools, from Rousseau’s écarter tous les faits to Judd’s Once we acquire the power to neglect all the concrete facts . . . we are free from the incumbrances that come through attention to the concrete facts. Cf. also on 529 B, 530 B and 534 A.) and leads it away from things here to those higher things.” “It may be obvious to everybody except me,” said I, “for I do not think so.” “What do you think?” he said. “As it is now handled by those who are trying to lead us up to philosophy,[*](ἀνάγοντες is tinged with the suggestions of 517 A, but the meaning here is those who use astronomy as a part of the higher education. φιλοσοφία is used in the looser sense of Isocrates. Cf. A.J.P. xvi. p. 237.) I think that it turns the soul’s gaze very much downward.” “What do you mean?” he said. “You seem to me in your thought to put a most liberal[*](For οὐκ ἀγεννῶς Gorg. 462 D, where it is ironical, as here, Phaedr. 264 B, Euthyph. 2 C, Theaet. 184 C. In Charm. 158 C it is not ironical.) interpretation on the study of higher things,” I said, “for apparently if anyone with back-thrown head should learn something by staring at decorations on a ceiling, you would regard him as contemplating them with the higher reason and not with the eyes.[*](The humorous exaggeration of the language reflects Plato’s exasperation at the sentimentalists who prefer star-gazing to mathematical science. Cf. Tim. 91 D on the evolution of birds from innocents who supposed that sight furnished the surest proof in such matters. Yet such is the irony of misinterpretation that this and the following pages are the chief support of the charge that Plato is hostile to science. Cf. on 530 B, p. 187, note c.) Perhaps you are right and I am a simpleton. For I, for my part, am unable to suppose that any other study turns the soul’s gaze upward[*](Cf. Theaet. 174 A ἄνω βλέποντα.) than that which deals with being and the invisible. But if anyone tries to learn about the things of sense, whether gaping up[*](Cf. Aristoph. Clouds 172.) or blinking down,[*](συμμύω probably refers to the eyes. But cf. Adam ad loc.) I would never say that he really learns—for nothing of the kind admits of true knowledge—nor would I say that his soul looks up, but down, even though he study floating on his back[*](Cf. Phaedr. 264 A, and Adam in Class. Rev. xiii. p. 11.) on sea or land.” “A fair retort,[*](Or rather, serves me right, or, in the American language, I’ve got what’s coming to me. The expression is colloquial. Cf. Epist. iii. 319 E, Antiphon cxxiv. 45. But δίκην ἔχει in 520 B = it is just.)” he said; “your rebuke is deserved. But how, then, did you mean that astronomy ought to be taught contrary to the present fashion if it is to be learned in a way to conduce to our purpose?” Thus, said I, “these sparks that paint the sky,[*](Cf. Tim. 40 A κόσμον ἀληθινὸν αὐτῷ πεποικιλμένον, Eurip. Hel. 1096 ἀστέρων ποικίλματα, Critias, Sisyphus, Diels ii.3 p. 321, lines 33-34 τό τ’ ἀστερωπὸν οὐρανοῦ δέμας χρόνου καλὸν ποίκιλμα τέκτονος σοφοῦ. Cf. also Gorg. 508 A, Lucretius v. 1205 stellis micantibus aethera fixum, ii. 1031 ff., Aeneid iv. 482 stellis ardentibus aptum, vi. 797, xi. 202, Ennius, Ann. 372. The word ποικίλματα may further suggest here the complication of the movements in the heavens) since they are decorations on a visible surface, we must regard, to be sure, as the fairest and most exact of material things but we must recognize that they fall far short of the truth,[*](The meaning of this sentence is certain, but the expression will no more bear a matter-of-fact logical analysis than that of Phaedo 69 A-B, or Rep. 365 C, or many other subtle passages in Plato. No material object perfectly embodies the ideal and abstract mathematical relation. These mathematical ideas are designated as the true,ἀληθινῶν, and the real,ὄν. As in the Timaeus (38 C, 40 A-B, 36 D-E) the abstract and ideal has the primacy and by a reversal of the ordinary point of view is said to contain or convey the concrete. The visible stars are in and are carried by their invisible mathematical orbits. By this way of speaking Plato, it is true, disregards the apparent difficulty that the movement of the visible stars then ought to be mathematically perfect. But this interpretation is, I think, more probable for Plato than Adam’s attempt to secure rigid consistency by taking τὸ ὂν τάχος etc., to represent invisible and ideal planets, and τὰ ἐνόντα to be the perfect mathematical realities, which are in them. ἐνόντα would hardly retain the metaphysical meaning of ὄντα. For the interpretation of 529 D cf. also my Platonism and the History of Science, Am. Philos. Soc, Proc. lxvi. p. 172.) the movements, namely, of real speed and real slowness in true number and in all true figures both in relation to one another and as vehicles of the things they carry and contain. These can be apprehended only by reason and thought, but not by sight; or do you think otherwise?” “By no means,” he said. Then, said I, “we must use the blazonry of the heavens as patterns to aid in the study of those realities, just as one would do who chanced upon diagrams drawn with special care and elaboration by Daedalus or some other craftsman or painter.

For anyone acquainted with geometry who saw such designs would admit the beauty of the workmanship, but would think it absurd to examine them seriously in the expectation of finding in them the absolute truth with regard to equals or doubles or any other ratio.” “How could it be otherwise than absurd?” he said. “Do you not think,” said I, “that one who was an astronomer in very truth would feel in the same way when he turned his eyes upon the movements of the stars? He will be willing to concede that the artisan[*](δημιουργῷ: an anticipation of the Timaeus.) of heaven fashioned it and all that it contains in the best possible manner for such a fabric; but when it comes to the proportions of day and night, and of their relation to the month, and that of the month to the year, and of the other stars to these and one another, do you not suppose that he will regard as a very strange fellow the man who believes that these things go on for ever without change[*](Cf. Bruno apud Höffding, History of Modern Philosophy, i. 125 and 128, and Galileo, ibid. i. 178; also Lucretius v. 302-305.) or the least deviation[*](Plato was right against the view that Aristotle imposed on the world for centuries. We should not therefore say with Adam that he would have attached little significance to the perturbations of Neptune and the consequent discovery of Uranus. It is to Plato that tradition attributes the problem of accounting by the simplest hypothesis for the movement of the heavenly bodies and saving the phenomena. The alleged contradiction between this and Laws 821 B ff. and Tim. 41 A is due to a misapprehension. That the stars in their movements do not perfectly express the exactness of mathematical conceptions is no more than modern astronomers say. In the Laws passage Plato protests against the idea that there is no law and order governing the movement of the planets, but that they are wandering stars, as irregular in their movements as they seem. In the Timaeus he is saying that astronomy or science took its beginning from the sight and observation of the heavenly bodies and the changing seasons. In the Republic Plato’s purpose is to predict and encourage a purely mathematical astronomy and the indicate its place in the type of education which he wishes to give his guardians. There is not the slightest contradiction or change of opinion in the three passages if interpreted rightly in their entire context.)—though they possess bodies and are visible objects—and that his unremitting quest[*](The meaning is not appreciably affected by a slight doubt as to the construction of ζητεῖν. It is usually taken with ἄτοπον (regarded as neuter), the meaning being that the Philosophic astronomer will think it strange to look for the absolute truth in these things. This double use of ἄτοπον is strained and it either makes παντὶ τρόπῳ awkward or attributes to Plato the intention of decrying the concrete study of astronomy. I think ζητεῖν etc. are added by a trailing anacoluthon such as occurs elsewhere in the Republic. Their subject is the real astronomer who, using the stars only as diagrams or patterns (529 D), seeks to learn a higher exacter mathematical truth than mere observation could yield. Madvig’s ζητήσει implies a like view of the meaning but smooths out the construction. But my interpretation of the passage as a whole does not depend on this construction. If we make ζητεῖν depend on ἄτοπον (neuter)ἡγήσεται, the meaning will be that he thinks it absurd to expect to get that higher truth from mere observation. At all events Plato is not here objecting to observation as a suggestion for mathematical studies but to its substitution for them, as the next sentence shows.) the realities of these things?” “I at least do think so,” he said, “now that I hear it from you.” “It is by means of problems,[*](That is just what the mathematical astronomy of today does, and it is a πολλαπλάσιον ἔργον compared with the merely observational astronomy of Plato’s day. Cf. the interesting remarks of Sir James Jeans, apud S. J. Woolf, Drawn from Life, p. 74: The day is gone when the astronomer’s work is carried on only at the eyepiece of a telescope. Naturally, observations must be made, but these must be recorded by men who are trained for that purpose, and I am not one of them, etc. Adam’s quotation of Browning’s Abt Vogler in connection with this passage will only confirm the opinion of those who regard Plato as a sentimental enemy of science.) then,” said I, “as in the study of geometry, that we will pursue astronomy too, and we will let be the things in the heavens,[*](Cf. also Phileb. 59 A, Aristot. Met. 997 b 35 οὐδὲ περὶ τὸν οὐρανὸν ἡ ἀστρολογία τόνδε. This intentional Ruskinian boutade has given great scandal. The Platonist, we are told ad nauseam, deduces the world from his inner consciousness. This is of course not true (Cf. Unity of Plato’s Thought, p. 45). But Plato, like some lesser writers, loves to emphasize his thought by paradox and surprise, and his postulation and of a mathematical astronomy required emphasis. Cf. my Platonism and the History of Science, pp. 171-174. This and similar passages cannot be used to prove that Plato was unscientific, as many hostile or thoughtless critics have attempted to do. Cf. e.g. the severe strictures of Arthur Platt, Nine Essays, Cambridge Univ. Press, 1921, pp. 12-16, especially p. 16: Plato being first and foremost a metaphysician with a sort of religious system would not have us study anything but metaphysics and a kind of mystic religion. Woodbridge Riley, From Myth to Reason, p. 47: . . . Plato...was largely responsible for turning back the clock of scientific progress. To explain the wonders of the world he preferred imagination to observation. Cf. also Benn, Greek Philosophers, vol. i. pp. 173 and 327, Herrick, The Thinking Machine, p. 335, f. C. s. Schiller, Plato and he Predecessors, p. 81: . . . that Plato’s anti-empirical bias renders him profoundly anti-scientific, and that his influence has always, openly or subtly, counteracted and thwarted the scientific impulse, or at least diverted it into unprofitable channels. Dampier-Whetham, A History of Science, pp. 27-28: Plato was a great philosopher but in the history of experimental science he must be counted a disaster. Such statements disregard the entire context of the Platonic passages they exploit, and take no account of Plato’s purpose or of other passages which counteract his seemingly unscientific remarks. Equally unfair is the practice of comparing Plato unfavorably with Aristotle in this respect, as Grote e.g. frequently does (Cf. Aristotle, p. 233). Plato was an artist and Aristotle an encyclopaedist; but Plato as a whole is far nearer the point of view of recent science than Aristotle. Cf. my Platonism and the History of Science, p. 163; also 532 A and on 529 A, p. 180, note a and What Plato Said, p. 236.) if we are to have a part in the true science of astronomy and so convert to right use from uselessness that natural indwelling intelligence of the soul.” “You enjoin a task,” he said, “that will multiply the labor[*](Cf. Phaedr. 272 B καίτοι οὐ σμικρόν γε φαίνεται ἔργον.) of our present study of astronomy many times.” “And I fancy,” I said, “that our other injunctions will be of the same kind if we are of any use as lawgivers. “However, what suitable studies have you to suggest?” Nothing, he said, “thus off-hand.” “Yet, surely,” said I, “motion[*](Plato here generalizes motion as a subject of science.) in general provides not one but many forms or species, according to my opinion. To enumerate them all will perhaps be the task of a wise man,[*](The modesty is in the tone of the Timaeus.) but even to us two of them are apparent.” “What are they?” “In addition to astronomy, its counterpart, I replied.” “What is that?” “We may venture to suppose,” I said, “that as the eyes are framed for astronomy so the ears are framed,[*](For πέπηγεν cf. 605 A.) for the movements of harmony; and these are in some sort kindred sciences,[*](The similar statement attributed to Archytas, Diels i.3 p. 331, is probably an imitation of this.) as the Pythagoreans[*](Pythagoras is a great name, but little is known of him. Pythagoreans in later usage sometimes means mystics, sometimes mathematical physicists, sometimes both. Plato makes use of both traditions but is dominated by neither. For Erich Frank’s recent book, Plato und die sogenannten Pythagoreer, cf. my article in Class. Phil. vol. xxiii. (1928) pp. 347 ff. The student of Plato will do well to turn the page when he meets the name Pythagoras in a commentator.) affirm and we admit,[*](For this turn of phrase cf. Vol. I. p. 333, 424 C, Protag. 316 A, Symp. 186 E.) do we not, Glaucon?” “We do,” he said. Then, said I, since the task is, so great, shall we not inquire of them[*](For the reference to experts Cf. 400 B, 424 C. Cf. also What Plato Said, p. 484, on Laches 184 D-E.) what their opinion is and whether they have anything to add? And we in all this[*](παρά of course here means throughout and not contrary.) will be on the watch for what concerns us.” “What is that?” “To prevent our fosterlings from attempting to learn anything that does not conduce to the end[*](I take the word ἀτελές etymologically (cf. pp. 66-67, note b, on 500 A), with reference to the end in view. Others take it in the ordinary Greek sense, imperfect, incomplete.) we have in view, and does not always come out at what we said ought to be the goal of everything, as we were just now saying about astronomy.