if the soul is really one, the definition of justice as a relation between its parts loses all meaning. But such "inconsistencies" are inherent in human thought, and prove nothing for the relative dates of Book X and Books II-V. Can any modern theologian produce definitions of the virtues that will apply to man in his earthly state and to the disembodied soul?615 Lutoslawski, while rejecting the fancies of Krohn and Pfleiderer, holds it possible to show that the first book of the Republic falls between the Gorgias and the Phædo, and that the remaining books follow the Phado and reveal traces of progressive development of doctrine. The following parallel illustrates the force of his arguments: P. 277: "This sharp and general formulation of the law of contradiction,616 not only as a law of thought as in Phado,617 but for the first time as a law of being . . . . is a very important step." 620 P. 318: "Here 618 for the first time occurs a formulation of the law of contradiction as a law of thought, while in the Phado and earlier books of the Republic it was a metaphysical law." Lastly, a word must be said of the attempt to trace a development in Plato's treatment of poetry. The contradictions of those who employ this method might be left to cancel one another.619 But the whole procedure is uncritical. Plato was always sensitive to poetic genius, and there was no time when he might not have praised Homer without conspicuous irony." But he always regarded the poet as an imitator, whose aim is pleasure rather than the good, whose ethical teaching must be interpreted or controlled by the philosopher, and whose fine sayings are the product of "inspiration" rather than of knowledge. The Apology 621 anticipates the Republic in the doctrine that the poets do not know whereof they speak, and the Phædrus in the theory of poetic inspiration. The Gorgias, 502 B CD, deals with the moral influence of poetry upon the masses in the tone of the Republic and Laws; and like Republic, 601 B, strips from the body of the poet's discourse the meretricious adornment of the poetic dress. The doctrine that poetry is uíunois is sufficiently implied in Cratylus, 423, where the mimetic value of words is discussed, and where μovouǹ is classified as piunois. The differences between the tenth and the third books of the Republic cannot be pressed. The third book hints that there is more to come; and the tenth book announces itself as a profounder discussion, based on psychological distinctions brought out in the intervening books. But it is begging the question to assume that they were discovered by Plato after the composition of the third book. The fact that 615 Cf. supra, pp. 6, 7, and HIRMER, p. 641. 616 436 B. 617 102 E. 618 602 E. 619 LUTOSLAWSKI says that Plato's scorn of poetry developed after the Symposium, and that the tenth book of the Republic is therefore later than the Phado, which praises Homer without irony, and earlier than Phaedrus and Theatetus, which take for granted the low estimate of the poet. But NATORP, thinking of other passages of the Phædrus, is positive that such a dialogue could not have been written after the rejection of poetry in the Republic; while DUMMLER (Vol. I, p. 269) places the Symposium after 622 624 623 in emphasizing the distinction between dramatic and narrative poetry Plato carelessly speaks as if the former alone were imitative, proves nothing." A far more important new point made in the tenth book is already distinctly implied in the Protagorasthe antithesis between the principle of measure in the soul and тoû paivoμévov Súvaus, to which poetry makes its appeal.625 The mood of the Symposium differs from that of the Gorgias and the Republic. But this does not prove either that the Symposium is earlier, or that Plato had been mellowed by success. A banquet at which Agathon was host and Aristophanes a guest was obviously not the place for a polemic against dramatic poetry. But even here the ironical superiority of the dialectician is maintained, and the inability of the poets to interpret or defend their art is revealed.626 CONCLUSION. IDEAS AND NUMBERS. THE LAWS The value of Plato's life-work would be very slightly affected even if it were true that in the weakness of extreme old age the noble light of his philosophy did "go out in a fog of mystical Pythagoreanism." It is not in the least true, however, and the prevalence of the notion is due mainly (1) to the uncritical acceptance of the tradition concerning Plato's "latest" doctrine of ideas and numbers; and (2) to the disparaging estimate of the Laws expressed by those who care only for dramatic charm of style, or by radicals like Grote, who are offended by the "bigotry" of a few passages. must be said on each of these points. A word 1. Aristotle's account of Plato's later identification of ideas and numbers has been generally accepted since Trendelenburg's dissertation on the subject.27 Zeller rightly points out that the doctrine is not found in the extant writings, but adds that for Plato numbers are entities intermediate between ideas and things of sense. In my discussion of the subject 628 I tried to establish two points: first, that we need not accept the testimony of Aristotle, who often misunderstood Plato, and was himself not clear as to the relation of mathematical and other ideas; second, that the doctrine of numbers as intermediate entities is not to be found in Plato, but that the passages which misled Zeller may well have been the chief source of the whole tradition about ideas and numbers. The first point is a matter of opinion. I did not deny the testimony of Aristotle, and no one who chooses to accept it can be refuted. The relation of ideas to numbers was doubtless much debated by the scholastics of the Academy. Aristotle's reports of the intolerable logomachy do not make it clear just how much of this nonsense he attributed to Plato. But I do not intend to enter upon the interpretation of the eleventh and twelfth books of the Metaphysics. No reader would 623 393 C, 394 D. 625 Rep., 602, 603. 624 Protag., 356 D. 626 201 Β, κινδυνεύω, ὦ Σώκρατες, οὐδὲν εἰδέναι ὧν τότε εἶπον. Καὶ μὴν καλῶς γε εἶπες, φάναι, ὦ ̓Αγάθων. Cf. also 223 D, where Socrates compels Agathon and Aristophanes to admit Tou αὐτοῦ ἀνδρὸς εἶναι κωμῳδίαν καὶ τραγῳδίαν ἐπίστασθαι ποιεῖν. This is thought to contradict Repub., 395 A, but the contradiction is removed by pressing réxvŋ in what follows. One man is "inspired" by the tragic muse, another by the 627 Plat. de id. et numeris doctrina, 1828. follow me, and no results could be won. If Aristotle's testimony be accepted, there is an end of controversy. Plato taught in his lectures the doctrine of ideas and numbers. But the second point is not so elusive. It is possible to test the argument that the extant writings do not recognize an intermediate class of mathematical numbers, and yet might easily suggest the notion to mechanical-minded students. Now Zeller in his fourth edition confounds the two questions. He gives the impression that he is answering me by a Quellenbelege from Aristotle and Philoponos. He wholly ignores my interpretation of a number of specific Platonic passages, which he apparently takes for the mere misunderstandings and blunders of a beginner. I have no hope of convincing Zeller, nor do I wish to force myself into a polemic with the honored master of all who study Greek philosophy. But, as Mr. J. Adam, a scholar whose scrupulous candor makes it a pleasure to argue with him, has expressed surprise in his edition of the Republic that I still adhere to my opinion in spite of the mass of evidence, I will endeavor to state my meaning more plainly. 630 629 The theory of ideas, the hypostatization of all concepts, once granted, numbers do not differ from other ideas. The phrase, Tеρì aνтŵν тŵν àρioμŵv (Rep., 525 D), denotes ideal numbers or the ideas of numbers, and ὁρατὰ ἢ ἁπτὰ σώματα ἔχοντας ȧpioμous are numbered things, things of sense participant in number." That is all there is of it, and there is no extant Platonic passage that this interpretation will not fit. For educational purposes it is true that mathematical science holds an intermediate place between dialectic and the perceptions of sense. Mathematical abstractions (teρì tò èv μálnσis, Rep., 525 A) are the best propedeutic to abstract reasoning generally. But there is no distinction of kind between them and other abstractions, σλŋpòv μaλaкóv (Rep., 524 A ff.). Mathematical science as diavola is midway between the pure voûs of dialectic and the doğa of sense. But that is because of its method—the reliance on diagrams (images) and hypotheses. In themselves its objects are explicitly stated to be pure vonтá. The "mathematical" numbers then are plainly the abstract, ideal numbers of the philosopher. The numbers of the vulgar are concrete numbered things. There is no trace of a third kind of number.632 Those who have not yet learned to apprehend abstractions mockingly ask the mathe 629 It may be permissible to add that he seems to have read other parts of the dissertation with more attention, since, to mention only two cases, he adds on p. 745 a reference à propos of the тpiros aveрwños to Republic, 596, 597, and Tim., 31 A, with the interpretation of their significance given on p. 30; and he omits from p. 547 of the third edition a sentence criticised on p. 49 of the dissertation. Another slight but significant point may be mentioned. Aristotle himself makes a not wholly clear distinction between mathematical ideas (τὰ ἐν ἀφαιρέσει λεγόμενα, almost technical) and other ideas. In illustration of this I objected to Zeller's interpretation of De An., 432a2, év roîs eideσí roîs αἰσθητοῖς τὰ νοητά ἐστι . . . . τά τε ἐν ἀφαιρέσει λεγόμενα (“die abstrakten Begriffe”) καὶ ὅσα τῶν αἰσθητῶν ἕξεις καὶ πάθη. My objection was that both grammar and Aristotelian usage showed that öoa Twv aiσ@ŋτŵv, etc., are also abstrakte Begriffe (in the German or English sense of the words), 631 the voŋrá being divided into two classes by re-kai. The sentence still stands, and I am quite willing to leave the question of Flüchtigkeit to any competent scholar, e. g., to M. Rodier, who translates "les intelligibles, aussi bien les concepts abstraits (ou mathématiques) que (ceux qui ont pour objet) les qualités, etc." 630 Adam translates avrov Tv åρíðμŵv, “numbers them. selves," which is quite right. My point is that "numbers themselves" are proved by the context and by Philebus, 56 E, to be ideal numbers. For Adam's further argument cf. infra, p. 84. 631 Rep., 510 D, τοῦ τετραγώνου αὐτοῦ ἕνεκα . . . . καὶ διαμέτρου αὐτῆς, αλλ' οὐ ταύτης ἣν γράφουσιν. 511 D, καίτοι νοητῶν ὄντων μετὰ ἀρχῆς. 632 Phileb., 56 D E. 634 maticians (Rep., 526 A), περὶ ποίων ἀριθμῶν διαλέγεσθε; and the answer is, περὶ τούτων ὧν διανοηθῆναι μόνον ἐγχωρεῖ, coupled with an exposition that recalls the Parmenides of the pure idea of unity.633 Simple as all this appears, it might easily be misunderstood by the pupils of the Academy. Mathematics was intermediate from an educational point of view. In cosmogony numbers and geometrical forms are the mediators between chaos and the general idea of harmony and measure. The expression, numbers (arithmetic), of the vulgar and numbers of the philosopher would lead a perverse ingenuity to ask of the mathematicians, in the words of the Republic, πeρì πоíwv åρíðμŵv diaλéyeode; Plato's use of "dyad” and “triad" as convenient synomyms for the pure idea of two and three would be mistakenly supposed to imply a distinction.65 The innocent question (Rep., 524 C), Tí Ovν TOT' ẻσTì tò μéya av kaì Tò σμikρóv,636 would suggest that it was a terminus technicus for some mysterious ultimate philosophical principle, and set students upon hunting it and its supposed synomyms through the dialogues, and, inasmuch as μéya + σμкpóv indubitably=2, it might well be identified with the indeterminate dyad and its supposed equivalents, or any other "principle" posited in antithesis to the one.637 The folly once set a-going, there are no limits to its plausible developments. All the unanswerable questions as to the relation of ideas to things may assume special forms for special classes of ideas. Plato himself shows this for ideas of relative terms in a much misunderstood passage of the Parmenides. The problem of the relations of numbered things, of the supposed mathematical numbers, and of ideal numbers, offered a rich feast for the quibblers and the opaleis of the Academy. "Before and after" is essential to number, but there is no "before and after" in the ideas. Multiplicity is inherent in number, but the "idea" even of a million must be one. Other ideas may be imperfectly copied by things, but is not the number five entirely present in five things? Echoes of this pitiful scholasticism are preserved for us in the metaphysics of Aristotle. But what possible reason can there be for attributing it to Plato? Adam himself (Vol. II, p. 160) repeats the disconsolate question: περὶ ποίων ἀριθμῶν διαλέγεσθε ἐν οἷς τὸ ἓν οἷον ὑμεῖς ἀξιοῦτέ ἐστιν, ἴσον τε ἕκαστον πᾶν παντὶ καὶ οὐδὲ σμικρὸν διαφέρον; and asks: "Are we then to suppose that there are many ideas of 'one'?" The answer is: "Yes, precisely, to the extent that there are many ideas of anything." We have already seen (Rep., 476A) that every idea is per se one, and yet, not merely as reflected in phenomena, but τῇ ἀλλήλων κοινωνία appears many. The contradiction is inherent in the theory of ideas. As against the multiplicity of phenomena, we insist on the indivisible unity of the idea. But when we find the idea involved with other ideas in a number of instances, we are forced to use the plural. Plato does not, however, here 638 633 Cf. Idea of Good, p. 222; Phileb., 56 E, ei μn μováda μονάδος ἑκάστης τῶν μυρίων μηδεμίαν ἄλλην ἄλλης διαφέρουσαν τις θήσει, 634 Tim., 53 B ff.; Phileb., 66 A. 635 Phædo, 101 C; Parmen., 149 C; Phado, 104. 636 Plato is using the terms precisely as BERKELEY does when he says (Principles of Human Knowledge, XI): "Again, great and small, swift and slow are allowed to exist nowhere without the mind, being entirely relative, and changing as the frame or position of the organs of sense varies." 637 De Plat. id., p. 37. 638 133 C ff.; cf. A. J. P., Vol. IX, p. 288. in terms pluralize the "one." He says: Of what numbers do you speak in which the one, i. e., the idea of one, present in each as a constituent and essential part of the more complex idea, etc.? Of course, this implies a multiplicity of units in each number, and still more in all; but only as any idea is multiplied when it appears in a number of others. The multiplication of the idea Tŷ tŵv owμátwv kovovíą is more easily evaded than that тộ ảλλýλwv koivwvíą, because in the first case we may use the imagery of pattern and copy, while, in the second case, the idea is an essential constituent part of that into which it enters. In the special case of numbers, the paradox is still more glaring. But Plato is not one to be frightened from the path of philosophical consistency by a paradox which he rightly regarded as largely verbal. In the Parmenides he amuses himself by showing that the idea of "one" itself apprehended τῇ διανοίᾳ μόνον καθ ̓ αὑτὸ breaks up into many. This does not make it the less necessary for the mathematician to apprehend the pure absolute idea of unity and restore it as fast as it is disintegrated by analysis or the senses. 639 640 2. Despite many passages of stately and impressive eloquence, the Laws will remain the type of "frigidity" for those who, like Lucian, read Plato mainly for the dramatic vivacity of the Phædrus or the artistic beauty of the Symposium. Our purpose is not to deny the altered mood and style that mark the masterpiece of Plato's old age, but merely to protest against the notion that it may be safely neglected by the serious student, or that it presents a doctrine essentially different from that of the Republic. 642 If Plato was not to rewrite the Republic, it was almost inevitable that his political studies should assume the form of a project of detailed legislation for a possible Greek city. But even here, while recognizing that many of his theoretic postulates will have to be mitigated in practice," he holds fast in principle to the ideals of the earlier work. A harmony of the Laws and Republic, however, though not a difficult task, would demand more space than can be given to it here. We need not delay to examine the contribution of the Laws to our knowledge of Greek institutions, or the very considerable influence which it exercised upon the speculations of Aristotle and later Greek thinkers. One service which it renders to students of the dialogues we have already often noted. 643 As the years wore on, Plato naturally grew weary of Socratic irony, of the game of question and answer, of the dramatic illustration or the polemical analysis of eristic. Even in the earlier dialogues he sometimes evades or contemptuously explains away an equivocation which elsewhere he dramatically portrays or elaborately refutes." In the Laws this is his habitual mood, and in consequence the Laws may often be quoted for the true Platonic solution of problems which Socratic irony or dramatic art seems to leave unsolved in the earlier dialogues.' 644 645 While acknowledging this change of mood, we must be on our guard against the 639 143 A, 144 E. 640 Rep.,525 E; supra, n. 647. 641 746. 642 739 C ff., 807 B. 643 Rep., 436 CD E, 437 A, 454 A; Cratyl., 431 A; Symp., 187 A; Euthyd., 277 E. 644 627 B, 627 D, 644 A, 864 B. 645 Supra, pp. 13, 19, nn. 70, 71, 293. |
