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Chapter Vii., the Pythagoreans

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Chapter Vii., the Pythagoreans CHAPTER VII., THE PYTHAGOREANS 138. ThePythagoreanSchool 139. Philolaus 140. PlatoandthePythagoreans 141. The"FragmentsofPhilolaus" 142. TheProblem 143. AristotleontheNumbers 144. TheElementsofNumbers 145. TheNumbersSpatial 146. TheNumbersasMagnitudes 147. TheNumbersandtheElements 148. TheDodecahedron 149. TheSoula"Harmony" 150. TheCentralFire 151. TheAntichthon 152. TheHarmonyoftheSpheres 153. ThingsLikenessesof Numbers 138.ThePythagoreanSchool AFTER losing their supremacy in the Achaiancities, the Pythagoreans concentratedthemselves at Rhegion; but the school foundedthere did not maintainitself for long, andonly Archytas stayed behindinItaly. Philolaos andLysis, the latter of whom hadescapedas a young manfrom the massacre of Kroton, had already found their way to Thebes.1 We know from Plato that Philolaos was there towards the close of the fifthcentury, andLysis was afterwards the teacher of Epameinondas.2 Some of the Pythagoreans, however, were able to return to Italy later. Philolaos certainly did so, and Plato implies that he hadleft Thebes some time before 399 B.C., the year Sokrates was put todeath. Inthe fourthcentury, the chief seat of the school is the Doriancity of Taras, and we findthe Pythagoreans heading the opposition to Dionysios of Syracuse. It is to this period that the activity of Archytas belongs. He was the friendof Plato, andalmost realisedthe ideal of the philosopher king. He ruled Taras for years, andAristoxenos tells us that he was never defeatedinthe fieldof battle.3 He was also the inventor of mathematical mechanics. At the same time, Pythagoreanism hadtaken root inthe East. Lysis remainedat Thebes, where Simmias andKebes hadheardPhilolaos, while the remnant of the 206 Pythagoreanschool of Rhegionsettledat Phleious. Aristoxenos was personally acquaintedwiththe last generation of this school, and mentioned by name Xenophilos the Chalkidian from Thrace, with Phanton, Echekrates, Diokles, and Polymnastos of Phleious. They were all, he said, disciples of Philolaos andEurytos,4 andwe learnfrom Platothat Simmias andKebes of Thebes andEchekrates of Phleious were also associates of Sokrates.5 Xenophilos was the teacher of Aristoxenos, and lived in perfecthealthatAthenstotheageofahundredandfive.6 139.Philolaos This generationof the school really belongs, however, toa later period; it is withPhilolaos we have now todeal. The facts we know about his teaching from external sources are few in number. The doxographers, indeed, ascribe tohim anelaborate theory of the planetary system, but Aristotle never mentions his name inconnexionwiththat. He gives it as the theory of "the Pythagoreans" or of "some Pythagoreans."7 It seems natural tosuppose, however, that the Pythagorean elements of Plato's Phaedo andGorgiascomemainlyfromPhilolaos.PlatomakesSokratesexpresssurprisethatSimmiasandKebes hadnot learnt from him why it is unlawful for a mantotake his life,8 andit seems tobe impliedthat the Pythagoreans at Thebes usedthe word"philosopher" inthe special sense of a manwhois seeking tofinda way of release from the burdenof this life.9 It is probable that Philolaos spoke of the body (σῶµα) as the tomb(σῆµα) of the soul.10 We seem tobe justified, then, in holding that he taught the old Pythagorean religious doctrine in some form, and that he laid special stress on knowledge as a meansofrelease.ThatistheimpressionwegetfromPlato,whoisfarthebestauthoritywehave. We know further that Philolaos wrote on "numbers"; for Speusippos followed him in the account he gave of the Pythagorean theories on that subject.11 It is probable that he busied himself mainly with arithmetic, andwe canhardly doubt that his geometry was of the primitive type described inanearlier chapter. Eurytos was his disciple, and we have seen (§ 47) that his views were still very crude. We alsoknow now that Philolaos wrote onmedicine,12 andthat, while apparently influencedby the theories of the Sicilian school, he opposedthem from the Pythagoreanstandpoint. Inparticular, he saidthat our bodies were composedonly of the warm, anddidnot participate inthe cold. It was only after birththat the coldwas introducedby respiration. The connexionof this withthe oldPythagorean theory is clear. Just as the Fire in the macrocosm draws in and limits the cold dark breath which surrounds the world (§ 53), so do our bodies inhale cold breath from outside. Philolaos made bile, blood, andphlegm the causes of disease; and, inaccordance withthis theory, he hadtodeny that the phlegm was cold, as the Sicilianschool held. Its etymology provedit tobe warm. We shall see that it 207 was probably this preoccupationwiththe medicine of the Sicilianschool that gave rise tosome of the moststrikingdevelopmentsoflaterPythagoreanism. 140.PlatoandthePythagoreans Such, sofar as I canjudge, was the historical Philolaos, thoughhe is usually representedin a very different light andhas evenbeencalleda predecessor of Copernicus. To understandthis, we must turnourattentiontothestoryofaliteraryconspiracy. We have seen that there are one or two references to Philolaos in Plato,13 but these hardly suggest that he played an important part in the development of Pythagorean science. The most elaborate account we have of this is put by Platointothe mouthof Timaios the Lokrian, of whom we know no more than he has chosen to tell us. It is clear at least that he is supposed to have visited Athens when Sokrates was still in the prime of life,14 and that he must have been practically a contemporary of Philolaos. It hardly seems likely that Plato should have given him the credit of discoveries which were really due to his better known contemporary. However, Plato had many enemies and detractors, and Aristoxenos was one of them. We know he made the extraordinary statement that most of the Republic was tobe foundina work by Protagoras,15 andhe seems alsotobe the original source of thestory that Platobought "three Pythagoreanbooks"from Philolaos andcopied the Timaeus out of them. According to this, the "three books" had come into the possession of Philolaos; and, as he hadfallenintogreat poverty, Dionwas able tobuy them from him, or from his relatives, at Plato's request, for a hundredminae.16 It is certain, at any rate, that this story was already current inthe thirdcentury; for the sillographer Timonof Phleious addresses Platothus: "Andof thee too, Plato, didthe desire of discipleshiplay hold. For many pieces of silver thou didst get inexchange a small book, andstarting from it didst learntowrite Timaeus."17 Hermippos, the pupil of Kallimachos, saidthat "some writer" saidPlatohimself bought the books from the relatives of Philolaos for forty Alexandrian minae and copied the Timaeus out of it; while Satyros, the Aristarchean, says he got it throughDionfor a hundredminae.18 There is nosuggestioninany of these accounts that the book was by Philolaos himself; they imply rather that what Platobought was either a book by Pythagoras, or at any rate authentic notes of his teaching, whichhad come intothe hands of Philolaos. Inlater times, it was generally supposed that the forgery entitled The Soul of the World, which goes by the name of Timaios the Lokrian, was meant;19 but it has now beenprovedthat this cannot have existedearlier than the first century A.D. Moreover, it is plain that it is based on Plato's Timaeus itself, and that it was written in order to bolster up the story of Plato's plagiarism. It does not, however, fulfil the most importantrequirement,thatofbeinginthreebooks,whichisalwaysanessentialfeatureofthatstory.20 208 Not one of the writers just mentionedprofesses tohave seen these famous "three books";21 but at a later date there were at least twoworks which claimedtorepresent them. Diels has shownhow a treatise inthree sections, entitledΠαιδευτικόν, πολιτικόν, φυσικόν, was composedinthe Ionic dialect andattributedtoPythagoras. It was largely basedonthe Πυθαγορικαὶ ἀποφάσειςof Aristoxenos, but its date is uncertain.22 In the first century B.C., Demetrios Magnes professes to quote the opening words of the work publishedby Philolaos.23 These, however, are inDoric. Demetrios does not actually say this work was writtenby Philolaos himself, thoughit is nodoubt the same from whicha number of extracts are preservedunder his name inStobaios andlater writers. If it professedtobe by Philolaos, that was not quite inaccordance withthe original story; but it is easy tosee how his name may have becomeattachedtoit.Wearetoldthattheother bookwhichpassedunderthenameofPythagoraswas really by Lysis.24 Boeckh has shown that the work ascribed to Philolaos probably consisted of three books also, and Proclus referred to it as the Bakchai,25 a fanciful Alexandrian title which recalls the "Muses" of Herodotos. Twoof the extracts inStobaios bear it. It must surely be confessedthat the wholestoryisverysuspicious. 141.The"FragmentsofPhilolaos" Boeckhargued that all the fragments preservedunder the name of Philolaos were genuine; but no one will now go so far as that. The lengthy extract on the soul is given up even by those who maintainthe genuineness of the rest.26 It cannot be saidthat this positionis plausible. Boeckhsaw there was nogroundfor supposing that there ever was more thana single work, andhe drew the conclusion that we must accept all the remains as genuine or reject all as spurious.27 As, however, many scholars still maintainthe genuineness of most of the fragments, we cannot ignore them altogether. Arguments basedontheir doctrine would, it is true, present the appearance of a vicious circle at this stage, but therearetwoseriousobjectionstothefragments,
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