A HISTOEYOFGEEEK PHILOSOPHYFKOM THE EAKLIEST PERIOD TO THE.TIME OF SOCRATESWITH A G ENERA L INTR DUCT10 XTRANSLATEDFROMTHEGERMANOFD^ E. ZELLEEyj^f^"^^PROFESSOR IX THE UKIVERSITY OF BERLINbjitb iht giutljor's sanctioitBYS. F. ALLEYNE7.Y TWO VOLUMESVOL. I.LONDONLONGMANS, GREEN, AND CO.1881,1/; rights i-eservedrLi f,lv..^ft......i"Is\OOOZ5TRANSLATOE'S PREFACE.The present work is a translation of the fourth andlast edition of the. first part of Dr. Zeller's'Philo-sophie der Grriechen.' That this part, containing theGeneralIntroduction tothe entire subject and thehis-tory of the earliest philosophers, should appear afterothersdealing* with the later periods, is in somemea-sure tobe regretted,because Greek Philosophy is besttreated as a whole, and gains immensely by beingstudied in the order of development;yet those whoareacquainted with the previouslytranslated portionsofDr. Zeller'sworkwill be themorereadytowelcomethe introductoryvolume,without which, indeed,manythingsinthe laterphilosophy,andinDr.Zeller's treat-mentofit, wouldhaveremainedcomparativelyobscure.Thereis noneed to speak highlyof aworksowellknown. Thetranslator has endeavoured to makeherversion as literal as possible, considering the require-ments of the English language and its deficiency inpreciseequivalents for German philosophicaltermsavi TRANSLATORSPREFACE.deficieucy giving rise to many difficulties which shecannothopetohavealwayssuccessfullyovercome.She desires to express her hearty thanks to Mr.Evelyn Abbott, Fellow and Tutor of Balliol College,Oxford,for his valuable assistance in reading overtheproof sheets, especiallyinregardtotheGreeknotes.It is, perhaps, necessary to add, respecting thenumerous references,thatVol. I. and II. stand for thevolumes of the presenttranslation,andPart I. II. andIII. forthedivisions of the Grermanwork.Clifton- : December6, 1880.AUTHOR'S PREFACE.Twenty years ago,whenI published in its laterformthe first volume of this work, originally designed ona different plan, and a far more limited scale, I ex-plained in the following words the principles whichhad guidedmein its composition:'In the treatmentof my subjectI have constantlykept in viewthe taskwhichIproposedto myselfin myfirst approachesto it;viz. to maintain a middle course betweenerudite en-quiryandthespeculative studyof history: neither, onthe one hand, to collect facts in a merely empiricalmanner ; nor, ontheother, toconstruct aprioritheories;butthroughthetraditionsthemselves,bymeansofcri-tical sifting and historical combination,to arrive ataknowledge of their importance and interdependence.Thistask,however, inregardto thepre-Socraticphilo-sophywasrendered peculiarly difficultbythecharacterofthesourcesandthedivergenciesof modernopinionsrespectingthem: it wasimpossible adequatelyto fulfilit without a number of critical discussions, oftendescendingto tlie minutestdetails. Thatthe clearnessviiiAUTHORSPREFACE.of the historical exposition, however, might not bethereby impaired, I have consigned these discussionsas muchas possible to the notes,where also thetesti-monies and references respecting the authorities finda fitting place. But thewritingsfromwhichthese aretaken are many,andsomeof themdifficult to obtain,so that it has often been necessary to givethequota-tions atlengthto makeit possibleforthereaderto testthe authenticityof myexpositionwithoutanunwarrant-able expenditure of time. Thus the amountof notes,and consequently the size of the whole volume, haveincreased to a considerable extent;but I hopeIhavechosen rightly in attending before all things to thescientific requirements of the reader,and in doubtfulcasespreferring to economise his timerather than theprinter's paper.'I have keptto the samepoints ofviewin the pre-paration of the following volumes, and of the neweditionswhich have sincebecomenecessary. Thehopethat I havethereinadoptedthepropercoursehas beenfullyjustified bythereceptiongiven tomywork;andthoughtheprinciple (not previouslyquite unknown tome)hasrecently beenpressedupon myattention, thattheancient philosophers must be treated philosophically,I haveneveryetbeenable to convincemyself thatthemethodhithertopursuedbymehasbeen a mistake. Istill hold,morestronglythan ever, thatthephilosophicapprehensionofsystemsofphilosophy(which,however,must be distinguished fromphilosophiccriticism) en-AUTHOR'S PREFACE.ixtirely coincideswith the historicapprehensionofthem.I can never indeedconsiderthat a proper historyhasbeenwritten iftheauthorhasstopped short at thebareenumerationofisolateddoctrinesandstatementswithoutenquiringas totheircentre ofgravity,examiningtheirinterconnection, or tracing out their exact meaning;without determining their relation and importanceto the various systems collectively. But, ontheotherhand, I must protest against the misuse ofthenoblename of philosophyfor the purpose of depriving his-torical phenomena of their distinctive character, offorcingupontheancient philosophers inferences whichtheyexpresslyrepudiate,ofeffacing the contradictionsandsupplyingthelacunaeoftheir systemswithadjunctsthatarepureinventions. Thegreatphenomenaofthepast are muchtoogreatinmyeyes formeto supposethatIcoulddothemanyservice byexalting themabovetheir historical conditions and limitations. In myopinion,such a false idealisation makes them smallerinstead of greater. Atall events,nothingcantherebybe gained for historic truth, beforewhich everypredi-lection for particularpersons andschools must giveway.Whoeverwould expoundaphilosophicsystemmustre-produce thetheories heldbyitsauthorintheconnectionwhich they had in his mind. Thiswe can onlylearnfromthetestimonyofthe philosophersthemselves,andfromthestatementsofothersconcerningtheirdoctrines;but, incomparingthesetestimonies,in examiningtheirauthenticityandcredibility, in completingthembyin-X AUTHORSPREFACE.ferencesandcombinationsof variouskinds,wemustbecarefultoremembertwo things: in the first place,theinductionswhichcarry us beyonddirecttestimonymustin eachcase be foundedonthetotality of evidenceinourpossession;andwhenaphilosophictheory seemstous to require certain furthertheories, we mustalwaysexamine whetherotherportions oftheauthorssystem,quite as importantin hisestimation,donotstand intheway. Secondly,wemustenquirewhetherwearejusti-fied insupposingthatthephilosopher weareconsideringpropoundedtohimselfthe questionswhichwearepro-poundingtohim,returnedtohimselfthe answerswhichwederivefromother statementsofhis, orhimselfdrewthe inferenceswhich to usappear necessary. Topro-ceedin this spirit ofscientific circumspectionhas beenat anyratemyownendeavour. Tothis end, aswillbeseeninthelaternolessthanintheearliereditionsof mywork, I havealso tried to learnfromthose writerswhohereandthere,onpointsofgreaterorlesserimportance,havediffered fromme. IfI amindebtedtothesewritersfor manythingsthat have assisted in the completionandcorrection of myexposition, it will neverthelessbeunderstoodthat, in all essential points, Icould onlyre-maintrue tomyown view of the pre-Socratic philo-sophy,and havedefendedthatviewas persistentlyanddecidedly as the interest of the subject demanded,against objections which seemed to meunconvincinganduntenable.I dedicated thesecond edition ofthepresentworkAUTHORSPREFACE. xito myfather-in-law, Dr. F. Che.Baur, of Tiibingen.In the third I was obliged to omit the dedication,because he to whom it was addressed wasno longeramongus. ButI cannotrefrainfrom recalling in thisplace, with affection and gratitude, the memory of amanwhowas not onlyto me in all personal relationsa friendandfather, butalso, in regard to myscientificlabours, has left formeandforall hisdisciplesashiningexampleof incorruptiblelove of truth, untiring perse-verancein research,inexhaustiblediligence,penetrativecriticism,and widthand coherence in the treatment ofhistory.Berlin: October 18, 1876.CONTENTS01'THE FIEST VOLUME,PACKTranslator's Preface . vAuthor's Preface . . . viiGENERAL IIS^TIlODUCTIO:sr.CHAPTER I.AIM, SCOPE,AND METHOD OF THE PRESENT WORK 1-25CHAPTER 11.ORIGIN OF GREEK PHILOSOPHY.i. Supposedderivation of Greek philosophyfrom Orientalspeculation .26ii. Nativesources of Greekphilosophy.1. Religion 49a. Greekreligion ....... 49b. TheMysteries 59iii. Nativesources of Greekphilosophy (continued).2. Morallife : civilandpoliticalconditions , . . 7oiv. NativesourcesofGreekphilosophy(continued).3. Cosmology 83v. Ethical reflection.4. Theologyand Aiithropologyin relation to Ethics . . 109CONTENTS OFTHEFIRST VOLUME.CHAPTER III.PACKON THE CHARACTER OF GREEK PHILOSOPHY 129-163CHAPTER IV.THE PRINCIPAL PERIODS IN THE DEVELOPMENT OF GREEKPHILOSOPHY 164-183FIRST PERIOD.THE PRE-SOCRATIC PHILOSOPHY.Introdl'ction. On the Character and Development ofPhilosophy in the First Period .... 184-210FIBST SECTION.THE EARLIER lOXTANS, PYTHAGOREANS, ANDELEATICS.I. The Earlier Ionian Phtsics.1. Thales 2112. Anaximander 2273. Anaximenes ..........2664. Lateradherentsof theIonian School. Diogenesof Apollonia 280II. The Pythagoreans.1. Sourcesof ourknowledge in regardto thePythagoreanphilo-sophy ......o062. Pythagorasandthe Pythagoreans3243. ThePythagorean philosophy: its fundamental conceptions:Numberandthe Elementsof Number . . ... 3684. Systematicdevelopmentof theNumber system,and its appli-cation to Physics419CONTENTS OF THEFIRST VOLUME. xvPACE0. Eeligiousandethicaldoctrines of the Pythagoreans . . . 4816. Eetrospectivesummary: cliaracter,origin,andantiquityofthePythagoreanphilosophy .......4967. Pythagorean ismincombinationwithotherelements: Alcmweon,Hippasus,Eephantus,Epicharmus o21III. The Eleatics.1. Sources in regard to their doctrines. Treatise on Melissus,Xenophanes,andGrorgias . . . . . . .5332. Xenophanes ..........^oQ3. ParmenidesobO4. Zeno6080. 3Ielis>us6276. Hibtoricalpositionandcharacterof the EleaticSchool . .638PaE E R A TA.:e 4. line i^forShepherdBoo-Koi read herdsof grazincr Boa/coi.54, line 2 fromfoot/orparticulars readparticular.72, line \'?iforseventeenthreadseventh.94, 2, line 17/orsup.p. 93 readsup. p. 91. 3;cf. 98, 4.14.5, 1, line2forthe Prota,2;oras readProtagoras.214, n. line28 (firstcolumn)/or AnacoliusreadAnatolius.219, 3, line 10 (secondcolumn);/r/r affinity readinfinity.231, n. line 20 (firstcolumn)/or233, 1 read228, 3.247,1/or223, 1 read233, 1.251,line 9/orsurroundsreadsurrounded.260, 4/ori:-l, 1 rend2.51, 1.2G3, 2/orpp.197,200read241, 244.265,3for197read241.269, 2, line8/or268, 1 rearf267, 1.288,3/or241, 1 read241, 2.289, 1, line9/or291, 1 read291^2.292,1/or290, 4 rea^i291, 1.352,1/or336,4 rearf336, 5.434, 2, fine2/or426. 6 read429, 6.444, 1,line3furconservationreadassertion.444,2for442, 1 read443, 1.468, 1,line 5fromfoot (secondcolumn)/or415 read526.527,Bfor372, 1 read372, 4.527,4,line4fromfoot/or491 read528.531,2for529, 5 read530, 2.538,1/or547, 1 read548, 1.543, 1,line 14(secondcolumn)/or547, 1 read548, 1.,554,Afor547, 1 read548, 1.554, 4/>r542, 1 read543, 1.560, 1,lines 18and19forinfra readsupra;for544, 1 read545, 1.566,1for549, 1 rea/i 548, 2;/or560, 2 read562, 5.587, line8omittherefore608, 2, lines4and7for543 read617, n.;for590, 1 read591, 1.623,line 19forconnections readconnection.THE PHILOSOPHY OF THE GEEEKSIX ITSHJSTOEICAL DEVELOPMENT.IXTRODUCTIOX.CHAPTER I.The teiTQ Philosophy, as in use among the Greeks,variedgreatly in its meaningandcompass.^ Originallyit denoted all mental culture, and all effort in thedirection of cultm'e;^even as crocpLa, the word fromwhichit is derived,wasappliedto everyart and everykind of knowledge.^ A more restricted significanceseems first to have been given to it in thetimeof theSophists,when it became usual to seek after a widerknowledge by means of more special and adequate*Cf. the valuable evidence of jxaXaKias. Thesame vagiieuseofHayminErschandGruber's^^Z^e- theword is long after to be metmeineEncyklofaedie,sect.iii. b.24, ^theven amongwriterswho arep. 3 sqq. notunacquainted withthe stricter-Thus Croesus says to Solon sense.(Herodotus,i.30)that hehad heard^Cf.Aristotle'sEth. Nic. vi.7,ws (jiiXoaocpeuuyriv TroXKif]v Oeoopirjs sub init., and the versequotedbyiiv^K^viiTfXrjXvdas. Similarly, Pe- him from the Homeric 3Iargites.ricles (Thucydides, ii.40),in the Cf. also infra, the section on thefuneral oration : (piXoKaKovfxevyap Sophists.fj-er eureXeiasKoi(pi\oG-0(pov/x(v&veuVOL. I.B2INTRODUCTIOIs\instructionthanordinaryeducationandtheunmethodi-cal routine of practical life could of themselves afford.^ByPhilosophywasnowunderstood the studyof thingsof the mind,piusued not as an accessoryemplo\Tnentand matter of amusement, but exclusively and as aseparatevocation. The wordPhilosophy,however,wasnot as yet limited to philosophic science in its presentacceptation, nor even to science in general, for whichother designationsweremuchmoreinvogue: tophilo-sophisewasto study, to devote oneself toanytheoreticacti\ity.^ Philosophersin the naiTowersense, downtothetimeof Socrates,were ordinarily designatedaswisemenor Sophists,^and,moreprecisely, asphysicists/. Amoredefinite use of the wordis first metwithinPlato. Plato calls thatmanaphilosopher who in hisspeculationandhis practice has regardto essence,andnotto appearance; Philosophy, as he apprehends it, is'Pythagorasindeed,according it in this way{Paneg.c.1)whenhetoawell-knoM'n anecdote,hadpre- callshisown activitytV""eplrovsviouslyassumedthe name of phi- Koyovs (piKoaocpiav, or evensimplylosopher;but the story is inthe . especially of the Ionian schools,vi. 1,41,

Gesch. derPhil. i. 172.44INTRODVCTIOX.theological character of Orientalspeculationshould beentii'ely absent from Greek philosophy. WhateversciencetherewasinEgypt,Babyloniaor Persia,was inpossession of the priestly caste, and had gTown up inonemasswith the religious doctrines and institutions.In regard to mathematics and astronomy, it is quiteconceivablethatOriental scienceshould have been de-tached from this its religious basis, and transplantedseparatelyinto foreignlands;butit is mostimprobablethat the priests should have held theories about theprimitiveconstituents and origin of the world,capableof beingtransmittedand adoptedapartfromtheirdoc-trines concerningthegodsandmythology. Nowinthemost ancient G-reek Philosophy we find no trace ofEgjrptian,Persian or Chaldseanmythology,andits con-nection even with Greek myths is very slight. Eventhe P}i:hagoreans and Empedoclesonlyborrowed fromthemysteriessuch doctrines as hadnointimaterelationwiththeirphilosophy(that is, their attempt at a scien-tific explanation of natm^e): neither the Pvlhagoreandoctrine of numbers,nor the Pythagorean and Empe-docleancosmology,canbeconnectedwith anytheologi-cal tradition as their som'ce. The rest of the pre-Socratic philosophy does, indeed,remind us in certainisolated notions of the mythic cosmogony, but in themain it developed itself either quite independentlyofthereligious belief,orinexpressoppositionto it. Howcouldthis possiblybe if Greeksciencewereanoffshootof thesacerdotalwisdomof theEast?Wemustfurtherenquirewhetherthe Greeksatthetime of tlieir first attempts at Philosopliy could haveIMPROBABILITYOFTHEORIEXTAL THEORY. 4obeen taught anytliing considerable in this sphere byOrientals. There is no historical or even probableevidencetoshowthateitherof theAsiaticnationswithwhichthey came in contact possessed any philosophicscience. We hear, indeed, of theological and cosmo-logicalnotions,but all these,so far astheyreallyappeartogobackto antiquity, are so rude and fanciful thatthe Grreeks couldscarcelyhavereceivedfrom them anyimpulse towards philosophic thought which their ownmythscouldnotjust as wellhaveafforded. Thesacredbooks of Egypt probably contained only prescripts forritual, ecclesiasticalandcivil laws,interspersedperhapswithreligious myths; in the scanty notices remainingof their contents there is no trace of the scientific,dogTQatictheologywhichmodernwritershavesoughttodiscover.^ To the Egyptian priests themselves,in thetime of Herodotus,thethought of an Egyptianoriginin regard to Greek Philosophy never seems to haveoccm-red, eagerly as they strove, even then, to deriveGrreek myths, laws, and religious ceremonies from^Eoth, loc. cit. p. 112 sqq., eventhe last-mentioned tenproba-andp.122. Heappeals to Cle- bly treate'l, not of the nature ofmens, Strom, vi. 633Bsqq. Sylh., the gods, butof religious -w-orship,where the Hermetic books being and perhaps, in connection withmentionedit is said : thereareten this, ofmythology: whenClemenshooks.TO. itsT7]vTiyirqvavi]KovTaTO)v says that these writings containedTrap' avToisdcuunal ttjv Pdyvirriav the whole'Philosophy' of the(vae^eiau Trepie'xoj/Taolou Trepi Egyptians,thewordmustbetakenGvixdruu. airapxcov, v^vwv, eux^j/, in theindeterminatesenseof whichTTOfxirSiv, kopjwv Kol ruv tovtois Ihavespokenabove,p.1 sq. More-dfioiaiu, and ten other books Trepi over, wedo notknow in the leastT6 fS/ioov Ka\ dwu Koi TTjs SAtjs how old these books were, oriratSeiastuvUp^wv. But thatthe whetherthey continued up to thecontents of these books were timeof Clemenswithout alterationseven in part scientific, cannot be andadditions.deduced from the wordsof Clemens;46 IXTB01) UC'TIOX.Egypt, and little as theyshrank from the most trans-parent inventions^in pm'suance of this end. Thescientific discoveries whichtheyclaim tohavegiventotheGreeks^areconfinedto astronomicaldeterminationsoftime. Thatthedoctrine oftransmigrationoriginatedinEgyptis onlya conjecture of Herodotus;^andwhenhe says (ii. 109)thatthe Greeksappeartohave learntgeometrythere, hefoundsthe assertionnotonEgyptianstatements,as Diodorus does, but on his own observa-tion. This justifies the supposition that in the fifthcentmy the Eg}^tians had not troubled themselvesmuch about Greek or any other Pliilosophy. EvenPlato,judging from the previously quoted passage inthe fom-th book of the'Eepublic,' must have beenignorant of the existence of aPhoenician or Egj-ptianPhilosophv. Nor does Aristotle seem to have beenawareof thephilosophic efforts of theEgyptians,will-ing as he was to acknowledge them as forerunners ofthe Greeks in mathematics and astronomy.'* Demo-1Thus" (ii.177)Solon is said b28;andinMctaph.i. 1, 981,b23tohaveborro'^'ed one of hislaws he says : 5tb Trepl AXyinrrov atfrom Amasis, who came to the fiaBrj/xariKal -KpSoTov t^xvoli avvi-thronetwentyyearslaterthanthe cnriaav. 4Ke7yap a(pei6r] axo\d(ivdate ofSolon'scode;and(c. 118) rb ruv lepewf edvos. This verythepriestsassure thehistorianthat passage, however, makes it pro-what they related to him about bablcthatAristotle knewnothingHelentheyhadheardfrom Mene- of anyphilosophicenquiry pursuedlaus' ownmouth.Wehavealready in Egj-pt. He contends loc. cit.seenexamples of this procedure, thatknowledge is onahigherlevelsupra, p. 27,note 1. whenit is pursuedonlyfor theend-Herod, ii. 4. ofknowing,than whenitservesthe3ii. 123. purposesof practicalnecessity,and*Totheastronomicalobserva- observes, in connection with this,tions of the Egyptians (on the that purely theoretic sciencesconjunctions of the planets with thereforefirstaroseinplaceswhereeacii other and with fixed stars) people were sufficiently freefromhe appeals in Metcorol. i. 6, 343, anxiety about the necessaries ofIMPROBABILITYOFTHEOlilENTAL THEORY. 47eritus assuresus tliat hehimself, in geometrical know-ledge,wasquite amatchfor the Egyptian sageswhoseacquaintancehemade.^ Solateasthe timeofDiodorus,whenGreeksciencehadlongbeennaturalisedinEgypt,andtheEgyptiansin consequenceclaimedfor themselvesthe visits of Plato,Pythagoras, and Democritus,^thatwhichtheGreeksare saidto have derived from Egyptis confined to mathematical and technical knowledge,civil laws, religious institutions, and m3rths;^theseonly are referred to in the assertion of the Thebans(i.50)'thatPhilosophyandtheaccurateknowledge ofthestarswas first invented amongthem,' forthe wordPhilosophyis hereequivalenttoAstronomy.Admitting, then, that the Egyptianmythologistsreferred to by Diodorus may have given to the con-ceptions of the gods a naturalisticinterpretation inthe spirit of the Stoics;"^thatlater syncretists (likethelifeto be able todevotethemselves eians; perhaps Eudemiis had al-tosuchsciences. Theabove-quoted readyexpressed thesameopinion,wordsindirectlyconfirm thisasser- if indeed Procliis in Euclid.19, otion. Had Aristotle considered(64 f. Friedl.)took this statementPhilosophyaswellasMathematics fromhim.to be an Egyptian product, he'In the fragmentin Clemens,would have been particularlyun- Strom, i. 304 A, where he savs oflikelytoomitit intliis connection, himself aftermentioninghisdistantsince it is Philosophyof whichhe journeys : Koi XoyicavapOpccirmassertsthatasapurelytheoretical irX^iaTwv ea^Kovaa koI ypa/xuewvscience it stands higher than all ^vi/d4(nos /xera airoSe'ltos ovdeis kmmerelytechnicalknowledge. That fie 7rap7jAAa|e, oi/S' ol Alyvmicovtherudiments of astronomy came KaKeo/xevoi 'ApTredo'dirrai.Tliein-tothe Greeksfromthe barbarians, terpretation of the last word isand more particularly from the questionable, butthetermmustinSyriansandEgyptians, wearetold any case include those of theintheEpwomisofPlato986Esq. Egyptian sageswhopossessedthe987-D sq. Similarly Strabo xvii. mostgeometricalknowledge.1,3, p. 787, af-cribes the invention^j gg^ gg,ofGeometrytotheEgyptians,and^(jf ^_ jg^ gg^ gj^ gg^^^^^thatofArithmeticto the Phceni-v, as in Plato. "We the Limited and Unlimited. Theare not even sure whether the proposition that God has engen-quotation is from the work of dered these elements he gives asPhilolausat all. Itmaybemerely Platonic,a vague reminiscence of the pas-*Videsupra, p. 383, 2.sagein Plato. ^ Supra,p. 375 ;ef.p.391, 2.3AccordingtoSyrian, -^ide su-DD 2404THEPYTHAGOREANS.thePythagoreansbelievedingods. It is also probablethat they followed the monotheistic tendency(whichafter the time of Xenophanes exercised such an im-portant influenceon Grreekphilosophy)so far as amidstthepluralityofgodsto proclaim, withgreateremphasisthanthepopularreligion, theunity (o Osos, to Oslov);^at the same time,however,the import of the idea ofGodin relation to their philosophic system seems tohavebeensmall,^ nordoes itappeartohavebeencloselyinterwovenwiththeirenquiryconcerningthe first prin-ciples of things.^Iamconsequentlythe less able to believe that thePythagoreans taught a development of Grod in theuniverse,bywhich He gradually arrived at perfectionthroughimperfection."^ Thistheoryis closelyconnected^But certainly in connection them an immediatepostulate,andwith the popular belief; so that notascientific problem. Eoth(ii.for them, as for thegeneralityof a, 769 sqq.) himself,repugnant aspeople, the 6e7ov is identical -with this assertion naturallyis to him,Zeus. Cf theirtheoriesasto the is obliged to confess that theoversightexercised by Zeusandall sacredness and inviolability ofconnected-with it. Pythagoras'circle of ideas, in re--Bockh, Phil. 148, observes gard to religious speculation, leftthat without the theory of a littleroomforthefree intellectualhigher Unity, above the Limited development of his school ; indand Unlimited, there would re- thatamongthewritings(authenticmain no trace in the system of according to Eoth) left to us bythe Pythagoreans, recowned as the Pythagoreans, there is nonetheywerefortheirreligiousideas, which has properly a speculativeofthe Divinity. Thisremarkdoes character; but that they are allnot prejudice my opinion in the religious and popular works. Isleast. I do not deny that they not this to say, as I do, that the-reducedeverythingtotheDivinity, logical convictions here appearbut I contend that in so doing, primarilyas theobjectofreligioustheydidnot proceedin a scientific faith,andnot ofscientific enquiry?manner; and this seemstomethe^Cf. what is said in the nexteasier to understand, because by section onthe theorythat thePy-virtueof theirreligious character, thagoreans taught theexistenceofthis dependance of all things in a world-soul,respect to the Divinity was for*Eitter, P^^A. Phil. 149 sqq.;DEVELOPMENT OF GOD IN THEWORLD.405with the statement that theyheld theOne to be theDeity. FortheOneis described asthe Even-Odd,andas theOddis theperfect, andthe Even the imperfect,so, it is argued,theysupposed notonlytheperfectbutthe imperfect,andthereasonof imperfection, tobeinGrod,and accordingly held that the perfect goodcanonly arise fromadevelopmentof Grod. Imustprotestagainstsuchaninference, if onlyuponthegroundthatI disputetheidentityoftheOnewith theDeity.Buteven irrespectively of this, it could not be true, forthoughthenumberonewascalledbythePythagoreanstheeven-odd,the Onewhich is opposed as oneof theprimitivecausesto indefiniteDualityisneversocalled,^andnevercouldhe; andthenumberone,asthatwhichis derivedfrom the primitive causes,andcompoundedof them,couldinnocasebeidentifiedwiththeDeity.^Aristotle certainly says that the Pythagoreans, likeSpeusippus,deniedthatthefairestandbest could haveexistedfrom the beginning;^andashementions thistheoryinconnectionwith hisowndoctrine of the eter-Gcsch. d. Phil. 398 sqq., 436;this assertion originallybelongs,againstRitter,videBrandis,/?Adn.2Cf,p. 400, 1.Mus. of Niebuhr and Erandis, ii.^Metaph. xii. 7. 1072 b, 28:227 sqq. (pafiev 5erhu Qehv elfci Qxov a'cZiov^Not even in Theophrastus apiaroi' . . . '6croi Se vnoXau^dvov-(mpra,p.395,4). Thestatements atu, uxnrep ot UvdayopeioL kol 2t6u-of Theophrastus would prove no- annros, rd KaKKiarov kol apia-rovthing in regard to this question, /xt] 4vapxf]dvai, 8ta to Kal t2veven if they couldas a whole be (pvrwvkol t2-v (wojvto?apxasairiaconsidered as applyingto thePy- ix\v ehaL, rh 5e Ka\ov Kal riXnovthagoreans. Forit doesnotfollow, ivroh e/c tovtwv,ovkopdws otovrai.because God is unable to conduct The ethical interpretation of thisall things to perfection, that he is, passage,attempted bySchleierma-therefore, himself imperfect. Other- cher {Gesch. d. Phil, ti'l), is notwise he would be imperfect more worthdiscussing,especially with Plato, to whom406THEPYTHAGOREANS.nityof God, it has theappearanceof having also beenapplied by the Pythagoreans to the notion of Deity.Inthe first place, however, it doesnotat all necessarilyfollowfromthisthattheDivinity wasatfirst imperfect,and afterwards attainedto perfection. As Speiisippusconcludedfromthis propositionthattheOneasthefirstprinciplemustbedistinct fromthegood and from theDeity,^ so the Pythagoreans mayin like manner haveseparatedthem.^ Butit is also a questionwhetherthetheoremwhichAristotle disputes waseveradvancedbythePythagoreanswithrespecttotheDeity: forAristotledoes not always quote the definitions of the earlierphilosophers quite in the connection in which theirauthors originally stated them, as may be provedbynumerousexamples.^ Wedonotknowwhatsensemayhavebeen given to this proposition in the Pythago-reansystem. Itmayhavereferred to thedevelopmentoftheworldfrom a pre\dous state of imperfection, orto the productionof the perfect number(the decad)fromthe less perfect;^or to the position of thegoodinthetableofopposites,^ or to someother object. We*Videthechapter on Speusip- logians ivho, accordingtoMetaph.pus,Partii. a, 653 sq. 2 a. xiv. 4, 1091 a, 29 sqq., maintEiined2Thisis alsothe opinionwhich that avTo rh ayadhvKal rh ipiarovAristotle attributes to them -when are varepoyeurj, andthat they onlyhesays thatthey didnot consider appearedin the courseof the de-theOneastheGooditself,butasa relopmentof the cosmos. But itcertainkindofgood. Eth. X. i. 4,resulrsfromtheprecedingcontext,1096 b, 5: Tridavwrepov 5' io'iKaffiv as well as from the expressionol nvday6p(:ioL Xfyeiv Trepl avrov, avrh ayadhv,thatthePlatonistsareTLdevTs iu T]7 TUPayaduv(TvaToixia hereintended(Speusippus). Aristo-To ei> (in the table of theten con- tie explicitly says : Trapa twv0o-tradictories) ofs Srj Kal '^Trevaiinros Xoywuruvuvvtictlv.iiraKoXoudricrai doKfl.'*As Steinhart says, Plato's*Chaignet, ii. 103, identifies Wcrke, vi. 227.the Pythagoreanswiththosetheo-*Cf. note 2.DEVELOPMENTOF GOD. 407arenottherefore justified bythis Aristotelian passage,in ascribingto the Pythagoreans a doctrinewhichnotonlycontradictsPhilolaus'representation of theDeity,butis quiteunknown to antiquity;^though,if it hadreally existed among the Pythagoreans, it might onthatveryaccount be expected to receive all themoredefinitementionfromtheancientwriters.Havingintheforegoing pages opposed thetheolo-gico-metaphysical interpretation of the Pythagoreanfirst principles, I must now declare myself no lessstrongly against the theorythat these principles pri-marilyrefer to space-relations, and side by side withthe arithmetical element, or instead of it, denotesomething geometrical, or even altogether material.Aristotle says the Pythagoreans treated numbers asspace-magnitudes;^he often mentions thetheorythatgeometrical figures are the substantial element ofwhichbodies consist,^ andhis commentatorsgofurther,1The ancient philosophers, it^Metaph. xiii. 6, 1080 b, 18is true, frequently maintain that sqq. after the quotation onp.the tcorld was developed from a 370, 1 : rhv yap '6\ov ovpavhv ku-rudimentary and formless state, raa-KevdCovaLv e| apiO/jioov, ttXtiv orhut never that the Divinity was fj.ovaZi.Kwv^ aKXa ras iwuddas vttq-developed Thedoctrineof Hera- Xafx^dvovcnv^x^'-^iJ.eye9os- ottws oecleitusandthe Stoicscontained no rh TrpwTou e^ (rwiarr)^xov{j.4yedos,suchteaching. Forthe successive airopelvioiKaaiv . . . /xovaSiKohs 5eforms of the Divine essence are rohs apidfxohs chaL irdvTes TLdeaaisomething entirely different from -rrAriv tmu UvOayopiicov, baoi to evadevelopmentof that essence out (xroix^^ov Koidpxv^(pacxiv eluaL rc2yof animperfect state. Theprimi- uvtwp- ^kUvqi5'^xoura fxey^dos.tive fire which,asthegermof the Cf. next note, and what has beenworld, is antecedent to the world, quotedp. 400, 1, from Metaph.is here regarded as themostper- xiv. 3.feet existence, the Kopos. Lastly,^Metaph. vii. 2, 1028 b, 15 :if theTheogonies represent parti- So/ccT 5e riai".arodcrwixaros Tv^para,culargods as generated, this doc- oJou iiTKpdveia koIypa/xfj-T]koIariy^iT]trinecannotbedirectly transferred Ka\ jxovas, ehai ovcriaiixaWov, ^toto theDeity, conceivedas One. awfia koI rh arepeov; iii.5,1002408THEPYTHAGOREANS.declaring that the Pythagoreans held mathematicalfigures tobetheprincipleofthecorporeal,andreducedthemto pointsor units;thattheyregarded these unitspartly as something extended in space, and partlyalsoas the constituents of numbers;and consequentlytaughtthat corporeal thingsconsist of numbers.^ Wefind similar thoughts among other writers of the laterperiod,- though they do not precisely attribute thema, 4: aKXa fir^v to ye crwjxa ^ttouovaiattjs iirKpaviias, koll avr-q rris7paujufjs. Kol7]ypafjL/xT]ttjs fxovdSosKal TTis (TTiyixris-tovtoisyapfipicTTOt7 b awixa, Koi ra fxkvavev (Tw,uaTosivSex^o'Oai SoKeT elvai, rh 5e craJ/xaavevirovTwv ^Jvai ahvvaTOV. dioirepol ixkvTToXXoX &c. (vide stipra,p.369.1),xiv. 3, 1090 a, 30 {supra,p. 370, 1),ibid. 1090 b, o : etVI 5eTLves ot eK Tov irepara ehai KaletrxaTa, rrju (myixTjv /lev ypa/xixris,TavTTju5'e7r:7rSou, toOto Se tovarepeov,oXovrai eJuaiavdyKr}uroiav-ras (pvaeis elvai. Dc Ca-lo, iii.1,298 b, 33 : d(T\ 5e' nves, o\ Ka\ -nav(rwfjLa yevurjThv iroioOci, cvvTidevTesKoi diaXvovTCSe'liirnr^dwv Kal elsiiriireSa. Aristotle,ho-svever,seemsto be thinking only of Plato, andquotes expresslytheTimaeus. Attheendofthechapter,afterhavingrefuted this opinion,hesays : to S'avrb (TVfx^ahei kol tols e| apidixwu(TwriQilffi TOVovpav6v evniyapttj**(pvcnv f| apidfJLwv avvicrTcicriy, wairepTwv HuOayopeiwu Tivii. Metaph.xiv. 5,1092 b, 11, can hardlyrefer to this subject. VidePseudo-Alex, ad. h. 1.'Alex, inMetaph. i.6, 987b,S3;p.41 Bon. :apx^-^i^icr tcUvuvTwv Tohs apiOixovs TlKdrcouTe koIol HvdayopeiOL virerldei'To, '6tl e5(5/c6avTo7s rh irpuropapxvehai Kal rhaawdsTOV, ruv Se (Tu:}xdTUV irpwraTO iir'nredaelvai (toyapaTrXovarepdre Ka) fXT] (jvvavaipovjxeva irpura rrj(pvaei) eVtTreSajvSeypaixp.alKararhvovTov \6yov. ypau.fj.oov Se (TTiyual,&j ol fxaOri uarLKol ar]ue7a.. ainol 5e/jLOvd^as iXeyov . . . al 5e ixovdSesdpid/uLol, ol opif/xoi &pa TrpooToi rwvovTuv. Ps.-Alex. 171 Metaph. xiii.6, p.723 Bon.: Kal ol Uvdayopeioi5e eVa dpiduhv eivai vo/xi^ovcri, KalTLvaTovrov;rovixaQ-t]p.aTiKuv, irXiqvoh K^x'^pi-O'iJ-evov Twv alaO-qruv, wsol Trepl s.evoKpdrrjv. ovde jxovoZikov,tovt4/xa ttoluvoTourecrwrLOe-Toryusualwithhimelsewhere. /ueVas outfiapos exe'i'. Mctaph. i.-WdiQsupra,p. 370, 1. 8, 990 a, 12, even supposing that3Metaph. xiii. 8, J083 b, 8: magnitudes could result from theb 8e Twj/ YlvQayop^icav rpoirosrfjyikv Limited and the Unlimited, rivaiKoLTTovsex^'Sutr^epetay rwv ttoo- rpotrou tffrai to juef Kovcpa to. 5erepov etp77jUVci)i' T17 5e Idlas kripas' fidpos ex^''"'''*^^^ ffwixaTwu;ihid.TO /uev yap jutj x^piarov -noLi^v tov xiv. 3 (videsnpra,p. 370, 1),whereapiQixdv(Kpaipilrai TzoXXatuuaBvud- alsothe PythagoreansarereckonedTuv TO Se TO au/jLaTa f| apidfxwv among those who only admittedclvaiavyKiijxiva.Koi rhvapid/xhutov- mathematicalnumber.TOi/ elrot /jLad-nixaTiKovaSvvaT6vNATURE OF THEIR PRIXCIFLES. 411onlybecompoundedout ofbodies,and so it inevitablyfollowsthatnumbersandtheirelementsmustbesome-thingcorporeal if bodiesare to consist of them. Thespecial characteristic of the Pythagorean Philosophyhowever lies in this, that such adistinction is as yetunrecognised,andthat,in consequence,numberas suchis regardednotonlyas theform,but as the matterofthecorporeal. Yetnumberitselfis notonthataccountnecessarily conceivedas corporeal ; for it is clear thatqualities andrelationswhichno oneexcept the Stoics,or before their time, ever considered as bodies, wereexpressedin the Pythagorean Philosophybynumbers.ThePythagoreans not onlydefined man,or plants, orthe earthbynumbers,butassertedthattwo is opinion,fourjustice, five marriage,seven the opportune time,etc.* Noris this simplecomparison. The meaninginbothcases is thatthespecified number is properlyanddirectlythethingwithwhichit is compared. It is aconfounding of symbol and concept, a mixture ofthe accidental and the substantial, which we cannotdiscardwithout mistaking the essential peculiarity ofPythagoreanthought. Aswecannotassert that bodieswereregardedas immaterial bythe Pythagoreans,be-cause,accordingtothem,bodies consistedof numbers,so neither, ontheother hand,canwe infer thatnum-bersmusthavebeensomethingcorporeal,because theycouldnototherwise havebeen the elementsof bodies.Bodiesmeantto them all that presents itself to thesense-perception; numbersmeantthatwhich is appre-hended bymathematical thought; and thetwothings^Videmfra,iv.412THEPYTHAGOREANS.weredirectly identified, while the inadmissibility ofsuch aprocedure was unnoticed. For similar reasons,it is of noavail to prove that theOne,the Unlimitedand the Void receive a material signification in thePythagorean physics. Weread, it is true, that in theforming of the world, the nearest part of the Un-limitedbecameattractedandlimitedbythe first One/and that outside the world was the Unlimited,fromwhich the wcrld inhaled emptyspace and time.- Inthis connection the One certainlyappears as materialunity, andthe Unlimitedto some extent asunlimitedspace, to someextent also as an infinite mass; but itby no means follows that the two conceptions havealwaysthesamemeaningapartfromthisorderofideas:on the contrary,wehave here an instance of what weso often find with the Pythagoreansthat ageneralconception receives a special determination from itsapplication to aparticular case, although this determi-nation doesnot on that account essentiallybelong totheconception, nor excludeother applications of it, inwhich it maybeused in a different sense. Itwasonlybythehelpof such a method that the Pythagoreanscould apply the theory of numbers to concrete phe-nomena. It is possiblethat incertain cases the One,the Unlimited, Xumber,&c.,mayhave been regardedas corporeal. Butwe cannot conclude from this thatthey were universally conceived as such. SVe mustremember that numerical determinations are veryva-riously employed by the Pythagoreans, and that theVide siqyra, p. 400, 1, and Cf. iii. 4, 203 a, 6;StoLaeus, Eel.p.407, 2. i. 380; Plut.Plac. ii. 9, 1. Further2Arist. Phys. ir. 6,213 b, 22. details, infr. Cosmology.NATURE OF THEIR PRINCIPLES. 413imlimitedandthelimited are ofdifferent kinds,^ whichare not clearly distinguished because the language ofPhilosophywas as yet too unformed,and thought toounpractised in logical deduction and the analysis ofconcepts.Forsimilar reasons I mustcontest Eitter's theory.ThatthePythagoreansderivedbodiesfromgeometricalfigures is true,and will be shown later on; it is alsotruethattheyreduced figures andspace-dimensionstonumbers,thepointtoUnity, theline to Duality,andsoon, and that theyreckonedinfinite space,intermediatespace,and the void underthe headof the Unlimited.^But it does not follow from this that byUnitytheyunderstood nothing but the point, by the Unlimitednothingbutemptyspace; here again all that we havejust said as to the application of their principles tophenomena holds good. They themselves designateby the name of the Unitynot the point merely,butthesoul; bythatof Duality,not the line merely,butopinion; theymake timeas well as emptyspaceenterthe world from the Unlimited. It is evident thatthe conceptions of the Limit, the Unlimited, Unity,Xumber,havea widercompassthanthose ofthe point,thevoidandfigures ; figures, at anyrate, are expresslydistinguished from the numbers by which they are'Ritter says (i. 414) that the besaidofthe Pythagoreansystem.Indeterminateas suchcanhaveno-Cf.p.414. 2, and Arist. Despecies; butin the first placethis Ccelo, ii. 13, 293 a, 30, where it isexpressionisinitselfincorrect; for spoken of as an opinion of thethe unlimited in space, the un- Pythagoreans that the limit islimited in time, qualitative un- more noble (rt/iiwrepoi/) than thatlimitedness, &c.. are so manykinds whichlies between. Fromthisweof the Unlimited. And in the may conclude that the /xeTa^v issecond place it couldnotpossibly closelyrelatedto the Unlimited.414THEPYTRAGOHEANS.defined;^and thevoid is spokenof in a manner that,strictly interpreted,must apply to the Limiting, andnotto the Unlimited.- Xotmuch stress, however,canbe laid upon the last-mentionedcircumstance,becausethePythagoreansseemtohavehereinvolvedthemselvesin acontradictionwiththeirothertheories.But the most decisive argument against the in-terpretations we have been enumerating is derivedfromtheconsiderationof theP}i;hagoreansystemas awhole ; for its arithmetical character can only beunderstoodif wesupposethat theconceptionof num->Arist. Metaph. vii. 11, 1036b, 12: aydyovai iravra els rovsapLdixohs Koi 7pa,u/i7}s rhu\6yovrhuTuv hvo cTvai (paffiv. Cf. xiv.5,1092 b, 10 : wsEvpvros eraTTe.risapidiihs Tiuos, OLOV65i juei/ dudpuirov,651 5e iTTTTov. Platospoke inasimi-lar manner of a number of theplaneandof the solid, butbedidnot therefore regard numbers asextended or corporeal (Arist. DeAn. i. 2, 404 b, 21;cf. Part ii. a,636, 4; 807, 2. thirdedition). InMetaph. xiii. 9. 1085 a, 7figures,fromthepointof viewofPlatonistswhofavouredPythagoreanism,areexpressly called to. vanpov yeyr}rod dpidfxov, the classwhichcomesafternumber(the genitive apidfxovis governed byvarepov, not byyivt];cf. Metaph. i. 9, 992 b, 13).-Thevoid is consideredasse-parating all things from eachother. Arist. Ph^/s. iv. 6, 213 b.22 : ilvai5'%iJ.aTaiv TQLs apidjxols i\youelvai irpos touuraTe Kol yivo^^ua, iS-fiXcoas. t?iS/Uvyap 5iKaL0crvj/T]S ^diov vTroXajx^d-uovres ilvai rh avrmer-oudos re Kal'[(Tov, iv ro7s apiQfxoiis rovro evpicr-Kovres ov, Bid rovro Kal rhvlaaKis"ktov dpiQfxhv irpuroveXeyou eivuL Sl-Kaio(Tvvj]V. . rovrovSeol /xhvrhvrea-aapaeXeyov(soalsoIambi. Th.Ar.p.2-1:,froma morecomplicatedrea-son). . ol5e rhvivvia,osiaritrpwrosrerpdyaivos. (This is a'reading avr7]v Kal iwlOeaLv(?).But here.of Bouitz,' instead of a-repihs. asgiven by the manuscripts.) dirhTrepLrrovrodrpia e^' avrhvyevofxe-vov (cf. Iambi,p. 29)Kaiphv 5eTToXiv tXeyovrhv eirrd' Soke?yap rd(pvfTiKa Toi/y reXeiovi Kaipovs ^crx^ivKal yevea^cvs Kal TeAeiwcrews Karaj85o;Ua5as. ws iir' dvQpu)irov. Kal yapriKrerai eTrraiJ.r]via7a, Kal 65ovro(pve7roaovravirwv. Kal rj^daKei irepl riijvSevripav ej35o,ua5a, Kal yeveiS. ireplrrjv rpirrjv Kal rhv rjXiov Se, cTretavrhsatTios elvai rchv KapirSsv, (prjo'l,duKel, ivravQd(paaiv[ZpvaOaiKaO'h6h^So/xosdpiQixosiariv(intheseventhplace of the periphery of theworld) t)V KaiphvXiyovanv . . , eVeiSe ouTeyevva rtvh rwviv rrj SewaSidpiQjX'^v 6 eTTTa ouTe yevvdrai vtt6rivos avrwv, Sia toGto Kal 'AflT?m^eXeyovavrhv (cf. Th. Ar.p. 42, 54,&c.) . . . ydjXQV Se eXeyov rhvnivre, on 6 fxkv ydjxos avvoBosdppevos iffri Kal drjXsos, enSe Ka.ravruvs dppev fiev rh irepirrhv drjXvSe rh dpriov, irpuiTos 5e ovros e|dprlov rov 5vo izpurov Kal irpwrovalready, especially in the reasonsadduced for the support of thevariousdesignations, many recentelements seemto be intermingled.This is still more largelythe casein regard to the othercommenta-tors of the passage in Aristotle[Schol. in Arist.p.540 b sqq.)andsuch writers asModeratusap.Porph. Vit. Pythaq. 49 sqq.; Stob.i. 18;Nicomachusap. Phot. Cod.187; Jambl. Theol. Arithm. 8 sq.;Theo, Math. e. 3, 40gqq.; Plut.Be Is. c. 10, 42, 75, p. 354, 367,381 ; Porph.Be Ahstin. ii. 36 &c.I therefore abstain from makingfurther citations from these au-thors, for althoiigh in what theyquote there may be many thingsreally belonging to the ancientPythagoreans,yetwecanneverbecertainonthis point. In general,the textthat we have quotedabove,from Aristotle, Met. xiii. 4,shouldmakeusmistrustfulofthese state-ments.'Cf. on this pointwhatis saidTHErYTHAGOBEAXS.similar maDiier,certain numbers,^ or certainfio^ures andfurther on, of the relation of theterrestrial regionto Olympus, andAri&r. Metaph. i. 8, 990 a, 18.How is it possible to explain thecelestial phenomenaon thePytha-gorean hypotheses? orav yap 4vT-^Sl fxev r fxip^i So|a koX KaiphsavTo7s77,jxiKpov ? i.v(siQev^KaruQevaoiKia (al. aviKia, according toIambi. Theol. Arithm.p. 28, wemightconjecture apeiKia, butAlex,thinksaviKiamore probable, cf.p.429, 6),Kol Kpiais ?] ui^is. airoSei^iv5e Kiyuaiv,ontovtwv/xev ei' eKacr-rovapidixos eVri, cvu^aiuii 5e KaTO.~hu TOTTou rovTOV tjStj irKriQosclvai TU!V (TvvKTTau^vuvixey^dwv 5 i aTd TO. irddT] ravra aKoXov6e7v to7sroTTOis eKaaTOLs, irorepoi' ovros 6avTos iariv apiOfJLos 6 ivtwovpavc^,%v Set Kafifitv on romoiv '^KacTTOVicrriv, i) irapa tovtov &Wos. Thispassage has never been fully ex-plained,eitherbyrecentcommenta-tors, or by Christ, Stud, in Arist.lihr. metaph. coll. (Berlin, 1853),p.23sq. Thebestexpedientseemstobetosubstitute for 5iarh'Sth'(as, perhaps,was donebyAlexan-der),and to insert 'tovto'beforet]5r} (I formerly conjectured roSt,instead of^Srj, IjutAlexanderisinfavourof ^Stj). The meaning be-comesthen : 'If thePythagoreansplacein cert//'a,p.425,2)quotes from Eurytus. Schaar-schmidt is especiallyperplexedbytheattributionofthedodecagontoZeus, -while thefragmentsof Phi-lolaus regard the decad as thenumberwhich rules the universe.This presents to me no greaterdifficultythantofindinthetheoryof Philolaus respecting the ele-ments,thedodecahedronmadetheprimitiveformofu.'Ether, orin thetheoryofharmonytheoctavedivi-dedinto six tones instead of ten.The system of number couldnotbe directlyapplied to geometricalfigures. In the same -way that,among solids, the dodecahedronwas attributed to the universalelement, so among plane figures,bounded by straight lines, theequilateraldodecagon, easytocon-struct out of a square by meansof equilateral triangles, taking asquare as point ofdeparture;easyalsotoinscribeinacircle andtheangle of which (=150 degs.)isequaltotheangleof thesquare(90degs.)andofthe equilateral triangle(60degs.), might have beenchosen asthesymbol of theuniverseandofthe supreme god -who rules the-world asa-whole (the t-welve godsofthemyth).'Cf. Arist. Mctaph. xiv.6,1093 a, 1 : et5'avayKT] -navra apid-fjLOv KoivoiveTu,avayKT]iroWa(rvu^ai-veLv TO. avTOL. ThatR'hichisdesig-natedbythesamenumbermustbesimilar.'Comparein thisrespect -withAPPLICATIONOFTHEXUMBER-TIIEORY. 425sameobject or concept should sometimes be denotedbyonefigure and sometimes byanother;whatwhim-sical vagarieswerepermitted in regard to this subjecteveninthe ancient Pythagoreanschool, wecanseefromtheexampleof Eurytus,who attempted to prove thesignification ofparticularnumbersbyputtingtogetherthe figures of the things they designated outof thecorrespondingnumberof pebbles.^ThePythagoreans,however,didnot content them-selveswiththisarbitraryapplication oftheir principles,but sought to carry them out methodically bymoreprecisely definingthenumerical proportions accordingtowhich all thingsare ordered, and applying themtothe different classes of the Eeal. We cannot indeedassert that thewhole school entered on these discus-sions, and observedin theirprocedure thesameplan;evenwith regard to thework of Philolaus,whichalonewhat results from the,preceding gards the rest, it is impossible tonotes, thestatements that justice say what really belonged to theis designated bythe number five ancient Pythagoreans,(lambL Theol. Arith.p. 30, 33)or'According to Aristotle, Me-three (Pint. Is.75);healthbythe taph. xiv. 5,1092 b, 10 (wherethenumber seven(Philolaus,ap. Iambi, words,twv(pvrwv, 1, 13, seemmore-Th. Ar.p. 56)or six (ihid.p.over to involve a fault certainly38); marriagebythenumbersfive, very ancient), and Theophr. Me-six, orthree (Theol.Arithm.p. 18,taph.p.312Br. (Fr. 12, 11) ;vide34);the sun by the decad {Th. the excellentcommentary ofAlex-Ar.p. 60); light by the number ander(in this case, therealAlex-seven (Philolaus, loc. cit.) and by ander) ad. Met.p. 805, Bon. ;cf.the number five {Theol. Ar.28) ;also Sj-rian in Metaph. Schol. 938thespirit by the monad,the soul a, 27. I cannot understand howbythedyad, opinion (5o|a) bythe Chaignet, ii. 125, can denytometriad, thebodyorsensationbythe the opinionthattheancient Pytha-tetrad(Theo of Smyrna, c. 38, p.gorean school'avaitaumoinsseme152; Asclep. loc. cit. 541 a, 17,le germe d'oil est sortie toute cettecf.p. 420, 2). It is truethat the symbohque de fajitaisie,'' in spite oflast-mentionedpassageiscertainly theprecedingdemonstrations,citedposteriortoPlato; andthat,as re- byhimself(p.126).426THEPYTHAGOREASS.couldgiveusanyclueon this subject, our knowledgeis too scantytoallowofourdetermining withcertaintythepositionwhich particular enquiries assumed in it.We shall, however, be adhering pretty closelyto thenatural connection of these enquiries if we first con-sider thenumber-system as such; next its applicationto tones and figures ; thirdly, the doctrine of the ele-mentary bodies and notions about the universe : andfinally, thetheories onthe terrestrial naturesandman.It would be easy to reduce these divisions to moregeneralpointsofview,butthis 1 thinkoughtnottobedone, since we know nothing of any division of thePythagorean system of philosophy correspondingwiththelater discriminationof three principal parts, oranyotherclassification ofthe kind.In order to reduce numbers themselves to a fixedschema, the Pythagoreans employed the division ofodd and even, and also the system of decads. Theformer has been already alluded to(p. 377) ;in itsfurther developmentvariousspecies werediscriminatedfromthe even as wellasfrom the odd;whether thesespecies were the same as are enumerated by laterwriters^ is not quite certain,nor can we be sure how^Nicom. Inst. Arithm.p. 9h.pTioTv4p'.(T(Tov(x\.dQsupra,^.^1'i,1).sq. : Theo. Math. i. c. 8 sq. Three Similarly three kinds ot numberskindsofnumbersare here distin- are distinguished in regardtoun-guishedamongthe even numbers, even numl>ers, the irpwrou koIthe apTiOLKis upriov (the numbers arrvvOeroy (the first nimilters) ; thethatcanbe dividedby even num- devrepou Kal (rvvQirov (numbersbersdown to Unity, like64); the which are the product of severalTrepia-adpTiov (the numbers which, uneven numbers, and are, there-divided by2,give evennumbers, fore, notdivisiblemerelybyunity,but which, divided by any even as 9, 15, 21, 25, 27);andlastly,numberhigherthan2,giveuneven the numbers divisible separatelynumberslike 12and20);andthe byothernumbers than unity, butTHENUMERICALSYSTEM. 427manyof theotherdivisions^ of numbers which^Ye findin more recent authors^ belong totheancientPytha-goreandoctrine. Manyofthese ideas, nodoubt,reallybelonged to the Pythagoreans.^ But all these arith-metical principles, if weexceptthegeneral distinctionof oddandeven,were far less importantin regard tothe Pythagorean cosmologythan toGreek arithmetic,which here also followed the direction given to it bythis school. Theimportance of the decuplesysteminrelation to thePythagoreans is muchgreater. Forastheyconsidered numbers overtentobeonlythe repe-tition of the first ten numbers,'* allnumbers and allpowersof numbersappearedto themto be comprehendedin the decad, which is therefore called byPhilolaus,''great, all-powerful and all-producing, the beginningand the guide of the divine and heaveuly, as of theterrestrial life. According to Aristotle,*^ it is thetherelation of which to others is^For example, the theory ofonlyto bedefined by unities, as 9 gnomons {supra,p. 378, 1)ofand25. squareandcubic numbers, apiBixol,'Onthe onehand,Philolausin reTpdywumandir^pofiriKeis, of dia-thefragment quoted onp. 377, 1, gonal numbers (Plato, Bep. viii.speaksof manykinds of evenand 546Bsq.;of. p. 429, 6).odd; on the other, he does not,^Hierocl. in Carm.Aur.p.166likemore recent writers, givethe {Fragm.Fkil.i. 464): toD5eaptdfxovapTioirepicrcrov as a subdivision of rh iz^irepaa-ixivov ^i6.(rr'r]ixa7]Se/ccis.theeven, butas athirdkind, side 6 yap i-nl irXiov apiQixilvie4\u>vdva-by side with the odd and the Kaa-m^i -kclXiv eVl rh eV. It is foreven. this reason that Aristotle blames2Such as the distinction of Plato,and indirectly alsothe Py-square, oblong, triangular, poly- thagoreans, foronly counting num-gonal, cylindric, spherical, corpo- bersup to ten. Fhys. iii. 6,206real, and superficial numbers, &c., b, 30: Metoph. xii. 8, 1073 a,togetherwiththeirnumerous sub- 19; xiii. 8,1084 a, 12:eln4xpi.divisions,api0|ubs Svi/ajuis,/ci;)8os,&c. 5e/ca5os 6 apLd/xhs, &0Tpwu Anatol.ap. Iambi,Z!^.^r.p.34(be-^leTe'xetv rrjs (pvcecos' apricf} fxkvyap sidesmanyotherpropertiesoftheTrpoo'TeSei/ TrepiTTbi/TTOiei, TrepiTTi^ 8e numl^er6): i^aprlov Koi ircpiaaov&pTLOu,oovKaurjSvuaTo, elfxrj afjLfpolu Twy irpcoTcov, 'dppeuos Kol 6r)\eos,raiv (pvaeoiu jueTeTxe, aproof which ^wdp-eiKaiTToXXairXacTLaaix^yLv^Tai,is as singularas theproposition it hence it is called appei/odrjAvs andis intendedto demonstrate (rvfj.(p4- yd/xos. These denominations areperaiSeTOwTOtsKol'Apxuras. Plu- alsofound loc. cit.p. 18; Plut.Betarchgivesthesamereason. Plut. Ei. c. 8;Theo,Mus.c. 6;Clemens.DeEi. c.8, p.388. Strora. vi. 683 C;Philop. Phys.3Arist. De C thePYTHAGOREANS.hewithoutorigin,and2,thattheworld-formingenergycanneverbeconceived as inactive. -Theformeridea,asfar asweknow,was first enunciatedbyParmenides,thelatterbyHeracleitus;andtheconclusiondrawnthenceevenbythem and their successorswasnotthe eternityof our universe : Parmenidesinferred from his propo-sition the impossibilityofbecomingandpassing away,andaccordinglyhedeclaredthephenomenalworldgene-rallytobeillusion and deception. Heracleitus,Empe-docles, and Democritus maintained, each in his ownway,aninfinity ofworlds ofwhicheveryonehadhadabeginning in time. Lastly, Anaxagoras, adopting theordinarytheoryofa soleanduniqueworld,supposedthislikewisetohaveshapeditselfat a definite periodoutofthe unformed primitive matter. Onthe other hand,Aristotlenever thought^ of attributing a descriptionoftheoriginoftheworld to the philosophers who main-tained its eternity so consciously, and on principle, asthereputedPhilolaus. Thereis, therefore,little reasontodoubtthatwhatis statedconcerningthePythagoreantheory of the formation of the world really refers toabeginning of the world in time. In flict, any otherinterpretationof the texts is inadmissible. Accordingto the Pythagoreans, the central fire was first formedin the heart of the universe;this is also called bythemtheOneortheMonad,becauseit is the first bodyoftheworld;themotherofthe Gods,becauseit is thiswhich engenderstheheavenlybodies;theyalso call itHestia, the hearth or the altar of the universe, theguard,the citadel orthe throne of Zeus,becauseit isthe central point in which theworld-sustaining energyFOBMATIOXOF THE WOr.LD. 443has its seat.^ Howthis beginniDg of the world itselfcame about, Aristotle {loc. cit.) says they were unableto explain,and we cannot certainlydiscoverfrom hislanguagewhethertheyevenattemptedanexplanation.^After the formation of the central fire, the nearestportions of the unlimited, which according to theobscure notions of the Pythagoreans signified at onceinfinite spaceandinfinitematter,wereconstantlybeingattracted to this centre,and becoming limitedthrough'Videp.444. 4; 446, 1 : Arist.Mctaph. xiv.3;xiii. 6 {supra,p,400; 407,2);Philol. ap. Stob. i.468: tJ) TTpcnov 6.pixoa6\v t^ %v ivTwjxia-ci) Tus (Tcpaipas(thesphereofthe world) 'Earia KaXelrai. Thesame,ibid. 360: 6 koctijlos ehi(TTivf}p^aTO Se yiyvecrOai oi-xpi- '^ov jxecrov.The text may be moreexact, buta-TTo Tov fiiaov "svould certainlybeclearer. Ihid.p. 452; vide infra,p.446,1; Plut.Xiima,c, 11 : k6(tij.ouov jxeaov 01 TlvdayopiKol rh irvpISpvadaivojULi^ov^'i. koI tovto'KtrriapKaXoiai KoX jxovaha. Cf. Iambi.Th. Arithm.p.8 : ifp^stovtoisipaal[ol ni'0.] Trept Th jjiiaov rcouTeaad-pav (TToix^'i-^v KslaOai tluo. kvdBiKbv5id-nvpov Kv^ov. ov rr^i/ ixi(r6Tr]raT77S Q4as (instead of this ^vord, weshould doubtless read Bia^ois) koL'OfJLT]povelSevaiXeyovra(II. riii. 16),Therefore, continues the author,Parmenides,Empedocles, and otherssay: rrju fxouaBiKrju (pvaiv 'EffTiasTp6-Kot/ iv fjLeau) iBpvaOai Kal SiatoIfTo^poTTou (pvXdaaeLU ttji/ avTTjvi'Spov. ^Ve seefromthese passageshowtheTTpwTov %v in Aristotle isto be understocHl. The centralfire, because of its place and itsimportance for the universe, wascalled the One in the samesensethat the earth, for example, wascalled two, and the sun, seven(vide sirfxra, p. 421). But howthisdeterminate partoftheworldwasrelated to the numberone, ordistinguished from it, was notstated. Videp.410 sq.2Aristotle says {Metaph. xiv.3),videsup.p.400: tov evhs avcr-TaBevTOS e%Te'liirnTcSoov e'lt' iKXpoias,which signifiesindeedmuchthesamethingas e| iiniTiZwv;cf.Arist. Be sensu,3, 439 a, 30 : olHvdayopeioi t^u inrKpaveiav xpoictviKakovve'lT iK GiripfxaTos etr' e| uuaTTopovcTLv etVeTy. But we cannotinferfrom this (as Brandis does,i. 487)thatthe Pythagoreansreallyfollowed all these methods to ex-plain the formation of the body,still less that all these modesofexplication had reference to theCentralfire. But Aristotlemightexpress himself in this way,evenhadthePythagoreanssaidnothingas to the manner in whichbodieswere formed. Similarlyin Metaph.xiv.0, 1092 a. 21 sq., heputsthequestion to the adherents of thenumber-theory' hownumbersre-sult from their elements,'M'I^'oravvdiaei, us e| iuunapxovTuv. or ccsairh (TTtipjxaTOs, or us iK toOiiavTiov:444 THEPYTHAGOREANS.this attraction,^ imtil by the perpetual continuationandextensionof that process (thus we must completethe accounts) the system of the universe was at lastfinished.The universe was conceived by the Pythagoreansas asphere.^ Inthe centre of the whole theyplaced,as we have seen, the central fire ; around this tenheavenly bodies^ moving from>x^west to east describetheir orbits;'^farthest off, the heaven of fixed stars,next the five planets;then the suiL,the moon, theearth, andtenth, andlast, the counter-earth,whichthePythagoreans inventedin ordertocomplete the sacrednumberoften. Theextremelimit of theuniversewasformedbythe fire ofthe jDeriphery,whichcorrespondedto the central fire.^ The stars they believed wereunlessthatmotion was from"westtoeast. "Whether the Pythagoreans,likeAristotle (cf. Bockh, d. Kosm.System,p.112 sq.), understoodthis movement from west to eastas a movement from east to east,or from right to right, andcalled^Arist. loc. cit.;cf. supra,p.400,1. Thesamedoctrineseemstobethefoundationof the conserva-tionin Plut. Plac. ii.6, 2 : UvQayo-pas airb Trvphs KOi rod irifxiTTOV(TTOtx^'ou [aplatr^at t^vyiveaivtovkoct/jlov], onlythatheretheunlimi-ted is confounded withthettepUxov the east side the right,becausetheof Aristotle, theiEther.-S^oTpais theusualexpression,p.442, 1; 436, 4.*ThePythagoreansaresaidtohave been the first to determinetheir order in a precise manner.Simpl. De Coelo, 212 a. 13 {Schol.497 a, 11):oos EvSriixosl(rrope'i,rT]i/rfjs SeVeoDS rd^iu eis tovs Tlvdayo-p^ious TrpwTousavacp^puf.*As follows as a matter ofcoursein regard to the earthandthe other bodies of the universe.For the apparent diurnal motionofthesun,fromeast towest,couldmovement starts from that side;as Stobreus thinks, Eel. i. 358(Plut. P/gc. ii. 10; Galen, c. 11,p. 269),seemstomedoubtful.^Arist. De Coelo, ii. 13, subinit. : ruv ttX^'kttwv eVl rov /xecrouKelaOai Xeyovruf [tt/v77Jv] . . .ii/ai>Tiws ol irepl r^u'iTakiav.Ka\ov-fxeuoi Se Yluday6peL0i X4yov7LV. eirlfikv yap rov fxeaou irvp elpai (paai,TTjr Se yr)v ef twv aaTpuu ovaavKiJK\(a(pepofxivr}viT(p\r}> /j-eaov vvKrare Kal Tj.ue'pai/ tvok'lu. en5'ipavriavaW-qu ravTT) KaracxKevd^ovffi yr\v,avrix^oua uvofxa Ka\ov. kosm. Syst. PL1U2sqq;cf. Kl. Schr. iii. 329).2Tint. Plac. iii. 13, 2(G-alen,c. 14, 21);^iXSKaos . . . KvK\cf)Trepi(f)4padai [_t^v7^1/]irep) rh irvpKarakvkKov Ao^ov. Ibid. ii. 12, 2(Stob. i. o02; Galen,c. 12):Uuda-ySpasirpwTos i-mvevovKevai AeyeraiT'ljv \6^w(Tiv Tov ^whiaKOv kvkKov,i]VTLva OIvott'lStjs 6Xios d'S Wiaveri-voiav (TcpeTepl^erai. Cf. C. 23, 6.According to others,Anaximanderhad already made this discovery(videsupra,p.254,3). Accordingto Theo {Astron.p.322 Mart,end;Fragm.ed. Spengel,p. 140),Eudemus attributeditto(Enopidesif wemayread in thefragmentKo^waivinstead of hia^waiv. Theassertion of the Placita, thatEu-demushadtakenit fromPythago-ras, would incline us to suppose(as Sehafer justly observes) thatEudemus had claimed it forhim-self(Sehafer, Die Astron. Geogra-phiederGriechen^'c, Gymn. progr.Elensb.1873, p. 17). In Diod. i.98, some Egyptian sages assertthatOEnopideshadlearnedthein-clination ofthe ecliptic in Egypt,whichequallypresupposesthathemusthavebeen the first to intro-duceit into Greece. In that easethe Pythagoreans would havede-rivedit from him. AccordingtoProclus{inEucl. 19, 66thFragm>)CEnopideswasalittle youngerthanAnaxagoras,andalittleolder thanPhilolaus.'On eclipses of the sun, videStob. i. 52&;onthoseofthemoon456 THErYTIIAGOREAXS.be vitreous spheres,^ which refle(ited back light andwarmthto the earth.^ At the sametimeweare toldthat theyconceived the stars_ns re.semb1iTio'_jtlLe_^_arth,and surrounded like the earth by an atmosphere;^videArist. De Cceh, ii. 13, 293b,21. Hesays, after speakingofthecounter-earth: iviois 5e hoKit kuITrXeico (Tu/xaTa TOiavra ivZiy^eadai(pepeadaL -nepl to ix. Platon. Staat,p.282sq.). This doctrine of the fire ofthe periphery, or at least of itsidentitywiththemilky way,seemstohave been confined to apart oftheschool. For in whatconcernsthe milkyway, Aristotle, althoughthe fire of the periphery was notunknown to him(vide De Coelo, ii.13; the words rh5*ecrxaroj/ /catrh n.i(Tov nepas. citedp. 444, 4,evidentlyrelatetothisfire),quotes{Mefereol. i.8)fromthe Pythago-rean school (t&)j/ Ka\ovfx4vci:u IluOa-yopeiwvrii/es) the opinionthatthemilky wayis thetrace orcourseofone of the stars that fell in thecatastrophe ofPhaeton; or else acourse once traversed bythe sun,butnowabandoned. Thisopinionis alsofoundin Olymp.andPhilo-ponus ad h. I. (i. 198, 203, Id.),andin Stob. Ed. i. 574 (Plut.Plac.iii.1, 2),-withoutanyotherindii-a-tion of its source. Such opinionscannotbe attributedto Philolaas.'Arist. Phys. iii.4, 203 a, 6 :oi fjikv UuOayopeioL . . . eluai thl|aj ToG ovpavov aweipou. Ibid. iv.6;vide supra,p. 414, 2; Stob. i.380 : eV 8e t(S TTfpl rris TlvOayopovia9 TrpJorco ypdrpei ['Api(TTO-tcAtjs], Thv ovpavhv dvai eVa, eVei-ady^o'daL5'eK rov aireipou ^povovT6 Kot TT/zoV KoXrh Kiphy, t 5iopi(eieKaaTwurasx rj pd^dos. StjXovStl koIdweipof. Koi el jxtv auixa, Se'SeiKxaiTO irpOKel/JLeuov et Se tottos, errri 5eTOTTOS ro ivw (Tu>u.d i(TTiv^Surojr'au eJvai, to Se Suvdixei is ovxphTiOevaL i-rrl rciu ai^iwv, kul outusavetTj au>ixa6.ireipov kol tSttos. Theexplanationsof Eudemns arehereadded to the demonstration ofArchytas, as is proved bythe ex-pressionsjSaSieTrai and e'pwTTjo'et,andthe Aristotelian phrase {Fhys.jii. 4. 203 b, 30;Mdaph. ix.8,1050 a. 6): rb Zwajxei ojs or, &c.,andas it ispreciselyonthatphrasethat the proof of the corporealnatureof theUnlimited rests, allrelating to that idea mustbelongtoEudemus; theonlythingwhichbelongs to Archytas is the ques-tion : ivTweaxarcpoiiK &v; Wefind another proof in favour ofemptyspacein Arist. Phys. iv. 9,astatement reproduced and com-mented onby Theraist. in h. 1. 43a (302 sq.); Simpl. Phys. 161 a:De Coeh, 267 a, 33. Accordingtohim,Xuthus said that -withouttheVoid,therecouldnot be rare-factionor condensation,andthatinorder that there might be move-ment,somebodies must transcendthe boundaries of the "world, tomake roomfortheboliesinmotion.The world must overflow[Kv/xaveTrh o\ov). Simplicius calls thisXuthuBEoD0os 6 UvOayopiKSs. Butit is not stilted whether he was atrue Pythagorean, or had merely(vide infra,p. 41-5), in themannerofEcphantus.combinedthe theoryof atoms with the Pythagoreandoctrine.2Arist.Phys.iv.6;Stob.i. 380.SYSTEM OF THE UNIVERSE. 469from the Unlimited,that is, from infinite space. Inthis we see the fantastic method of the Pythagoreanschool, of which we have alreadyhad so manyproofs.Wehavenorightto attempt to destroy it bya precisedefinition of the concepts,norto drawfrom it conclu-sions, which have no other certainwarrant within thesystem.^ For the same reason it oughtnotto surpriseus thattime,which,accordingtothe above representa-tion,enteredthefirmamentfromthe Unlimited, shoulditselfagainbeidentified^withthe celestialsphere;theformerdoctrineinvolvestheconceptof timeas withoutlimit; the latter asserts that the skyis byits motionthemeasureoftime:^theperfect reconciliationoftheseCf.p.411 sq.2Plut. PJac. i. 21 (Stob. i.248; Galen, c.10, p. 2,5):Uvda-yo-pas rhuXP^^^^"^^l^afpatpau tovirepLexoi'TO'i(Galen. : t. irepiex-VM-^sovpavov) elvai, a statementwhichisconfirmed by Aristotle and Sim-plicius. ForAristotle says, P/i7/s.iv. 10, 218 a, 33 : ol fxeu yap rwTOV b\ov Kivrimv elfai (paaiu [rbi/Xpopov~\,ol Se TT]u a(pa7pav aurrju,andSimpliciusfurtherremarks,p.165: ol p.eu Trju rod o\ov KLprjcnpKOI ir^pLcpopav rhuXP^^'^^^ivai(pacTiv, ojs rouYWaLTwva vop.i^.ovo'tv 6re Evdrj/j-os, k. t. A.., ol 5e ttjurrcpdlpau avTTjurod ovpavov, uis tovsTlvdayopLKovs iTTopovaL Xeyecv olTrapaKovaavTSS Xcrcas tov 'Apx^TOv(the categories falsely ascribedtoArchytas;cf Pt. iii. b, 113, 2 ed.)AeyouTosKaQoXovThv xpoj/oi/StacT-TTjaa TTjs rodTravros (picreois. Inasimilarmanner,accordingto Plut,BeIs.32, p.364;Clem. StrGm. x.571 B; Porph, Vit. Pyth. 41, theseawasspokenofbythe Pythago-reans as the tears of Cronos.Cronosis thegodoftheskywhosetears(the rain) had, as theycon-cen-ed, formedthesea, videszopra.p. 91, 2. I cannot recognise myopinionin the terms employedbyChaignet, ii. 171 sq., toreproducetheaboveremark. NorcanI dis-cuss either his objections or hisattempt to find the sense of thePythagorean definition inPseudo-Pythagoreanwritings,^Arist. I. c, gives anothermo-tive: T] Se TOV oKov (TcpaTpa eSo^e[xeuTOiS eliTOvaiv elvuL 6 xpovos, oneuT6 T6JXP^'^'VTraira^cttI kuX 4v ttjTOVb\ouacpaipa, andthedefinitionattributed to Archytas inSimpli-cius may be interpreted in thisseas-e. But this reason does notseemtohavecomefromArchytas.I should rather conjecture it tohave been given after his time.Cronos must at first have beenwith the Pythagoreans, as withPherecydes, asymbolical nameforthe sky. Videprecedingnote.470 THEPYTHAGOREAyS.two doctrines was doubtless not attempted by thePythagoreans.^This theory necessitated the abandonment of theoriginalviewof the world asa surface vaulted overbya hemispherical cavity;and the conception of upperand lower was reduced to that of greater or lesserdistance from the centre;2 the lower, or that lyingnearer to thecentre, wascalledby thePythagoreansthe'I cannot regardthem as ac-cordant, nor can I agree withBockh {Fhilol98) that the Py-thagoreanscalledTime thesphereof the embracing, sofar as it hasits foundation in the Unlimited.Por, on the one hand, the Unli-mitedcouldnot be designated asacpaipa Tov Tt^pUxouTos;and, onthe other, this expressionis other-wise explained in the passageofAristotlehithertooverlooked. Theindication of Plutarch {Plat. Qu.viii.4, 3, p. 1007), according towhichPythagoras definedTimeasthe soul of the All or of Zeus,meritsnoreliance. Cf.p.466sq.-Thispoint, it is true, is notestablished by the testimony ofAristotle, De Ceelo, ii. 2,285 a, 10.Aristotle, in considering theques-tion whether theheavenshaveanaboveanda below, a right andalift, abeforeandabehind, finds itstrangethatthe Pythagoreans5vojxovasravTasapxo.s\yov,rhSe^ihuKoi rb apicTTephv, ras 5erirrapasirapiKiTTov ovdevrjTTOv Kvpias ovaas.!But this means to say that inthetableofopposites, videp. 381,these two categories alune arementioned. In fact, however,theAboveand the Below in theuni-versewerereducedtotheExteriorandthe Interior. Philol.ap.8tob.Ed. i. 360 (Bockh, Philol. 90 flf;jD. kosm. Syst. 120 sq.): airh tovfxiaot) TOE &v(t} ?m tw*/ avTwv rolsKara} i(TTl, to 6,vco rod fieaov vire-vavriws Keijxiva rols Karw(i.e., theorder of the spheres,from aboveto the centre,is the contraryoftheorderfromthecentre tothe lowestpoint) Tols yap KaratoKarcoTdTwjxicra iopo7evelsThuTerpriiievovtt'lQov vBwp erepcctoiovtwreTpr^fxevu}KoffKLvw. It is aquestion-whetherin this text it is merelythecom-parisonof theawixa-with the ariaa,andthemythusofthepunishmentof the auuTjTot, that comes fromPhilolaus or some Pythagorean,onvhetherthemoral interpretationofthismythalso comesfromhim.Thisinterpretation is attributetoPhilolaus by Bockh {Phihl.183,186 sq.); Brandis{Gr.Bom.Phil.i. 497): Susemihl {Genet. EntuK d.Flat. Phil. i. 107 sq.). andothers.Brandisislesspositive in theGesch.d. Entw. i. 187. The interpreta-tion, asa -svhole, seems to me tohaveapurely Platonic character,andtobeout of harmonywiththetreatise of Philolaus. Platodoesnot saythat he borrowedfromtheKoix^os av7]p the interpretation ofthe myth, but the myth itself.When,connecting this mythwitha popular song, 2t/feA.bs KoiJL\\/hsavrip ttotI rau fxarepa ecpa. Timoc-reon, Fr. 6 b; Bergk. Lyr. Gr.p.941,hemakesamythus. Si/ceAby^'IraXiKos;hemeanstosaythatthemythoftheperforated vesselintowhich the unconsecrated weretoput water with a sievei.e., thetradition which extends thepunishment of the Danaidsto allthe profanebelongs to the Or-phico-Pythagorean cycle. In theCratylus. 400 B, Plato refers forthecomparisonof crccjia -n-irh nrifxato the Orphics, whom Philolausalso had in view : koi yaparinaTiues (pacriv avrh [rb acoixa] eluairfjsr^uxv^- ^y re6aufxevr]s ev rw vvvirapdvTi . . . BoKovcTL fxevroi jxoifxd-KiCTa deaOaiol aurpl 'Opcpea tovtoTh ovofxa. cos BiK7}v BiBovrrris t7)s\f)VXV^^v Brj eveKa BiBoorri tovtqvBeirepi&oXov e^ftf, Xva ad^rjTai,Beafxu-T-qpiov elK6va.TRANSMIGRATIONOFSOULS.483to free itself by a presumptuous act.^So longasthesoul is in the bodyit requires the body; for throughthebodyalonecanit feelandperceive; separatedfromthebodyit leadsanincorporeal life inahigherworld.^This, however, is of course only the casewhen it hasrendereditself capableand worthy of suchhappiness;otherwise it can but look forward to thepenance ofmateriallife, orthetormentsofTartarus.^ThePytha-gorean doctrine was therefore, accordingto these themost ancient authorities, essentiallythe same that weafterwards find associated with otherPythagoreannotions,inPlato;'*and which ismaintainedbyEmpe-docles,^viz., thatthe soulonaccountofprevioustrans-gressions is sentintothebody,andthatafterdeatheachsoul, accordingto its deserts,enters theCosmosorTar->Plato, Crat 1. c. ; Id. Phcsdo,62 B(afterhaving remarkedthatPhilolaiis forbade suicide) : 6 fxhvovv iv airoppr]TOis Xeyofxevos ireplavTcavXoyos,ons%vtivi(ppoupaiafxepol auBpooTTOi Koi ov Set Srj eaurhv e/cravTrjs \v6iv ouS' d7ro5tSpda'/tti/,which Cic. (Cafo,20, 73 ;Somn.Scip. e.3)reproduces ratherinac-curately, without, however,havinganyotherauthority thanthispas-sage. Clearchus (ap. Athen, iv.157 c)attributes thesamedoctrinetoan unknown PythagoreannamedEuxitheus.'^Philol. ap. Claudian. BeStatuAn. ii, 7: diligiturcorpusahanima^ quia sineeo tion potest utisetisibus: a quo postqico/rn mortedediicta est agit in rmindo (kSct/xosasdistinguishedfromovpavhs, sup,p.471,2)incorpoi^alemvitam.Carm.Aur. V. 70sq. : ^v S' airoK^A^aserut/jia is alQip i\ev9epoi/ ^Adrjs,%tTa^ai aOdvaros OsosauQpcnos, ou-/ceViOvriros.Perhaps this is theorigin ofthe stat-inent ofEpipha-nius(Exp.fid. 1807). accordingtowhichPythagorascalledhimselfagod.^Euxitheus,ap. Athen, I.e.,threatens thosewho commit sui-cide: Siei7rafT0atrhv Qcou, a>s eluhfxevovaiv iwi tovtois, coos au ^KwyavTovs XvffT), Trk4o(TtKal }xL^o(nuififrea-ovvrai. roreKiifxais,and ac-cordingtoArht.Anal.Post. ii.11,94b,32, Pythagorasthoughtthatthunderfrightenedsinners in Tar-tarus. For I agree with Eitter(Gesch. d. Phil, i,425)that iftheparallel passage, in Plato, I^ep. x,615 D. f. be duly considered,wemustsupposethatthesinners,andnotthe Titans, are heremeant.*Cf, PartII. a, 691, 3rd ed.*Videinfra, vol. ii. Emped.I I 2484 THEPYTHAGOREANS.tarus,or is destinedto fresh wanderingsthroughhumanoranimalforms. ^ When,therefore,wemeetwithsucharepresentationof the doctrine,amongrecentwriters,^we have every reason to accept it^ as true, without onthataccountadmittingall that they combinewith it.'*Thesouls,we are told, after departing from the body,float about in theair;^andthis no doubt is the foun-dation of the opinion quoted above, that the solarcorpuscles are souls;^an opinion which must not be*The Pythagoreansare saidtohavedenominated thisreturn intothebody by the wordtrdkiyy^ve^ia.Sei'v. Aen. iii. 68 : PythagorasnonfXTeix\pvxoo(nvsedTraXiyyevea-iavesseelicit, h. e. redire [animam'] postterapics. Vgl.p.47-A, 3.-E.g.Alexander, -who seemsheretoreproducethePythagoreanideas -with less admixture thanusual,ap.Diog.viii.31: iKpi(p9e7(rav8'auTVV [ttjj/\\/vxw]^^ri yrjs ttAo.-^eadaibjxoiav rw awpLari (cf. Plato,Phc-do, 81 C; Iambi. V. P. 139,148): TovB^'Epurjv raixiav elvaL Tu>uxlw^^v KalSiarovTOTrouira7ov\eye(r-BollKalirvKaiovKa\x^oviov,iir^iBriTrepnuTus etCTre'uTrei airh tuu (TooixoltcovTAS \pvxo.sairo reyrisKoi eK BaXdr-TTjs" KoX &yadai tcls fiev Kadapas(irl rov VipLffTov. ras5'aKaOdprovs/jL-fiT iKsivco TreXa^eij/ fx-qr' a\Xi'i\ais.SilarBai8'eV appT]' yapaawuaTOv.'p7}(Tiv, ovdhv,exv 54 thesystemof Xenophanes a unionBLfiepTj TTji/ (piXo(ro(piav viro(TTrj(raij.4- of Ionian and Pythagorean ele-vwv H. iJ.ub KuXocpwvios rh (pvcTLKhv meets,butthetheologicaldoctrinesaua Kal KoyiKhv, ws (paai ti.vs, of Xenophanes are more likelytofxer-fipx^TO. havecomefromhimto thePytha-2Aristocles, ap. Eus. Pr. Ev. goreans than vice versa. Thexi.3, 1 : E. 5e koI ot o.-jt'' eKiii/ov chronology also is against thisToys ipiariKovs Kivriaavres \6yovs theory,especiallyifCousinisrighttroKvv /j.ei> evf^aAou tXiyyov rols in placing Xenophanes' birth in(pi\oa6(pois, oh ixT]v i-Kopiadv76riva theyear617B.C.fio-ndeiau.*Cf. Diog.ix.21,quotedinfra,^Brandis, Gr. Rom. Phil. i. Par/?i., note 1.359. The view of Cousin is less^Cf.p.569,withp.255,251, 1.correct(/.c.p. 40,46). HeseesinYOL. I. PP578 XENOPHANES.returnedto it again,and Xenophanestaughtthe samein regard to the earth, whichforhim is the most im-portant part of the universe. His opinion that theheavenlybodies are merelymassesof vapour^remindsusof the earlier doctrine that their fires arenourishedby the exhalations of the earth;^and the infiniteextension of the earth beneath, and the air above,^recalls the imlimitedness of Anaximander's primitivematter. But the theories of Xenophanes about theuniversegenerallyarewidelydifferentfrom thesystemofAnaximander. Anaximandermakes,atanyrate,anattempt to explain the formation and constitution oftheuniversein aphysicalmanner. OfXenophanesweare toldnothingof thekind,andhisconception of thestarsshowsclearlyhowlittle the naturalistictreatmentofphenomenasuitedhismentaltendency. Heenquires,indeed, concerning the principle of things, but theenquiry immediately takes a theological turn,leadinghimto test the currentopinionsconcerningthebeingsinwhomthe ultimate cause is usuallysought,tothecriticismofthebeliefin godsandthusto thethoughtof the One eternal unchangeable Being who is nottobecomparedwith any finite thing. Hisphilosophy isonly naturalistic in regard to its point of departure;in its development it becomes a theological metaphy-'Cf. p.252, tomeoflittle consequence;for we2Accordingto thePlac. ii, 25, do not knowwhether Xenophanes2,Xenophanes thought the moon himself used the expression; andwasa ve(pos irnnXrifxivou, and that if he did, his meaning could notthecometsand similarphenomena have beenthesameas Anaximan-were TriXriuara vi(puiv, in the same der's. Hemeant a firmcombina-way that Anaximander, according tion, and Anaximander merely ato Stob. Ed. i. 510. regarded the looseaggregation.starsasTTtArj/ixaTaof'pos. Thisseems'Su^.p. 565, 5.CHARACTER OFHISDOCTRINE.679sic.^ Butsincetheprimitiveessence is notapprehendedin a purely metaphysical manner as Beingwithoutfurther specific determination,but theologicallyas theDeity, or as the divine spirit ruling in the universe,Xenophanesis not obligedto disputethe reality of theMany and the changeable, or to declare the pheno-menon to be a deceptive appearance. He says, it istrue, thateverythingin its deepestprinciple is eternaland One, but he does not denythat, side byside withtheOne,thereexistsapluralityofderivedandtransitorythings;andhepassesover,apparentlywithoutobservingit, the difficulty which,from his ownpointof view, isinvolved in this theoryand the problemwhichit pro-poses forenquiry. Parmenideswasthe first whorecog-'Teichmiiller {Stud. z. Gesch.d. Bcgr.612) is sofar quite rightin his remark that 'metaphysicswithXenophanes sprang, notfromthe consideration of nature, butfrom the conflicts of Eeason-withthe existing theology.' Only it israther inconsistent with this thatweshould be told also, in relationto Xenophanes {ibid. 620,598),'If wewouldunderstandthemeta-physicsoftheancientphilosophers,wemustfirst study theirtheoriesof nature.' Even in itself, as itseems to me, this proposition isnot universally true of the pre-Socratics (it is only in a certainsense that wecanascribe tothemanydistinction between metaphy-sics and natural enquiries at all);andamongthose towhomit is in-applicable, I should nameParme-nides, Heracleitus, and Xenophanes.Icannotdiscover from Teichmiil-ler's exposition inwhatmannerhistheories oftheDeityandtheunityoftheworldcanhavearisen outofthe veryfewphysical propositionsthathavecomedownto us. EvenAnaxiraander's&Kipou is inno wavconnected withthem. Teichmiiller(p.620 sq.) indeed thinks thatXenophanesdenied themovementof theuniverse,becausethe circularmotion ascribed to it by Anaxi-manderwould only be possible ifthe earthhungin themidstoftheair, and this seemed to him muchtooimprobable. Theideaappearsto mefar-fetched,and it has twoconsiderations against it1,thatXenophanes (as observed onp.570,1),thoughhedeniedthecrea-tion and destruction of theworld,yet expresslymaintainedaperiodi-calchangein its conditions; and2,that Anaximander(cf.p.252, 1)didnotbelieveina circularmovementof theuniverse,andtherotation oftheheavens,which,hetaught,wouldbe quite compatible with the un-limitedness of the subterraneanregion ofthe earth (cf.p. 572, 5).p p 2530PARMENIDES.nised this, andwhocarried out the Eleatic doctrine inopposition to the popular notions with logical consis-tency,andregardless of results.PAEMENWES.The great advance madebytheEleatic philosophyinParmenides ultimately consists in this, that the unity'Parmenidesof Elea was theson of Pyres or Pyrrhes, Theo-phrast. ap. Alex, in Metai^h. i.3,981b, 1; Diog.ix.21; Suid. suhvoc.;Theod. Cwr. Gr.off.iv.7, p. 57;also ap. Diog. ix. 25, -where (ac-cording to the usual reading) heis called the sonof Teleutagoras;whether,with Cobet,whomay ormaynotbefollowingthe evidenceof 3ISS., weomitthewordsUvpr\-Tos Thv Se Yiapjx^vi'B'qv, or withKarsten, PkU. Grac. Bell. i. b, 3,alter their position thus : Z-f]voov'EA.6aTTjs' Tovrov 'AiroWSBwpos(prjaiveli/at ivxPO''"^TTvpuSrjs