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1、Plato’sForms,Pythagorean*Mathematics,andStichometryJ.B.KennedyThisessayadvancesaseriesofstrongthesesaboutPlato’sphilosophyandaimstocorroboratetheviewofAristotleandothermembersoftheearlyAcademythatitwasfundamentallyPythagorean.Theargu-mentreconceptualisestheli
2、terarystrategiesofthedialoguesandthusrequiressomehistoricalstage-setting.Theargumentisinductiveinform.Thismeansthatitgainsinstrengthbyaccumulatingavarietyofindependent,yetmutuallyreinforcingkindsofevidence.StichometricanalysesfindunexpectedevidenceforPythagore
3、anisminthedialoguesthemselves,andtherebydevelopapregnantargumentmadebySayre.Heobserved,inshort,thatthestructureofthetextoftheStatesmanseemedtoreflectitsmetaphysics.Thereisatthemath-ematicalcentreofthedialogue‘referencetothemiddlebetweenExcessandDeficiency,’andt
4、hus‘thedialoguebeginswithareferencetoabe-ginning,endswithreferencetoanending,andincludesreferenceatits1midpointtoameanormiddle.”Thiscorrespondencebetweentextualstructureandmetaphysicsissubstantiallyamplifiedhere.Infact,the*ThislineofresearchoriginatedwhenIwast
5、eachingonecoursedevotedtoPlato’sRepublic,andsorehearsingtheliteratureonitspuzzlingstructure,andanothercourseonthehistoryofmathematics,includingPythagoreanmusictheory.ThankyoutoMichaelWorboysandmyfriendsandcolleaguesinCHSTMatManches-terUniversity,wherethispape
6、rwasfirstread.MyworkonPlatobeganinthephilosophydepartmentsatNotreDameandStanford,andIthankmyfriends,colleagues,andteachersfromthoseinstitutions.Forhelpwithearlydraftsofthispaper,thankstoAnthonyLesser,JohnPickstone,ThomasUebel,MichaelRush,JohnShand,andLouiseCra
7、scall.1Sayre[58],183.Cf.Statesman,283c3-5c2.Sayreproceedstomakeasimilarargu-mentaboutthestructureofthePhilebus.APEIRONajournalforancientphilosophyandscience003-6390/2010/4301001-03232.00©AcademicPrintingandPublishing2J.B.KennedymusicalstructureSayretakesaspar
8、adigmaticofPlato’smathematical2ontologycan,itwillbeargued,befoundembeddedinthedialogues.RecentworkontheDerveniPapyrushashelpedtosparkawide-spreadreappraisaloftheinterestinsymbolicalandall
