Those，then，whosaytheuniverseisoneandpositonekindof
　　thingasmatter，andascorporealmatterwhichhasspatial
　　magnitude，evidentlygoastrayinmanyways。Fortheypositthe
　　elementsofbodiesonly，notofincorporealthings，thoughthereare
　　alsoincorporealthings。Andintryingtostatethecausesof
　　generationanddestruction，andingivingaphysicalaccountofall
　　things，theydoawaywiththecauseofmovement。Further，theyerr
　　innotpositingthesubstance，i。e。theessence，asthecauseof
　　anything，andbesidesthisinlightlycallinganyofthesimplebodies
　　exceptearththefirstprinciple，withoutinquiringhowtheyare
　　producedoutofoneanothers-Imeanfire，water，earth，andair。For
　　somethingsareproducedoutofeachotherbycombination，othersby
　　separation，andthismakesthegreatestdifferencetotheirpriority
　　andposteriority。For1inawaythepropertyofbeingmost
　　elementaryofallwouldseemtobelongtothefirstthingfromwhich
　　theyareproducedbycombination，andthispropertywouldbelongto
　　themostfine-grainedandsubtleofbodies。Forthisreasonthose
　　whomakefiretheprinciplewouldbemostinagreementwiththis
　　argument。Buteachoftheotherthinkersagreesthattheelementof
　　corporealthingsisofthissort。Atleastnoneofthosewhonamedone
　　elementclaimedthatearthwastheelement，evidentlybecauseofthe
　　coarsenessofitsgrain。Oftheotherthreeelementseachhasfound
　　somejudgeonitsside；forsomemaintainthatfire，othersthat
　　water，othersthatairistheelement。Yetwhy，afterall，dotheynot
　　nameearthalso，asmostmendo？Forpeoplesayallthingsareearth
　　Hesiodsaysearthwasproducedfirstofcorporealthings；soprimitive
　　andpopularhastheopinionbeen。Accordingtothisargument，then，
　　noonewouldberightwhoeithersaysthefirstprincipleisanyof
　　theelementsotherthanfire，orsupposesittobedenserthanairbut
　　rarerthanwater。But2ifthatwhichislateringenerationis
　　priorinnature，andthatwhichisconcoctedandcompoundedislater
　　ingeneration，thecontraryofwhatwehavebeensayingmustbe
　　true，-watermustbepriortoair，andearthtowater。
　　Somuch，then，forthosewhopositonecausesuchaswementioned；
　　butthesameistrueifonesupposesmoreofthese，asEmpedoclessays
　　matterofthingsisfourbodies。Forhetooisconfrontedby
　　consequencessomeofwhicharethesameashavebeenmentioned，
　　whileothersarepeculiartohim。Forweseethesebodiesproduced
　　fromoneanother，whichimpliesthatthesamebodydoesnotalways
　　remainfireorearthwehavespokenaboutthisinourworkson
　　nature；andregardingthecauseofmovementandthequestion
　　whetherwemustpositoneortwo，hemustbethoughttohavespoken
　　neithercorrectlynoraltogetherplausibly。Andingeneral，change
　　ofqualityisnecessarilydoneawaywithforthosewhospeakthus，for
　　ontheirviewcoldwillnotcomefromhotnorhotfromcold。Forifit
　　didtherewouldbesomethingthatacceptedthecontraries
　　themselves，andtherewouldbesomeoneentitythatbecamefireand
　　water，whichEmpedoclesdenies。
　　AsregardsAnaxagoras，ifoneweretosupposethathesaidthere
　　weretwoelements，thesuppositionwouldaccordthoroughlywithan
　　argumentwhichAnaxagorashimselfdidnotstatearticulately，but
　　whichhemusthaveacceptedifanyonehadledhimontoit。True，
　　tosaythatinthebeginningallthingsweremixedisabsurdbothon
　　othergroundsandbecauseitfollowsthattheymusthaveexisted
　　beforeinanunmixedform，andbecausenaturedoesnotallowany
　　chancethingtobemixedwithanychancething，andalsobecauseon
　　thisviewmodificationsandaccidentscouldbeseparatedfrom
　　substancesforthesamethingswhicharemixedcanbeseparated；yet
　　ifoneweretofollowhimup，piecingtogetherwhathemeans，hewould
　　perhapsbeseentobesomewhatmoderninhisviews。Forwhennothing
　　wasseparatedout，evidentlynothingcouldbetrulyassertedofthe
　　substancethatthenexisted。Imean，e。g。thatitwasneitherwhite
　　norblack，norgreynoranyothercolour，butofnecessitycolourless；
　　forifithadbeencoloured，itwouldhavehadoneofthesecolours。
　　Andsimilarly，bythissameargument，itwasflavourless，norhadit
　　anysimilarattribute；foritcouldnotbeeitherofanyqualityorof
　　anysize，norcoulditbeanydefinitekindofthing。Forifit
　　were，oneoftheparticularformswouldhavebelongedtoit，and
　　thisisimpossible，sinceallweremixedtogether；forthe
　　particularformwouldnecessarilyhavebeenalreadyseparatedout，but
　　heallweremixedexceptreason，andthisalonewasunmixedand
　　pure。Fromthisitfollows，then，thathemustsaytheprinciples
　　aretheOneforthisissimpleandunmixedandtheOther，whichis
　　ofsuchanatureaswesupposetheindefinitetobebeforeitis
　　definedandpartakesofsomeform。Therefore，whileexpressinghimself
　　neitherrightlynorclearly，hemeanssomethinglikewhatthelater
　　thinkerssayandwhatisnowmoreclearlyseentobethecase。
　　Butthesethinkersare，afterall，athomeonlyinargumentsabout
　　generationanddestructionandmovement；foritispracticallyonlyof
　　thissortofsubstancethattheyseektheprinciplesandthecauses。
　　Butthosewhoextendtheirvisiontoallthingsthatexist，andof
　　existingthingssupposesometobeperceptibleandothersnot
　　perceptible，evidentlystudybothclasses，whichisallthemore
　　reasonwhyoneshoulddevotesometimetoseeingwhatisgoodintheir
　　viewsandwhatbadfromthestandpointoftheinquirywehavenow
　　beforeus。
　　The’Pythagoreans’treatofprinciplesandelementsstranger
　　thanthoseofthephysicalphilosophersthereasonisthattheygot
　　theprinciplesfromnon-sensiblethings，fortheobjectsof
　　mathematics，exceptthoseofastronomy，areoftheclassofthings
　　withoutmovement；yettheirdiscussionsandinvestigationsareall
　　aboutnature；fortheygeneratetheheavens，andwithregardto
　　theirpartsandattributesandfunctionstheyobservethephenomena，
　　anduseuptheprinciplesandthecausesinexplainingthese，which
　　impliesthattheyagreewiththeothers，thephysicalphilosophers，
　　thattherealisjustallthatwhichisperceptibleandcontainedby
　　theso-called’heavens’。Butthecausesandtheprincipleswhich
　　theymentionare，aswesaid，sufficienttoactasstepsevenupto
　　thehigherrealmsofreality，andaremoresuitedtothesethanto
　　theoriesaboutnature。Theydonottellusatall，however，how
　　therecanbemovementiflimitandunlimitedandoddandevenare
　　theonlythingsassumed，orhowwithoutmovementandchangethere
　　canbegenerationanddestruction，orthebodiesthatmovethroughthe
　　heavenscandowhattheydo。
　　Further，ifoneeithergrantedthemthatspatialmagnitude
　　consistsoftheseelements，orthiswereproved，stillhowwould
　　somebodiesbelightandothershaveweight？Tojudgefromwhatthey
　　assumeandmaintaintheyarespeakingnomoreofmathematicalbodies
　　thanofperceptible；hencetheyhavesaidnothingwhateverabout
　　fireorearthortheotherbodiesofthissort，Isupposebecausethey
　　havenothingtosaywhichappliespeculiarlytoperceptiblethings。
　　Further，howarewetocombinethebeliefsthattheattributes
　　ofnumber，andnumberitself，arecausesofwhatexistsandhappensin
　　theheavensbothfromthebeginningandnow，andthatthereisno
　　othernumberthanthisnumberoutofwhichtheworldiscomposed？When
　　inoneparticularregiontheyplaceopinionandopportunity，and，a
　　littleaboveorbelow，injusticeanddecisionormixture，and
　　allege，asproof，thateachoftheseisanumber，andthatthere
　　happenstobealreadyinthisplaceapluralityoftheextendedbodies
　　composedofnumbers，becausetheseattributesofnumberattachto
　　thevariousplaces，-thisbeingso，isthisnumber，whichwemust
　　supposeeachoftheseabstractionstobe，thesamenumberwhichis
　　exhibitedinthematerialuniverse，orisitanotherthanthis？
　　Platosaysitisdifferent；yetevenhethinksthatboththese
　　bodiesandtheircausesarenumbers，butthattheintelligiblenumbers
　　arecauses，whiletheothersaresensible。
　　LetusleavethePythagoreansforthepresent；foritisenoughto
　　havetouchedonthemasmuchaswehavedone。Butasforthosewho
　　posittheIdeasascauses，firstly，inseekingtograspthecauses
　　ofthethingsaroundus，theyintroducedothersequalinnumberto
　　these，asifamanwhowantedtocountthingsthoughthewouldnot
　　beabletodoitwhiletheywerefew，buttriedtocountthemwhen
　　hehadaddedtotheirnumber。FortheFormsarepracticallyequal
　　to-ornotfewerthan-thethings，intryingtoexplainwhichthese
　　thinkersproceededfromthemtotheForms。Fortoeachthingthere
　　answersanentitywhichhasthesamenameandexistsapartfromthe
　　substances，andsoalsointhecaseofallothergroupsthereisaone
　　overmany，whetherthemanyareinthisworldorareeternal。
　　Further，ofthewaysinwhichweprovethattheFormsexist，
　　noneisconvincing；forfromsomenoinferencenecessarilyfollows，
　　andfromsomeariseFormsevenofthingsofwhichwethinkthereare
　　noForms。Foraccordingtotheargumentsfromtheexistenceofthe
　　sciencestherewillbeFormsofallthingsofwhichtherearesciences
　　andaccordingtothe’oneovermany’argumenttherewillbeFormseven
　　ofnegations，andaccordingtotheargumentthatthereisanobject
　　forthoughtevenwhenthethinghasperished，therewillbeFormsof
　　perishablethings；forwehaveanimageofthese。Further，ofthemore
　　accuratearguments，someleadtoIdeasofrelations，ofwhichwesay
　　thereisnoindependentclass，andothersintroducethe’thirdman’。
　　AndingeneraltheargumentsfortheFormsdestroythethings
　　forwhoseexistencewearemorezealousthanfortheexistenceof
　　theIdeas；foritfollowsthatnotthedyadbutnumberisfirst，
　　i。e。thattherelativeispriortotheabsolute，-besidesalltheother
　　pointsonwhichcertainpeoplebyfollowingouttheopinionsheld
　　abouttheIdeashavecomeintoconflictwiththeprinciplesofthe
　　theory。
　　Further，accordingtotheassumptiononwhichourbeliefinthe
　　Ideasrests，therewillbeFormsnotonlyofsubstancesbutalsoof
　　manyotherthingsfortheconceptissinglenotonlyinthecaseof
　　substancesbutalsointheothercases，andtherearesciencesnot
　　onlyofsubstancebutalsoofotherthings，andathousandother
　　suchdifficultiesconfrontthem。Butaccordingtothenecessities
　　ofthecaseandtheopinionsheldabouttheForms，ifFormscanbe
　　sharedintheremustbeIdeasofsubstancesonly。Fortheyarenot
　　sharedinincidentally，butathingmustshareinitsFormasin
　　somethingnotpredicatedofasubjectby’beingsharedin
　　incidentally’Imeanthate。g。ifathingsharesin’doubleitself’，
　　itsharesalsoin’eternal’，butincidentally；for’eternal’happens
　　tobepredicableofthe’double’。ThereforetheFormswillbe
　　substance；butthesametermsindicatesubstanceinthisandinthe
　　idealworldorwhatwillbethemeaningofsayingthatthereis
　　somethingapartfromtheparticulars-theoneovermany？。Andifthe
　　Ideasandtheparticularsthatshareinthemhavethesameform，there
　　willbesomethingcommontothese；forwhyshould’2’beoneandthe
　　sameintheperishable2’sorinthosewhicharemanybuteternal，and
　　notthesameinthe’2’itself’asintheparticular2？Butifthey
　　havenotthesameform，theymusthaveonlythenameincommon，andit
　　isasifoneweretocallbothCalliasandawoodenimagea’man’，
　　withoutobservinganycommunitybetweenthem。
　　AboveallonemightdiscussthequestionwhatonearththeForms
　　contributetosensiblethings，eithertothosethatareeternalor
　　tothosethatcomeintobeingandceasetobe。Fortheycause
　　neithermovementnoranychangeinthem。Butagaintheyhelpinno
　　wiseeithertowardstheknowledgeoftheotherthingsfortheyare
　　noteventhesubstanceofthese，elsetheywouldhavebeeninthem，
　　ortowardstheirbeing，iftheyarenotintheparticularswhichshare
　　inthem；thoughiftheywere，theymightbethoughttobecauses，as
　　whitecauseswhitenessinawhiteobjectbyenteringintoits
　　composition。Butthisargument，whichfirstAnaxagorasandlater
　　Eudoxusandcertainothersused，isveryeasilyupset；foritisnot
　　difficulttocollectmanyinsuperableobjectionstosuchaview。
　　But，further，allotherthingscannotcomefromtheFormsinany
　　oftheusualsensesof’from’。Andtosaythattheyarepatternsand
　　theotherthingsshareinthemistouseemptywordsandpoetical
　　metaphors。Forwhatisitthatworks，lookingtotheIdeas？And
　　anythingcaneitherbe，orbecome，likeanotherwithoutbeingcopied
　　fromit，sothatwhetherSocratesornotamanSocrateslikemight
　　cometobe；andevidentlythismightbesoevenifSocrateswere
　　eternal。Andtherewillbeseveralpatternsofthesamething，and
　　thereforeseveralForms；e。g。’animal’and’two-footed’andalso
　　’manhimself’willbeFormsofman。Again，theFormsarepatterns
　　notonlysensiblethings，butofFormsthemselvesalso；i。e。the
　　genus，asgenusofvariousspecies，willbeso；thereforethesame
　　thingwillbepatternandcopy。