Wemightraisesimilarquestionsabouttheoneandthemany。For
　　ifthemanyareabsolutelyopposedtotheone，certainimpossible
　　resultsfollow。Onewillthenbefew，whetherfewbetreatedhereas
　　singularorplural；forthemanyareopposedalsotothefew。Further，
　　twowillbemany，sincethedoubleismultipleand’double’derives
　　itsmeaningfrom’two’；thereforeonewillbefew；forwhatisthatin
　　comparisonwithwhichtwoaremany，exceptone，whichmusttherefore
　　befew？Forthereisnothingfewer。Further，ifthemuchandthe
　　littleareinpluralitywhatthelongandtheshortareinlength，and
　　whateverismuchisalsomany，andthemanyaremuchunless，
　　indeed，thereisadifferenceinthecaseofaneasily-bounded
　　continuum，thelittleorfewwillbeaplurality。Thereforeone
　　isapluralityifitisfew；andthisitmustbe，iftwoaremany。But
　　perhaps，whilethe’many’areinasensesaidtobealso’much’，itis
　　withadifference；e。g。waterismuchbutnotmany。But’many’is
　　appliedtothethingsthataredivisible；intheonesenseitmeans
　　apluralitywhichisexcessiveeitherabsolutelyorrelatively
　　while’few’issimilarlyapluralitywhichisdeficient，andin
　　anothersenseitmeansnumber，inwhichsensealoneitisopposedto
　　theone。Forwesay’oneormany’，justasifoneweretosay’oneand
　　ones’or’whitethingandwhitethings’，ortocomparethethingsthat
　　havebeenmeasuredwiththemeasure。Itisinthissensealsothat
　　multiplesaresocalled。Foreachnumberissaidtobemanybecauseit
　　consistsofonesandbecauseeachnumberismeasurablebyone；and
　　itis’many’asthatwhichisopposedtoone，nottothefew。In
　　thissense，then，eventwoismany-not，however，inthesenseofa
　　pluralitywhichisexcessiveeitherrelativelyorabsolutely；itis
　　thefirstplurality。Butwithoutqualificationtwoisfew；foritis
　　firstpluralitywhichisdeficientforthisreasonAnaxagoraswasnot
　　rightinleavingthesubjectwiththestatementthat’allthings
　　weretogether，boundlessbothinpluralityandinsmallness’-wherefor
　　’andinsmallness’heshouldhavesaid’andinfewness’；forthey
　　couldnothavebeenboundlessinfewness，sinceitisnotone，as
　　somesay，buttwo，thatmakeafew。
　　Theoneisopposedthentothemanyinnumbersasmeasuretothing
　　measurable；andtheseareopposedasaretherelativeswhicharenot
　　fromtheirverynaturerelatives。Wehavedistinguishedelsewhere
　　thetwosensesinwhichrelativesaresocalled:-1ascontraries；
　　2asknowledgetothingknown，atermbeingcalledrelative
　　becauseanotherisrelativetoit。Thereisnothingtopreventone
　　frombeingfewerthansomething，e。g。thantwo；forifoneisfewer，
　　itisnotthereforefew。Pluralityisasitweretheclasstowhich
　　numberbelongs；fornumberispluralitymeasurablebyone，andoneand
　　numberareinasenseopposed，notascontrary，butaswehavesaid
　　somerelativetermsareopposed；forinasmuchasoneismeasureand
　　theothermeasurable，theyareopposed。Thisiswhynoteverything
　　thatisoneisanumber；i。e。ifthethingisindivisibleitisnot
　　anumber。Butthoughknowledgeissimilarlyspokenofasrelativeto
　　theknowable，therelationdoesnotworkoutsimilarly；forwhile
　　knowledgemightbethoughttobethemeasure，andtheknowablethe
　　thingmeasured，thefactthatallknowledgeisknowable，butnotall
　　thatisknowableisknowledge，becauseinasenseknowledgeis
　　measuredbytheknowable-Pluralityiscontraryneithertothefew
　　themanybeingcontrarytothisasexcessivepluralitytoplurality
　　exceeded，nortotheoneineverysense；butintheonesensethese
　　arecontrary，ashasbeensaid，becausetheformerisdivisibleand
　　thelatterindivisible，whileinanothersensetheyarerelativeas
　　knowledgeistoknowable，ifpluralityisnumberandtheoneisa
　　measure。
　　Sincecontrariesadmitofanintermediateandinsomecaseshave
　　it，intermediatesmustbecomposedofthecontraries。For1all
　　intermediatesareinthesamegenusasthethingsbetweenwhichthey
　　stand。Forwecallthosethingsintermediates，intowhichthatwhich
　　changesmustchangefirst；e。g。ifweweretopassfromthehighest
　　stringtothelowestbythesmallestintervals，weshouldcome
　　soonertotheintermediatenotes，andincoloursifweweretopass
　　fromwhitetoblack，weshouldcomesoonertocrimsonandgreythanto
　　black；andsimilarlyinallothercases。Buttochangefromone
　　genustoanothergenusisnotpossibleexceptinanincidentalway，as
　　fromcolourtofigure。Intermediates，then，mustbeinthesame
　　genusbothasoneanotherandasthethingstheystandbetween。
　　But2allintermediatesstandbetweenoppositesofsomekind；
　　foronlybetweenthesecanchangetakeplaceinvirtueoftheirown
　　naturesothatanintermediateisimpossiblebetweenthingswhichare
　　notopposite；forthentherewouldbechangewhichwasnotfromone
　　oppositetowardstheother。Ofopposites，contradictoriesadmitofno
　　middleterm；forthisiswhatcontradictionis-anopposition，oneor
　　othersideofwhichmustattachtoanythingwhatever，i。e。whichhas
　　nointermediate。Ofotheropposites，somearerelative，others
　　privative，otherscontrary。Ofrelativeterms，thosewhicharenot
　　contraryhavenointermediate；thereasonisthattheyarenotin
　　thesamegenus。Forwhatintermediatecouldtherebebetweenknowledge
　　andknowable？Butbetweengreatandsmallthereisone。
　　3Ifintermediatesareinthesamegenus，ashasbeenshown，and
　　standbetweencontraries，theymustbecomposedofthesecontraries。
　　Foreithertherewillbeagenusincludingthecontrariesorthere
　　willbenone。Andifathereistobeagenusinsuchawaythat
　　itissomethingpriortothecontraries，thedifferentiaewhich
　　constitutedthecontraryspecies-of-a-genuswillbecontrariesprior
　　tothespecies；forspeciesarecomposedofthegenusandthe
　　differentiae。E。g。ifwhiteandblackarecontraries，andoneisa
　　piercingcolourandtheotheracompressingcolour，these
　　differentiae-’piercing’and’compressing’-areprior；sothattheseare
　　priorcontrariesofoneanother。But，again，thespecieswhichdiffer
　　contrariwisearethemoretrulycontraryspecies。Andthe
　　other。species，i。e。theintermediates，mustbecomposedoftheirgenus
　　andtheirdifferentiae。E。g。allcolourswhicharebetweenwhite
　　andblackmustbesaidtobecomposedofthegenus，i。e。colour，and
　　certaindifferentiae。Butthesedifferentiaewillnotbetheprimary
　　contraries；otherwiseeverycolourwouldbeeitherwhiteorblack。
　　Theyaredifferent，then，fromtheprimarycontraries；andtherefore
　　theywillbebetweentheprimarycontraries；theprimary
　　differentiaeare’piercing’and’compressing’。
　　Thereforeitisbwithregardtothesecontrarieswhichdonot
　　fallwithinagenusthatwemustfirstaskofwhattheirintermediates
　　arecomposed。Forthingswhichareinthesamegenusmustbecomposed
　　oftermsinwhichthegenusisnotanelement，orelsebethemselves
　　incomposite。Nowcontrariesdonotinvolveoneanotherintheir
　　composition，andarethereforefirstprinciples；buttheintermediates
　　areeitherallincomposite，ornoneofthem。Butthereissomething
　　compoundedoutofthecontraries，sothattherecanbeachangefroma
　　contrarytoitsoonerthantotheothercontrary；foritwillhave
　　lessofthequalityinquestionthantheonecontraryandmorethan
　　theother。Thisalso，then，willcomebetweenthecontraries。All
　　theotherintermediatesalso，therefore，arecomposite；forthatwhich
　　hasmoreofaqualitythanonethingandlessthananotheris
　　compoundedsomehowoutofthethingsthanwhichitissaidtohave
　　moreandlessrespectivelyofthequality。Andsincethereareno
　　otherthingspriortothecontrariesandhomogeneouswiththe
　　intermediates，allintermediatesmustbecompoundedoutofthe
　　contraries。Thereforealsoalltheinferiorclasses，boththe
　　contrariesandtheirintermediates，willbecompoundedoutofthe
　　primarycontraries。Clearly，then，intermediatesare1allinthe
　　samegenusand2intermediatebetweencontraries，and3all
　　compoundedoutofthecontraries。
　　Thatwhichisotherinspeciesisotherthansomethingin
　　something，andthismustbelongtoboth；e。g。ifitisananimalother
　　inspecies，bothareanimals。Thethings，then，whichareotherin
　　speciesmustbeinthesamegenus。ForbygenusImeanthatone
　　identicalthingwhichispredicatedofbothandisdifferentiatedin
　　nomerelyaccidentalway，whetherconceivedasmatterorotherwise。
　　Fornotonlymustthecommonnatureattachtothedifferentthings，
　　e。g。notonlymustbothbeanimals，butthisveryanimalitymust
　　alsobedifferentforeache。g。intheonecaseequinity，inthe
　　otherhumanity，andsothiscommonnatureisspecificallydifferent
　　foreachfromwhatitisfortheother。One，then，willbeinvirtue
　　ofitsownnatureonesortofanimal，andtheotheranother，e。g。
　　oneahorseandtheotheraman。Thisdifference，then，mustbean
　　othernessofthegenus。ForIgivethenameof’differenceinthe
　　genus’anothernesswhichmakesthegenusitselfother。
　　This，then，willbeacontrarietyascanbeshownalsoby
　　induction。Forallthingsaredividedbyopposites，andithasbeen
　　provedthatcontrariesareinthesamegenus。Forcontrarietywasseen
　　tobecompletedifference；andalldifferenceinspeciesisa
　　differencefromsomethinginsomething；sothatthisisthesamefor
　　bothandistheirgenus。Hencealsoallcontrarieswhichare
　　differentinspeciesandnotingenusareinthesamelineof
　　predication，andotherthanoneanotherinthehighestdegree-for
　　thedifferenceiscomplete-，andcannotbepresentalongwithone
　　another。Thedifference，then，isacontrariety。
　　This，then，iswhatitistobe’otherinspecies’-tohavea
　　contrariety，beinginthesamegenusandbeingindivisibleand
　　thosethingsarethesameinspecieswhichhavenocontrariety，
　　beingindivisible；wesay’beingindivisible’，forintheprocess
　　ofdivisioncontrarietiesariseintheintermediatestagesbeforewe
　　cometotheindivisibles。Evidently，therefore，withreferencetothat
　　whichiscalledthegenus，noneofthespecies-of-a-genusiseither
　　thesameasitorotherthanitinspeciesandthisisfitting；for
　　thematterisindicatedbynegation，andthegenusisthematterof
　　thatofwhichitiscalledthegenus，notinthesenseinwhichwe
　　speakofthegenusorfamilyoftheHeraclidae，butinthatinwhich
　　thegenusisanelementinathing’snature，norisitsowith
　　referencetothingswhicharenotinthesamegenus，butitwill
　　differingenusfromthem，andinspeciesfromthingsinthesame
　　genus。Forathing’sdifferencefromthatfromwhichitdiffersin
　　speciesmustbeacontrariety；andthisbelongsonlytothingsin
　　thesamegenus。