第34章

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，andthemanyaremuch(unless， indeed，thereisadifferenceinthecaseofaneasily-bounded continuum)，thelittle(orfew)willbeaplurality。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 firstpluralitywhichisdeficient(forthisreasonAnaxagoraswasnot rightinleavingthesubjectwiththestatementthat’allthings weretogether，boundlessbothinpluralityandinsmallness’-wherefor ’andinsmallness’heshouldhavesaid’andinfewness’；forthey couldnothavebeenboundlessinfewness)，sinceitisnotone，as somesay，buttwo，thatmakeafew。 Theoneisopposedthentothemanyinnumbersasmeasuretothing measurable；andtheseareopposedasaretherelativeswhicharenot fromtheirverynaturerelatives。Wehavedistinguishedelsewhere thetwosensesinwhichrelativesaresocalled:-(1)ascontraries； (2)asknowledgetothingknown，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。For(1)all intermediatesareinthesamegenusasthethingsbetweenwhichthey stand。Forwecallthosethingsintermediates，intowhichthatwhich changesmustchangefirst；e。g。ifweweretopassfromthehighest stringtothelowestbythesmallestintervals，weshouldcome soonertotheintermediatenotes，andincoloursifweweretopass fromwhitetoblack，weshouldcomesoonertocrimsonandgreythanto black；andsimilarlyinallothercases。Buttochangefromone genustoanothergenusisnotpossibleexceptinanincidentalway，as fromcolourtofigure。Intermediates，then，mustbeinthesame genusbothasoneanotherandasthethingstheystandbetween。 But(2)allintermediatesstandbetweenoppositesofsomekind； foronlybetweenthesecanchangetakeplaceinvirtueoftheirown nature(sothatanintermediateisimpossiblebetweenthingswhichare 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。 (3)Ifintermediatesareinthesamegenus，ashasbeenshown，and standbetweencontraries，theymustbecomposedofthesecontraries。 Foreithertherewillbeagenusincludingthecontrariesorthere willbenone。Andif(a)thereistobeagenusinsuchawaythat 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’。) Thereforeitis(b)withregardtothesecontrarieswhichdonot 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，intermediatesare(1)allinthe samegenusand(2)intermediatebetweencontraries，and(3)all compoundedoutofthecontraries。 Thatwhichisotherinspeciesisotherthansomethingin something，andthismustbelongtoboth；e。g。ifitisananimalother inspecies，bothareanimals。Thethings，then，whichareotherin speciesmustbeinthesamegenus。ForbygenusImeanthatone identicalthingwhichispredicatedofbothandisdifferentiatedin nomerelyaccidentalway，whetherconceivedasmatterorotherwise。 Fornotonlymustthecommonnatureattachtothedifferentthings， e。g。notonlymustbothbeanimals，butthisveryanimalitymust alsobedifferentforeach(e。g。intheonecaseequinity，inthe otherhumanity)，andsothiscommonnatureisspecificallydifferent foreachfromwhatitisfortheother。One，then，willbeinvirtue ofitsownnatureonesortofanimal，andtheotheranother，e。g。 oneahorseandtheotheraman。Thisdifference，then，mustbean othernessofthegenus。ForIgivethenameof’differenceinthe genus’anothernesswhichmakesthegenusitselfother。 This，then，willbeacontrariety(ascanbeshownalsoby 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，beinginthesamegenusandbeingindivisible(and thosethingsarethesameinspecieswhichhavenocontrariety， beingindivisible)；wesay’beingindivisible’，forintheprocess ofdivisioncontrarietiesariseintheintermediatestagesbeforewe cometotheindivisibles。Evidently，therefore，withreferencetothat whichiscalledthegenus，noneofthespecies-of-a-genusiseither thesameasitorotherthanitinspecies(andthisisfitting；for thematterisindicatedbynegation，andthegenusisthematterof thatofwhichitiscalledthegenus，notinthesenseinwhichwe speakofthegenusorfamilyoftheHeraclidae，butinthatinwhich thegenusisanelementinathing’snature)，norisitsowith referencetothingswhicharenotinthesamegenus，butitwill differingenusfromthem，andinspeciesfromthingsinthesame genus。Forathing’sdifferencefromthatfromwhichitdiffersin speciesmustbeacontrariety；andthisbelongsonlytothingsin thesamegenus。