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。