Theoneandthemanyareopposedinseveralways，ofwhichone
　　istheoppositionoftheoneandpluralityasindivisibleand
　　divisible；forthatwhichiseitherdividedordivisibleiscalleda
　　plurality，andthatwhichisindivisibleornotdividediscalledone。
　　Nowsinceoppositionisoffourkinds，andoneofthesetwotermsis
　　privativeinmeaning，theymustbecontraries，andneither
　　contradictorynorcorrelativeinmeaning。Andtheonederivesitsname
　　anditsexplanationfromitscontrary，theindivisiblefromthe
　　divisible，becausepluralityandthedivisibleismoreperceptible
　　thantheindivisible，sothatindefinitionpluralityispriorto
　　theindivisible，becauseoftheconditionsofperception。
　　Totheonebelong，asweindicatedgraphicallyinour
　　distinctionofthecontraries，thesameandthelikeandtheequal，
　　andtopluralitybelongtheotherandtheunlikeandtheunequal。’The
　　same’hasseveralmeanings；1wesometimesmean’thesame
　　numerically’；again，2wecallathingthesameifitisonebothin
　　definitionandinnumber，e。g。youareonewithyourselfbothin
　　formandinmatter；andagain，3ifthedefinitionofitsprimary
　　essenceisone；e。g。equalstraightlinesarethesame，andsoare
　　equalandequal-angledquadrilaterals；therearemanysuch，butin
　　theseequalityconstitutesunity。
　　Thingsarelikeif，notbeingabsolutelythesame，norwithout
　　differenceinrespectoftheirconcretesubstance，theyarethesame
　　inform；e。g。thelargersquareislikethesmaller，andunequal
　　straightlinesarelike；theyarelike，butnotabsolutelythesame。
　　Otherthingsarelike，if，havingthesameform，andbeingthingsin
　　whichdifferenceofdegreeispossible，theyhavenodifferenceof
　　degree。Otherthings，iftheyhaveaqualitythatisinformoneand
　　same-e。g。whiteness-inagreaterorlessdegree，arecalledlike
　　becausetheirformisone。Otherthingsarecalledlikeifthe
　　qualitiestheyhaveincommonaremorenumerousthanthoseinwhich
　　theydiffer-eitherthequalitiesingeneralortheprominent
　　qualities；e。g。tinislikesilver，quawhite，andgoldislike
　　fire，quayellowandred。
　　Evidently，then，’other’and’unlike’alsohaveseveral
　　meanings。Andtheotherinonesenseistheoppositeofthesameso
　　thateverythingiseitherthesameasorotherthaneverything
　　else。Inanothersensethingsareotherunlessboththeirmatter
　　andtheirdefinitionareonesothatyouareotherthanyour
　　neighbour。Theotherinthethirdsenseisexemplifiedintheobjects
　　ofmathematics。’Otherorthesame’canthereforebepredicatedof
　　everythingwithregardtoeverythingelse-butonlyifthethingsare
　　oneandexistent，for’other’isnotthecontradictoryof’the
　　same’；whichiswhyitisnotpredicatedofnon-existentthingswhile
　　’notthesame’issopredicated。Itispredicatedofallexisting
　　things；foreverythingthatisexistentandoneisbyitsvery
　　natureeitheroneornotonewithanythingelse。
　　Theother，then，andthesamearethusopposed。Butdifference
　　isnotthesameasotherness。Fortheotherandthatwhichitisother
　　thanneednotbeotherinsomedefiniterespectforeverythingthat
　　isexistentiseitherotherorthesame，butthatwhichis
　　differentisdifferentfromsomeparticularthinginsomeparticular
　　respect，sothattheremustbesomethingidenticalwherebythey
　　differ。Andthisidenticalthingisgenusorspecies；foreverything
　　thatdiffersdifferseitheringenusorinspecies，ingenusifthe
　　thingshavenottheirmatterincommonandarenotgeneratedoutof
　　eachotheri。e。iftheybelongtodifferentfiguresof
　　predication，andinspeciesiftheyhavethesamegenus’genus’
　　meaningthatidenticalthingwhichisessentiallypredicatedofboth
　　thedifferentthings。
　　Contrariesaredifferent，andcontrarietyisakindofdifference。
　　Thatwearerightinthissuppositionisshownbyinduction。Forall
　　ofthesetooareseentobedifferent；theyarenotmerelyother，
　　butsomeareotheringenus，andothersareinthesamelineof
　　predication，andthereforeinthesamegenus，andthesameingenus。
　　Wehavedistinguishedelsewherewhatsortofthingsarethesameor
　　otheringenus。
　　Sincethingswhichdiffermaydifferfromoneanothermoreor
　　less，thereisalsoagreatestdifference，andthisIcall
　　contrariety。Thatcontrarietyisthegreatestdifferenceismadeclear
　　byinduction。Forthingswhichdifferingenushavenowaytoone
　　another，butaretoofardistantandarenotcomparable；andfor
　　thingsthatdifferinspeciestheextremesfromwhichgenerationtakes
　　placearethecontraries，andthedistancebetweenextremes-and
　　thereforethatbetweenthecontraries-isthegreatest。
　　Butsurelythatwhichisgreatestineachclassiscomplete。For
　　thatisgreatestwhichcannotbeexceeded，andthatiscompletebeyond
　　whichnothingcanbefound。Forthecompletedifferencemarksthe
　　endofaseriesjustastheotherthingswhicharecalledcomplete
　　aresocalledbecausetheyhaveattainedanend，andbeyondtheend
　　thereisnothing；forineverythingitistheextremeandincludesall
　　else，andthereforethereisnothingbeyondtheend，andthe
　　completeneedsnothingfurther。Fromthis，then，itisclearthat
　　contrarietyiscompletedifference；andascontrariesaresocalledin
　　severalsenses，theirmodesofcompletenesswillanswertothevarious
　　modesofcontrarietywhichattachtothecontraries。
　　Thisbeingso，itisclearthatonethinghavemorethanone
　　contraryforneithercantherebeanythingmoreextremethanthe
　　extreme，norcantherebemorethantwoextremesfortheone
　　interval，and，toputthemattergenerally，thisisclearif
　　contrarietyisadifference，andifdifference，andthereforealsothe
　　completedifference，mustbebetweentwothings。
　　Andtheothercommonlyaccepteddefinitionsofcontrariesarealso
　　necessarilytrue。Fornotonlyis1thecompletedifferencethe
　　greatestdifferenceforwecangetnodifferencebeyonditof
　　thingsdifferingeitheringenusorinspecies；forithasbeen
　　shownthatthereisno’difference’betweenanythingandthethings
　　outsideitsgenus，andamongthethingswhichdifferinspeciesthe
　　completedifferenceisthegreatest；butalso2thethingsinthe
　　samegenuswhichdiffermostarecontraryforthecompletedifference
　　isthegreatestdifferencebetweenspeciesofthesamegenus；and3
　　thethingsinthesamereceptivematerialwhichdiffermostare
　　contraryforthematteristhesameforcontraries；and4ofthe
　　thingswhichfallunderthesamefacultythemostdifferentare
　　contraryforonesciencedealswithoneclassofthings，andinthese
　　thecompletedifferenceisthegreatest。
　　Theprimarycontrarietyisthatbetweenpositivestateand
　　privation-noteveryprivation，howeverfor’privation’hasseveral
　　meanings，butthatwhichiscomplete。Andtheothercontrariesmust
　　becalledsowithreferencetothese，somebecausetheypossessthese，
　　othersbecausetheyproduceortendtoproducethem，othersbecause
　　theyareacquisitionsorlossesoftheseorofothercontraries。Now
　　ifthekindsofoppositionarecontradictionandprivationand
　　contrarietyandrelation，andofthesethefirstiscontradiction，and
　　contradictionadmitsofnointermediate，whilecontrariesadmitof
　　one，clearlycontradictionandcontrarietyarenotthesame。But
　　privationisakindofcontradiction；forwhatsuffersprivation，
　　eitheringeneralorinsomedeterminateway，eitherthatwhichis
　　quiteincapableofhavingsomeattributeorthatwhich，beingof
　　suchanatureastohaveit，hasitnot；herewehavealreadya
　　varietyofmeanings，whichhavebeendistinguishedelsewhere。
　　Privation，therefore，isacontradictionorincapacitywhichis
　　determinateortakenalongwiththereceptivematerial。Thisisthe
　　reasonwhy，whilecontradictiondoesnotadmitofanintermediate，
　　privationsometimesdoes；foreverythingisequalornotequal，but
　　noteverythingisequalorunequal，orifitis，itisonlywithinthe
　　sphereofthatwhichisreceptiveofequality。If，then，the
　　comings-to-bewhichhappentothematterstartfromthecontraries，
　　andproceedeitherfromtheformandthepossessionoftheformor
　　fromaprivationoftheformorshape，clearlyallcontrarietymustbe
　　privation，butpresumablynotallprivationiscontrarietythereason
　　beingthatthathassufferedprivationmayhavesuffereditinseveral
　　ways；foritisonlytheextremesfromwhichchangesproceedthatare
　　contraries。
　　Andthisisobviousalsobyinduction。Foreverycontrariety
　　involves，asoneofitsterms，aprivation，butnotallcasesare
　　alike；inequalityistheprivationofequalityandunlikenessof
　　likeness，andontheotherhandviceistheprivationofvirtue。But
　　thecasesdifferinawayalreadydescribed；inonecasewemean
　　simplythatthethinghassufferedprivation，inanothercasethat
　　ithasdonesoeitheratacertaintimeorinacertainparte。g。
　　atacertainageorinthedominantpart，orthroughout。Thisis
　　whyinsomecasesthereisameantherearemenwhoareneither
　　goodnorbad，andinothersthereisnotanumbermustbeeitherodd
　　oreven。Further，somecontrarieshavetheirsubjectdefined，
　　othershavenot。Thereforeitisevidentthatoneofthecontrariesis
　　alwaysprivative；butitisenoughifthisistrueofthefirst-i。e。
　　thegeneric-contraries，e。g。theoneandthemany；fortheothers
　　canbereducedtothese。
　　Sinceonethinghasonecontrary，wemightraisethequestion
　　howtheoneisopposedtothemany，andtheequaltothegreatandthe
　　small。Forifweusedtheword’whether’onlyinanantithesissuchas
　　’whetheritiswhiteorblack’，or’whetheritiswhiteornot
　　white’wedonotask’whetheritisamanorwhite’，unlessweare
　　proceedingonapriorassumptionandaskingsomethingsuchas’whether
　　itwasCleonorSocratesthatcame’asthisisnotanecessary
　　disjunctioninanyclassofthings；yeteventhisisanextensionfrom
　　thecaseofopposites；foroppositesalonecannotbepresenttogether；
　　andweassumethisincompatibilityheretooinaskingwhichofthetwo
　　came；foriftheymightbothhavecome，thequestionwouldhavebeen
　　absurd；butiftheymight，evensothisfallsjustasmuchintoan
　　antithesis，thatofthe’oneormany’，i。e。’whetherbothcameor
　　oneofthetwo’:-if，then，thequestion’whether’isalways
　　concernedwithopposites，andwecanask’whetheritisgreateror
　　lessorequal’，whatistheoppositionoftheequaltotheother
　　two？Itisnotcontraryeithertoonealoneortoboth；forwhyshould
　　itbecontrarytothegreaterratherthantotheless？Further，the
　　equaliscontrarytotheunequal。Thereforeifitiscontrarytothe
　　greaterandtheless，itwillbecontrarytomorethingsthanone。But
　　iftheunequalmeansthesameasboththegreaterandtheless
　　together，theequalwillbeoppositetobothandthedifficulty
　　supportsthosewhosaytheunequalisa’two’，butitfollowsthat
　　onethingiscontrarytotwoothers，whichisimpossible。Again，the
　　equalisevidentlyintermediatebetweenthegreatandthesmall，but
　　nocontrarietyiseitherobservedtobeintermediate，or，fromits
　　definition，canbeso；foritwouldnotbecompleteifitwere
　　intermediatebetweenanytwothings，butratheritalwayshas
　　somethingintermediatebetweenitsownterms。
　　Itremains，then，thatitisopposedeitherasnegationoras
　　privation。Itcannotbethenegationorprivationofoneofthetwo；
　　forwhyofthegreatratherthanofthesmall？Itis，then，the
　　privativenegationofboth。Thisiswhy’whether’issaidwith
　　referencetoboth，nottooneofthetwoe。g。’whetheritis
　　greaterorequal’or’whetheritisequalorless’；thereare
　　alwaysthreecases。Butitisnotanecessaryprivation；fornot
　　everythingwhichisnotgreaterorlessisequal，butonlythe
　　thingswhichareofsuchanatureastohavetheseattributes。
　　Theequal，then，isthatwhichisneithergreatnorsmallbutis
　　naturallyfittedtobeeithergreatorsmall；anditisopposedto
　　bothasaprivativenegationandthereforeisalsointermediate。And
　　thatwhichisneithergoodnorbadisopposedtoboth，buthasno
　　name；foreachofthesehasseveralmeaningsandtherecipientsubject
　　isnotone；butthatwhichisneitherwhitenorblackhasmoreclaim
　　tounity。Yeteventhishasnotonename，thoughthecoloursof
　　whichthisnegationisprivativelypredicatedareinawaylimited；
　　fortheymustbeeithergreyoryelloworsomethingelseofthe
　　kind。Thereforeitisanincorrectcriticismthatispassedbythose
　　whothinkthatallsuchphrasesareusedinthesameway，sothatthat
　　whichisneitherashoenorahandwouldbeintermediatebetweena
　　shoeandahand，sincethatwhichisneithergoodnorbadis
　　intermediatebetweenthegoodandthebad-asiftheremustbean
　　intermediateinallcases。Butthisdoesnotnecessarilyfollow。For
　　theonephraseisajointdenialofoppositesbetweenwhichthereis
　　anintermediateandacertainnaturalinterval；butbetweenthe
　　othertwothereisno’difference’；forthethings，thedenialsof
　　whicharecombined，belongtodifferentclasses，sothatthe
　　substratumisnotone。