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　　Thingsaresaidtobenamed'equivocally'when，thoughtheyhaveacommonname，thedefinitioncorrespondingwiththenamediffersforeach。Thus，arealmanandafigureinapicturecanbothlayclaimtothename'animal'；yettheseareequivocallysonamed，for，thoughtheyhaveacommonname，thedefinitioncorrespondingwiththenamediffersforeach。Forshouldanyonedefineinwhatsenseeachisananimal，hisdefinitionintheonecasewillbeappropriatetothatcaseonly。
　　Ontheotherhand，thingsaresaidtobenamed'univocally'whichhaveboththenameandthedefinitionansweringtothenameincommon。
　　Amanandanoxareboth'animal'，andtheseareunivocallysonamed，inasmuchasnotonlythename，butalsothedefinition，isthesameinbothcases：forifamanshouldstateinwhatsenseeachisananimal，thestatementintheonecasewouldbeidenticalwiththatintheother。
　　Thingsaresaidtobenamed'derivatively'，whichderivetheirnamefromsomeothername，butdifferfromitintermination。Thusthegrammarianderiveshisnamefromtheword'grammar'，andthecourageousmanfromtheword'courage'。
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　　Formsofspeechareeithersimpleorcomposite。Examplesofthelatteraresuchexpressionsas'themanruns'，'themanwins'；oftheformer'man'，'ox'，'runs'，'wins'。
　　Ofthingsthemselvessomearepredicableofasubject，andareneverpresentinasubject。Thus'man'ispredicableoftheindividualman，andisneverpresentinasubject。
　　Bybeing'presentinasubject'Idonotmeanpresentaspartsarepresentinawhole，butbeingincapableofexistenceapartfromthesaidsubject。
　　Somethings，again，arepresentinasubject，butareneverpredicableofasubject。Forinstance，acertainpointofgrammaticalknowledgeispresentinthemind，butisnotpredicableofanysubject；oragain，acertainwhitenessmaybepresentinthebody（forcolourrequiresamaterialbasis），yetitisneverpredicableofanything。
　　Otherthings，again，arebothpredicableofasubjectandpresentinasubject。Thuswhileknowledgeispresentinthehumanmind，itispredicableofgrammar。
　　Thereis，lastly，aclassofthingswhichareneitherpresentinasubjectnorpredicableofasubject，suchastheindividualmanortheindividualhorse。But，tospeakmoregenerally，thatwhichisindividualandhasthecharacterofaunitisneverpredicableofasubject。Yetinsomecasesthereisnothingtopreventsuchbeingpresentinasubject。Thusacertainpointofgrammaticalknowledgeispresentinasubject。
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　　Whenonethingispredicatedofanother，allthatwhichispredicableofthepredicatewillbepredicablealsoofthesubject。
　　Thus，'man'ispredicatedoftheindividualman；but'animal'ispredicatedof'man'；itwill，therefore，bepredicableoftheindividualmanalso：fortheindividualmanisboth'man'and'animal'。
　　Ifgeneraaredifferentandco-ordinate，theirdifferentiaearethemselvesdifferentinkind。Takeasaninstancethegenus'animal'
　　andthegenus'knowledge'。'Withfeet'，'two-footed'，'winged'，'aquatic'，aredifferentiaeof'animal'；thespeciesofknowledgearenotdistinguishedbythesamedifferentiae。Onespeciesofknowledgedoesnotdifferfromanotherinbeing'two-footed'。
　　Butwhereonegenusissubordinatetoanother，thereisnothingtopreventtheirhavingthesamedifferentiae：forthegreaterclassispredicatedofthelesser，sothatallthedifferentiaeofthepredicatewillbedifferentiaealsoofthesubject。
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　　Expressionswhichareinnowaycompositesignifysubstance，quantity，quality，relation，place，time，position，state，action，oraffection。Tosketchmymeaningroughly，examplesofsubstanceare'man'or'thehorse'，ofquantity，suchtermsas'twocubitslong'
　　or'threecubitslong'，ofquality，suchattributesas'white'，'grammatical'。'Double'，'half'，'greater'，fallunderthecategoryofrelation；'inamarketplace'，'intheLyceum'，underthatofplace；'yesterday'，'lastyear'，underthatoftime。'Lying'，'sitting'，aretermsindicatingposition，'shod'，'armed'，state；
　　'tolance'，'tocauterize'，action；'tobelanced'，'tobecauterized'，affection。
　　Nooneoftheseterms，inandbyitself，involvesanaffirmation；itisbythecombinationofsuchtermsthatpositiveornegativestatementsarise。Foreveryassertionmust，asisadmitted，beeithertrueorfalse，whereasexpressionswhicharenotinanywaycompositesuchas'man'，'white'，'runs'，'wins'，cannotbeeithertrueorfalse。
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　　Substance，inthetruestandprimaryandmostdefinitesenseoftheword，isthatwhichisneitherpredicableofasubjectnorpresentinasubject；forinstance，theindividualmanorhorse。Butinasecondarysensethosethingsarecalledsubstanceswithinwhich，asspecies，theprimarysubstancesareincluded；alsothosewhich，asgenera，includethespecies。Forinstance，theindividualmanisincludedinthespecies'man'，andthegenustowhichthespeciesbelongsis'animal'；these，therefore-thatistosay，thespecies'man'andthegenus'animal，-aretermedsecondarysubstances。
　　Itisplainfromwhathasbeensaidthatboththenameandthedefinitionofthepredicatemustbepredicableofthesubject。Forinstance，'man'ispredictedoftheindividualman。Nowinthiscasethenameofthespeciesman'isappliedtotheindividual，forweusetheterm'man'indescribingtheindividual；andthedefinitionof'man'willalsobepredicatedoftheindividualman，fortheindividualmanisbothmanandanimal。Thus，boththenameandthedefinitionofthespeciesarepredicableoftheindividual。
　　Withregard，ontheotherhand，tothosethingswhicharepresentinasubject，itisgenerallythecasethatneithertheirnamenortheirdefinitionispredicableofthatinwhichtheyarepresent。
　　Though，however，thedefinitionisneverpredicable，thereisnothingincertaincasestopreventthenamebeingused。Forinstance，'white'beingpresentinabodyispredicatedofthatinwhichitispresent，forabodyiscalledwhite：thedefinition，however，ofthecolourwhite'isneverpredicableofthebody。
　　Everythingexceptprimarysubstancesiseitherpredicableofaprimarysubstanceorpresentinaprimarysubstance。Thisbecomesevidentbyreferencetoparticularinstanceswhichoccur。'Animal'
　　ispredicatedofthespecies'man'，thereforeoftheindividualman，foriftherewerenoindividualmanofwhomitcouldbepredicated，itcouldnotbepredicatedofthespecies'man'atall。Again，colourispresentinbody，thereforeinindividualbodies，foriftherewerenoindividualbodyinwhichitwaspresent，itcouldnotbepresentinbodyatall。Thuseverythingexceptprimarysubstancesiseitherpredicatedofprimarysubstances，orispresentinthem，andiftheselastdidnotexist，itwouldbeimpossibleforanythingelsetoexist。
　　Ofsecondarysubstances，thespeciesismoretrulysubstancethanthegenus，beingmorenearlyrelatedtoprimarysubstance。Forifanyoneshouldrenderanaccountofwhataprimarysubstanceis，hewouldrenderamoreinstructiveaccount，andonemorepropertothesubject，bystatingthespeciesthanbystatingthegenus。Thus，hewouldgiveamoreinstructiveaccountofanindividualmanbystatingthathewasmanthanbystatingthathewasanimal，fortheformerdescriptionispeculiartotheindividualinagreaterdegree，whilethelatteristoogeneral。Again，themanwhogivesanaccountofthenatureofanindividualtreewillgiveamoreinstructiveaccountbymentioningthespecies'tree'thanbymentioningthegenus'plant'。
　　Moreover，primarysubstancesaremostproperlycalledsubstancesinvirtueofthefactthattheyaretheentitieswhichunderlieevery。
　　else，andthateverythingelseiseitherpredicatedofthemorpresentinthem。Nowthesamerelationwhichsubsistsbetweenprimarysubstanceandeverythingelsesubsistsalsobetweenthespeciesandthegenus：forthespeciesistothegenusassubjectistopredicate，sincethegenusispredicatedofthespecies，whereasthespeciescannotbepredicatedofthegenus。Thuswehaveasecondgroundforassertingthatthespeciesismoretrulysubstancethanthegenus。
　　Ofspeciesthemselves，exceptinthecaseofsuchasaregenera，nooneismoretrulysubstancethananother。Weshouldnotgiveamoreappropriateaccountoftheindividualmanbystatingthespeciestowhichhebelonged，thanweshouldofanindividualhorsebyadoptingthesamemethodofdefinition。Inthesameway，ofprimarysubstances，nooneismoretrulysubstancethananother；anindividualmanisnotmoretrulysubstancethananindividualox。
　　Itis，then，withgoodreasonthatofallthatremains，whenweexcludeprimarysubstances，weconcedetospeciesandgeneraalonethename'secondarysubstance'，forthesealoneofallthepredicatesconveyaknowledgeofprimarysubstance。Foritisbystatingthespeciesorthegenusthatweappropriatelydefineanyindividualman；andweshallmakeourdefinitionmoreexactbystatingtheformerthanbystatingthelatter。Allotherthingsthatwestate，suchasthatheiswhite，thatheruns，andsoon，areirrelevanttothedefinition。Thusitisjustthatthesealone，apartfromprimarysubstances，shouldbecalledsubstances。
　　Further，primarysubstancesaremostproperlysocalled，becausetheyunderlieandarethesubjectsofeverythingelse。Nowthesamerelationthatsubsistsbetweenprimarysubstanceandeverythingelsesubsistsalsobetweenthespeciesandthegenustowhichtheprimarysubstancebelongs，ontheonehand，andeveryattributewhichisnotincludedwithinthese，ontheother。Forthesearethesubjectsofallsuch。Ifwecallanindividualman'skilledingrammar'，thepredicateisapplicablealsotothespeciesandtothegenustowhichhebelongs。Thislawholdsgoodinallcases。
　　Itisacommoncharacteristicofallsub。stancethatitisneverpresentinasubject。Forprimarysubstanceisneitherpresentinasubjectnorpredicatedofasubject；while，withregardtosecondarysubstances，itisclearfromthefollowingarguments（apartfromothers）thattheyarenotpresentinasubject。For'man'ispredicatedoftheindividualman，butisnotpresentinanysubject：
　　formanhoodisnotpresentintheindividualman。Inthesameway，'animal'isalsopredicatedoftheindividualman，butisnotpresentinhim。Again，whenathingispresentinasubject，thoughthenamemayquitewellbeappliedtothatinwhichitispresent，thedefinitioncannotbeapplied。Yetofsecondarysubstances，notonlythename，butalsothedefinition，appliestothesubject：weshoulduseboththedefinitionofthespeciesandthatofthegenuswithreferencetotheindividualman。Thussubstancecannotbepresentinasubject。
　　Yetthisisnotpeculiartosubstance，foritisalsothecasethatdifferentiaecannotbepresentinsubjects。Thecharacteristics'terrestrial'and'two-footed'arepredicatedofthespecies'man'，butnotpresentinit。Fortheyarenotinman。Moreover，thedefinitionofthedifferentiamaybepredicatedofthatofwhichthedifferentiaitselfispredicated。Forinstance，ifthecharacteristic'terrestrial'ispredicatedofthespecies'man'，thedefinitionalsoofthatcharacteristicmaybeusedtoformthepredicateofthespecies'man'：for'man'isterrestrial。
　　Thefactthatthepartsofsubstancesappeartobepresentinthewhole，asinasubject，shouldnotmakeusapprehensivelestweshouldhavetoadmitthatsuchpartsarenotsubstances：forinexplainingthephrase'beingpresentinasubject'，westated'thatwemeant'otherwisethanaspartsinawhole'。
　　Itisthemarkofsubstancesandofdifferentiaethat，inallpropositionsofwhichtheyformthepredicate，theyarepredicatedunivocally。Forallsuchpropositionshavefortheirsubjecteithertheindividualorthespecies。Itistruethat，inasmuchasprimarysubstanceisnotpredicableofanything，itcanneverformthepredicateofanyproposition。Butofsecondarysubstances，thespeciesispredicatedoftheindividual，thegenusbothofthespeciesandoftheindividual。Similarlythedifferentiaearepredicatedofthespeciesandoftheindividuals。Moreover，thedefinitionofthespeciesandthatofthegenusareapplicabletotheprimarysubstance，andthatofthegenustothespecies。Forallthatispredicatedofthepredicatewillbepredicatedalsoofthesubject。Similarly，thedefinitionofthedifferentiaewillbeapplicabletothespeciesandtotheindividuals。Butitwasstatedabovethattheword'univocal'
　　wasappliedtothosethingswhichhadbothnameanddefinitionincommon。Itis，therefore，establishedthatineveryproposition，ofwhicheithersubstanceoradifferentiaformsthepredicate，thesearepredicatedunivocally。
　　Allsubstanceappearstosignifythatwhichisindividual。Inthecaseofprimarysubstancethisisindisputablytrue，forthethingisaunit。Inthecaseofsecondarysubstances，whenwespeak，forinstance，of'man'or'animal'，ourformofspeechgivestheimpressionthatweareherealsoindicatingthatwhichisindividual，buttheimpressionisnotstrictlytrue；forasecondarysubstanceisnotanindividual，butaclasswithacertainqualification；foritisnotoneandsingleasaprimarysubstanceis；
　　thewords'man'，'animal'，arepredicableofmorethanonesubject。
　　Yetspeciesandgenusdonotmerelyindicatequality，liketheterm'white'；'white'indicatesqualityandnothingfurther，butspeciesandgenusdeterminethequalitywithreferencetoasubstance：
　　theysignifysubstancequalitativelydifferentiated。Thedeterminatequalificationcoversalargerfieldinthecaseofthegenusthatinthatofthespecies：hewhousestheword'animal'ishereinusingawordofwiderextensionthanhewhousestheword'man'。
　　Anothermarkofsubstanceisthatithasnocontrary。Whatcouldbethecontraryofanyprimarysubstance，suchastheindividualmanoranimal？Ithasnone。Norcanthespeciesorthegenushaveacontrary。Yetthischaracteristicisnotpeculiartosubstance，butistrueofmanyotherthings，suchasquantity。Thereisnothingthatformsthecontraryof'twocubitslong'orof'threecubitslong'，orof'ten'，orofanysuchterm。Amanmaycontendthat'much'isthecontraryof'little'，or'great'of'small'，butofdefinitequantitativetermsnocontraryexists。
　　Substance，again，doesnotappeartoadmitofvariationofdegree。I
　　donotmeanbythisthatonesubstancecannotbemoreorlesstrulysubstancethananother，forithasalreadybeenstated'thatthisisthecase；butthatnosinglesubstanceadmitsofvaryingdegreeswithinitself。Forinstance，oneparticularsubstance，'man'，cannotbemoreorlessmaneitherthanhimselfatsomeothertimeorthansomeotherman。Onemancannotbemoremanthananother，asthatwhichiswhitemaybemoreorlesswhitethansomeotherwhiteobject，orasthatwhichisbeautifulmaybemoreorlessbeautifulthansomeotherbeautifulobject。Thesamequality，moreover，issaidtosubsistinathinginvaryingdegreesatdifferenttimes。Abody，beingwhite，issaidtobewhiteratonetimethanitwasbefore，or，beingwarm，issaidtobewarmerorlesswarmthanatsomeothertime。Butsubstanceisnotsaidtobemoreorlessthatwhichitis：amanisnotmoretrulyamanatonetimethanhewasbefore，norisanything，ifitissubstance，moreorlesswhatitis。Substance，then，doesnotadmitofvariationofdegree。
　　Themostdistinctivemarkofsubstanceappearstobethat，whileremainingnumericallyoneandthesame，itiscapableofadmittingcontraryqualities。Fromamongthingsotherthansubstance，weshouldfindourselvesunabletobringforwardanywhichpossessedthismark。Thus，oneandthesamecolourcannotbewhiteandblack。Norcanthesameoneactionbegoodandbad：thislawholdsgoodwitheverythingthatisnotsubstance。Butoneandtheselfsamesubstance，whileretainingitsidentity，isyetcapableofadmittingcontraryqualities。Thesameindividualpersonisatonetimewhite，atanotherblack，atonetimewarm，atanothercold，atonetimegood，atanotherbad。Thiscapacityisfoundnowhereelse，thoughitmightbemaintainedthatastatementoropinionwasanexceptiontotherule。Thesamestatement，itisagreed，canbebothtrueandfalse。
　　Forifthestatement'heissitting'istrue，yet，whenthepersoninquestionhasrisen，thesamestatementwillbefalse。Thesameappliestoopinions。Forifanyonethinkstrulythatapersonissitting，yet，whenthatpersonhasrisen，thissameopinion，ifstillheld，willbefalse。Yetalthoughthisexceptionmaybeallowed，thereis，nevertheless，adifferenceinthemannerinwhichthethingtakesplace。Itisbythemselveschangingthatsubstancesadmitcontraryqualities。Itisthusthatthatwhichwashotbecomescold，forithasenteredintoadifferentstate。Similarlythatwhichwaswhitebecomesblack，andthatwhichwasbadgood，byaprocessofchange；andinthesamewayinallothercasesitisbychangingthatsubstancesarecapableofadmittingcontraryqualities。Butstatementsandopinionsthemselvesremainunalteredinallrespects：itisbythealterationinthefactsofthecasethatthecontraryqualitycomestobetheirs。Thestatement'heissitting'
　　remainsunaltered，butitisatonetimetrue，atanotherfalse，accordingtocircumstances。Whathasbeensaidofstatementsappliesalsotoopinions。Thus，inrespectofthemannerinwhichthethingtakesplace，itisthepeculiarmarkofsubstancethatitshouldbecapableofadmittingcontraryqualities；foritisbyitselfchangingthatitdoesso。
　　If，then，amanshouldmakethisexceptionandcontendthatstatementsandopinionsarecapableofadmittingcontraryqualities，hiscontentionisunsound。Forstatementsandopinionsaresaidtohavethiscapacity，notbecausetheythemselvesundergomodification，butbecausethismodificationoccursinthecaseofsomethingelse。Thetruthorfalsityofastatementdependsonfacts，andnotonanypoweronthepartofthestatementitselfofadmittingcontraryqualities。Inshort，thereisnothingwhichcanalterthenatureofstatementsandopinions。As，then，nochangetakesplaceinthemselves，thesecannotbesaidtobecapableofadmittingcontraryqualities。
　　Butitisbyreasonofthemodificationwhichtakesplacewithinthesubstanceitselfthatasubstanceissaidtobecapableofadmittingcontraryqualities；forasubstanceadmitswithinitselfeitherdiseaseorhealth，whitenessorblackness。Itisinthissensethatitissaidtobecapableofadmittingcontraryqualities。
　　Tosumup，itisadistinctivemarkofsubstance，that，whileremainingnumericallyoneandthesame，itiscapableofadmittingcontraryqualities，themodificationtakingplacethroughachangeinthesubstanceitself。
　　Lettheseremarkssufficeonthesubjectofsubstance。
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　　Quantityiseitherdiscreteorcontinuous。Moreover，somequantitiesaresuchthateachpartofthewholehasarelativepositiontotheotherparts：othershavewithinthemnosuchrelationofparttopart。
　　Instancesofdiscretequantitiesarenumberandspeech；ofcontinuous，lines，surfaces，solids，and，besidesthese，timeandplace。
　　Inthecaseofthepartsofanumber，thereisnocommonboundaryatwhichtheyjoin。Forexample：twofivesmaketen，butthetwofiveshavenocommonboundary，butareseparate；thepartsthreeandsevenalsodonotjoinatanyboundary。Nor，togeneralize，woulditeverbepossibleinthecaseofnumberthatthereshouldbeacommonboundaryamongtheparts；theyarealwaysseparate。Number，therefore，isadiscretequantity。
　　Thesameistrueofspeech。Thatspeechisaquantityisevident：
　　foritismeasuredinlongandshortsyllables。Imeanherethatspeechwhichisvocal。Moreover，itisadiscretequantityforitspartshavenocommonboundary。Thereisnocommonboundaryatwhichthesyllablesjoin，buteachisseparateanddistinctfromtherest。
　　Aline，ontheotherhand，isacontinuousquantity，foritispossibletofindacommonboundaryatwhichitspartsjoin。Inthecaseoftheline，thiscommonboundaryisthepoint；inthecaseoftheplane，itistheline：forthepartsoftheplanehavealsoacommonboundary。Similarlyyoucanfindacommonboundaryinthecaseofthepartsofasolid，namelyeitheralineoraplane。
　　Spaceandtimealsobelongtothisclassofquantities。Time，past，present，andfuture，formsacontinuouswhole。Space，likewise，isacontinuousquantity；forthepartsofasolidoccupyacertainspace，andthesehaveacommonboundary；itfollowsthatthepartsofspacealso，whichareoccupiedbythepartsofthesolid，havethesamecommonboundaryasthepartsofthesolid。Thus，notonlytime，butspacealso，isacontinuousquantity，foritspartshaveacommonboundary。
　　Quantitiesconsisteitherofpartswhichbeararelativepositioneachtoeach，orofpartswhichdonot。Thepartsofalinebeararelativepositiontoeachother，foreachliessomewhere，anditwouldbepossibletodistinguisheach，andtostatethepositionofeachontheplaneandtoexplaintowhatsortofpartamongtheresteachwascontiguous。Similarlythepartsofaplanehaveposition，foritcouldsimilarlybestatedwhatwasthepositionofeachandwhatsortofpartswerecontiguous。Thesameistruewithregardtothesolidandtospace。Butitwouldbeimpossibletoshowthattheartsofanumberhadarelativepositioneachtoeach，oraparticularposition，ortostatewhatpartswerecontiguous。Norcouldthisbedoneinthecaseoftime，fornoneofthepartsoftimehasanabidingexistence，andthatwhichdoesnotabidecanhardlyhaveposition。
　　Itwouldbebettertosaythatsuchpartshadarelativeorder，invirtueofonebeingpriortoanother。Similarlywithnumber：incounting，'one'ispriorto'two'，and'two'to'three'，andthusthepartsofnumbermaybesaidtopossessarelativeorder，thoughitwouldbeimpossibletodiscoveranydistinctpositionforeach。Thisholdsgoodalsointhecaseofspeech。Noneofitspartshasanabidingexistence：whenonceasyllableispronounced，itisnotpossibletoretainit，sothat，naturally，asthepartsdonotabide，theycannothaveposition。Thus，somequantitiesconsistofpartswhichhaveposition，andsomeofthosewhichhavenot。
　　Strictlyspeaking，onlythethingswhichIhavementionedbelongtothecategoryofquantity：everythingelsethatiscalledquantitativeisaquantityinasecondarysense。Itisbecausewehaveinmindsomeoneofthesequantities，properlysocalled，thatweapplyquantitativetermstootherthings。Wespeakofwhatiswhiteaslarge，becausethesurfaceoverwhichthewhiteextendsislarge；wespeakofanactionoraprocessaslengthy，becausethetimecoveredislong；thesethingscannotintheirownrightclaimthequantitativeepithet。Forinstance，shouldanyoneexplainhowlonganactionwas，hisstatementwouldbemadeintermsofthetimetaken，totheeffectthatitlastedayear，orsomethingofthatsort。Inthesameway，hewouldexplainthesizeofawhiteobjectintermsofsurface，forhewouldstatetheareawhichitcovered。Thusthethingsalreadymentioned，andthesealone，areintheirintrinsicnaturequantities；nothingelsecanclaimthenameinitsownright，but，ifatall，onlyinasecondarysense。
　　Quantitieshavenocontraries。Inthecaseofdefinitequantitiesthisisobvious；thus，thereisnothingthatisthecontraryof'twocubitslong'orof'threecubitslong'，orofasurface，orofanysuchquantities。Amanmight，indeed，arguethat'much'wasthecontraryof'little'，and'great'of'small'。Butthesearenotquantitative，butrelative；thingsarenotgreatorsmallabsolutely，theyaresocalledratherastheresultofanactofcomparison。Forinstance，amountainiscalledsmall，agrainlarge，invirtueofthefactthatthelatterisgreaterthanothersofitskind，theformerless。Thusthereisareferenceheretoanexternalstandard，foriftheterms'great'and'small'wereusedabsolutely，amountainwouldneverbecalledsmalloragrainlarge。Again，wesaythattherearemanypeopleinavillage，andfewinAthens，althoughthoseinthecityaremanytimesasnumerousasthoseinthevillage：orwesaythatahousehasmanyinit，andatheatrefew，thoughthoseinthetheatrefaroutnumberthoseinthehouse。Theterms'twocubitslong，"threecubitslong，'andsoonindicatequantity，theterms'great'and'small'indicaterelation，fortheyhavereferencetoanexternalstandard。Itis，therefore，plainthatthesearetobeclassedasrelative。
　　Again，whetherwedefinethemasquantitativeornot，theyhavenocontraries：forhowcantherebeacontraryofanattributewhichisnottobeapprehendedinorbyitself，butonlybyreferencetosomethingexternal？Again，if'great'and'small'arecontraries，itwillcomeaboutthatthesamesubjectcanadmitcontraryqualitiesatoneandthesametime，andthatthingswillthemselvesbecontrarytothemselves。Forithappensattimesthatthesamethingisbothsmallandgreat。Forthesamethingmaybesmallincomparisonwithonething，andgreatincomparisonwithanother，sothatthesamethingcomestobebothsmallandgreatatoneandthesametime，andisofsuchanatureastoadmitcontraryqualitiesatoneandthesamemoment。Yetitwasagreed，whensubstancewasbeingdiscussed，thatnothingadmitscontraryqualitiesatoneandthesamemoment。Forthoughsubstanceiscapableofadmittingcontraryqualities，yetnooneisatthesametimebothsickandhealthy，nothingisatthesametimebothwhiteandblack。Noristhereanythingwhichisqualifiedincontrarywaysatoneandthesametime。
　　Moreover，ifthesewerecontraries，theywouldthemselvesbecontrarytothemselves。Forif'great'isthecontraryof'small'，andthesamethingisbothgreatandsmallatthesametime，then'small'or'great'isthecontraryofitself。Butthisisimpossible。Theterm'great'，therefore，isnotthecontraryoftheterm'small'，nor'much'of'little'。Andeventhoughamanshouldcallthesetermsnotrelativebutquantitative，theywouldnothavecontraries。
　　Itisinthecaseofspacethatquantitymostplausiblyappearstoadmitofacontrary。Formendefinetheterm'above'asthecontraryof'below'，whenitistheregionatthecentretheymeanby'below'；andthisisso，becausenothingisfartherfromtheextremitiesoftheuniversethantheregionatthecentre。Indeed，itseemsthatindefiningcontrariesofeverykindmenhaverecoursetoaspatialmetaphor，fortheysaythatthosethingsarecontrarieswhich，withinthesameclass，areseparatedbythegreatestpossibledistance。
　　Quantitydoesnot，itappears，admitofvariationofdegree。Onethingcannotbetwocubitslonginagreaterdegreethananother。
　　Similarlywithregardtonumber：whatis'three'isnotmoretrulythreethanwhatis'five'isfive；norisonesetofthreemoretrulythreethananotherset。Again，oneperiodoftimeisnotsaidtobemoretrulytimethananother。Noristhereanyotherkindofquantity，ofallthathavebeenmentioned，withregardtowhichvariationofdegreecanbepredicated。Thecategoryofquantity，therefore，doesnotadmitofvariationofdegree。
　　Themostdistinctivemarkofquantityisthatequalityandinequalityarepredicatedofit。Eachoftheaforesaidquantitiesissaidtobeequalorunequal。Forinstance，onesolidissaidtobeequalorunequaltoanother；number，too，andtimecanhavethesetermsappliedtothem，indeedcanallthosekindsofquantitythathavebeenmentioned。
　　Thatwhichisnotaquantitycanbynomeans，itwouldseem，betermedequalorunequaltoanythingelse。Oneparticulardispositionoroneparticularquality，suchaswhiteness，isbynomeanscomparedwithanotherintermsofequalityandinequalitybutratherintermsofsimilarity。Thusitisthedistinctivemarkofquantitythatitcanbecalledequalandunequal。
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　　Thosethingsarecalledrelative，which，beingeithersaidtobeofsomethingelseorrelatedtosomethingelse，areexplainedbyreferencetothatotherthing。Forinstance，theword'superior'isexplainedbyreferencetosomethingelse，foritissuperiorityoversomethingelsethatismeant。Similarly，theexpression'double'hasthisexternalreference，foritisthedoubleofsomethingelsethatismeant。Soitiswitheverythingelseofthiskind。Thereare，moreover，otherrelatives，e。g。habit，disposition，perception，knowledge，andattitude。Thesignificanceofalltheseisexplainedbyareferencetosomethingelseandinnootherway。Thus，ahabitisahabitofsomething，knowledgeisknowledgeofsomething，attitudeistheattitudeofsomething。Soitiswithallotherrelativesthathavebeenmentioned。Thoseterms，then，arecalledrelative，thenatureofwhichisexplainedbyreferencetosomethingelse，thepreposition'of'orsomeotherprepositionbeingusedtoindicatetherelation。Thus，onemountainiscalledgreatincomparisonwithsonwithanother；forthemountainclaimsthisattributebycomparisonwithsomething。Again，thatwhichiscalledsimilarmustbesimilartosomethingelse，andallothersuchattributeshavethisexternalreference。Itistobenotedthatlyingandstandingandsittingareparticularattitudes，butattitudeisitselfarelativeterm。Tolie，tostand，tobeseated，arenotthemselvesattitudes，buttaketheirnamefromtheaforesaidattitudes。
　　Itispossibleforrelativestohavecontraries。Thusvirtuehasacontrary，vice，thesebothbeingrelatives；knowledge，too，hasacontrary，ignorance。Butthisisnotthemarkofallrelatives；
　　'double'and'triple'havenocontrary，norindeedhasanysuchterm。
　　Italsoappearsthatrelativescanadmitofvariationofdegree。For'like'and'unlike'，'equal'and'unequal'，havethemodifications'more'and'less'appliedtothem，andeachoftheseisrelativeincharacter：fortheterms'like'and'unequal'bear'unequal'bearareferencetosomethingexternal。Yet，again，itisnoteveryrelativetermthatadmitsofvariationofdegree。Notermsuchas'double'admitsofthismodification。Allrelativeshavecorrelatives：
　　bytheterm'slave'wemeantheslaveofamaster，bytheterm'master'，themasterofaslave；by'double'，thedoubleofitshall；by'half'，thehalfofitsdouble；by'greater'，greaterthanthatwhichisless；by'less，'lessthanthatwhichisgreater。
　　Soitiswitheveryotherrelativeterm；butthecaseweusetoexpressthecorrelationdiffersinsomeinstances。Thus，byknowledgewemeanknowledgetheknowable；bytheknowable，thatwhichistobeapprehendedbyknowledge；byperception，perceptionoftheperceptible；bytheperceptible，thatwhichisapprehendedbyperception。
　　Sometimes，however，reciprocityofcorrelationdoesnotappeartoexist。Thiscomesaboutwhenablunderismade，andthattowhichtherelativeisrelatedisnotaccuratelystated。Ifamanstatesthatawingisnecessarilyrelativetoabird，theconnexionbetweenthesetwowillnotbereciprocal，foritwillnotbepossibletosaythatabirdisabirdbyreasonofitswings。Thereasonisthattheoriginalstatementwasinaccurate，forthewingisnotsaidtoberelativetothebirdquabird，sincemanycreaturesbesidesbirdshavewings，butquawingedcreature。If，then，thestatementismadeaccurate，theconnexionwillbereciprocal，forwecanspeakofawing，havingreferencenecessarilytoawingedcreature，andofawingedcreatureasbeingsuchbecauseofitswings。
　　Occasionally，perhaps，itisnecessarytocoinwords，ifnowordexistsbywhichacorrelationcanadequatelybeexplained。Ifwedefinearudderasnecessarilyhavingreferencetoaboat，ourdefinitionwillnotbeappropriate，fortherudderdoesnothavethisreferencetoaboatquaboat，asthereareboatswhichhavenorudders。Thuswecannotusethetermsreciprocally，fortheword'boat'cannotbesaidtofinditsexplanationintheword'rudder'。Asthereisnoexistingword，ourdefinitionwouldperhapsbemoreaccurateifwecoinedsomewordlike'ruddered'asthecorrelativeof'rudder'。Ifweexpressourselvesthusaccurately，atanyratethetermsarereciprocallyconnected，forthe'ruddered'thingis'ruddered'invirtueofitsrudder。Soitisinallothercases。A
　　headwillbemoreaccuratelydefinedasthecorrelativeofthatwhichis'headed'，thanasthatofananimal，fortheanimaldoesnothaveaheadquaanimal，sincemanyanimalshavenohead。
　　Thuswemayperhapsmosteasilycomprehendthattowhichathingisrelated，whenanamedoesnotexist，if，fromthatwhichhasaname，wederiveanewname，andapplyittothatwithwhichthefirstisreciprocallyconnected，asintheaforesaidinstances，whenwederivedtheword'winged'from'wing'andfrom'rudder'。
　　Allrelatives，then，ifproperlydefined，haveacorrelative。I
　　addthisconditionbecause，ifthattowhichtheyarerelatedisstatedashaphazardandnotaccurately，thetwoarenotfoundtobeinterdependent。LetmestatewhatImeanmoreclearly。Eveninthecaseofacknowledgedcorrelatives，andwherenamesexistforeach，therewillbenointerdependenceifoneofthetwoisdenoted，notbythatnamewhichexpressesthecorrelativenotion，butbyoneofirrelevantsignificance。Theterm'slave，'ifdefinedasrelated，nottoamaster，buttoaman，orabiped，oranythingofthatsort，isnotreciprocallyconnectedwiththatinrelationtowhichitisdefined，forthestatementisnotexact。Further，ifonethingissaidtobecorrelativewithanother，andtheterminologyusediscorrect，then，thoughallirrelevantattributesshouldberemoved，andonlythatoneattributeleftinvirtueofwhichitwascorrectlystatedtobecorrelativewiththatother，thestatedcorrelationwillstillexist。Ifthecorrelativeof'theslave'issaidtobe'themaster'，then，thoughallirrelevantattributesofthesaid'master'，suchas'biped'，'receptiveofknowledge'，'human'，shouldberemoved，andtheattribute'master'aloneleft，thestatedcorrelationexistingbetweenhimandtheslavewillremainthesame，foritisofamasterthataslaveissaidtobetheslave。Ontheotherhand，if，oftwocorrelatives，oneisnotcorrectlytermed，then，whenallotherattributesareremovedandthataloneisleftinvirtueofwhichitwasstatedtobecorrelative，thestatedcorrelationwillbefoundtohavedisappeared。
　　Forsupposethecorrelativeof'theslave'shouldbesaidtobe'theman'，orthecorrelativeof'thewing"thebird'；iftheattribute'master'bewithdrawnfrom'theman'，thecorrelationbetween'theman'and'theslave'willceasetoexist，forifthemanisnotamaster，theslaveisnotaslave。Similarly，iftheattribute'winged'
　　bewithdrawnfrom'thebird'，'thewing'willnolongerberelative；
　　foriftheso-calledcorrelativeisnotwinged，itfollowsthat'thewing'hasnocorrelative。
　　Thusitisessentialthatthecorrelatedtermsshouldbeexactlydesignated；ifthereisanameexisting，thestatementwillbeeasy；
　　ifnot，itisdoubtlessourdutytoconstructnames。Whentheterminologyisthuscorrect，itisevidentthatallcorrelativesareinterdependent。
　　Correlativesarethoughttocomeintoexistencesimultaneously。Thisisforthemostparttrue，asinthecaseofthedoubleandthehalf。Theexistenceofthehalfnecessitatestheexistenceofthatofwhichitisahalf。Similarlytheexistenceofamasternecessitatestheexistenceofaslave，andthatofaslaveimpliesthatofamaster；thesearemerelyinstancesofageneralrule。
　　Moreover，theycanceloneanother；forifthereisnodoubleitfollowsthatthereisnohalf，andviceversa；thisrulealsoappliestoallsuchcorrelatives。Yetitdoesnotappeartobetrueinallcasesthatcorrelativescomeintoexistencesimultaneously。Theobjectofknowledgewouldappeartoexistbeforeknowledgeitself，foritisusuallythecasethatweacquireknowledgeofobjectsalreadyexisting；itwouldbedifficult，ifnotimpossible，tofindabranchofknowledgethebeginningoftheexistenceofwhichwascontemporaneouswiththatofitsobject。
　　Again，whiletheobjectofknowledge，ifitceasestoexist，cancelsatthesametimetheknowledgewhichwasitscorrelative，theconverseofthisisnottrue。Itistruethatiftheobjectofknowledgedoesnotexisttherecanbenoknowledge：fortherewillnolongerbeanythingtoknow。Yetitisequallytruethat，ifknowledgeofacertainobjectdoesnotexist，theobjectmayneverthelessquitewellexist。Thus，inthecaseofthesquaringofthecircle，ifindeedthatprocessisanobjectofknowledge，thoughititselfexistsasanobjectofknowledge，yettheknowledgeofithasnotyetcomeintoexistence。Again，ifallanimalsceasedtoexist，therewouldbenoknowledge，buttheremightyetbemanyobjectsofknowledge。
　　Thisislikewisethecasewithregardtoperception：fortheobjectofperceptionis，itappears，priortotheactofperception。
　　Iftheperceptibleisannihilated，perceptionalsowillceasetoexist；buttheannihilationofperceptiondoesnotcanceltheexistenceoftheperceptible。Forperceptionimpliesabodyperceivedandabodyinwhichperceptiontakesplace。Nowifthatwhichisperceptibleisannihilated，itfollowsthatthebodyisannihilated，forthebodyisaperceptiblething；andifthebodydoesnotexist，itfollowsthatperceptionalsoceasestoexist。Thustheannihilationoftheperceptibleinvolvesthatofperception。
　　Buttheannihilationofperceptiondoesnotinvolvethatoftheperceptible。Foriftheanimalisannihilated，itfollowsthatperceptionalsoisannihilated，butperceptiblessuchasbody，heat，sweetness，bitterness，andsoon，willremain。
　　Again，perceptionisgeneratedatthesametimeastheperceivingsubject，foritcomesintoexistenceatthesametimeastheanimal。
　　Buttheperceptiblesurelyexistsbeforeperception；forfireandwaterandsuchelements，outofwhichtheanimalisitselfcomposed，existbeforetheanimalisananimalatall，andbeforeperception。
　　Thusitwouldseemthattheperceptibleexistsbeforeperception。