1
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\'。
2
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。
3
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。
4
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。
7
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。