Itisclearalsothatthesoulistheprimarysubstanceandthe
　　bodyismatter，andmanoranimalisthecompoundofbothtaken
　　universally；and’Socrates’or’Coriscus’，ifeventhesoulof
　　SocratesmaybecalledSocrates，hastwomeaningsforsomemeanby
　　suchatermthesoul，andothersmeantheconcretething，butif
　　’Socrates’or’Coriscus’meanssimplythisparticularsoulandthis
　　particularbody，theindividualisanalogoustotheuniversalinits
　　composition。
　　Whetherthereis，apartfromthematterofsuchsubstances，
　　anotherkindofmatter，andoneshouldlookforsomesubstanceother
　　thanthese，e。g。numbersorsomethingofthesort，mustbe
　　consideredlater。Foritisforthesakeofthisthatwearetryingto
　　determinethenatureofperceptiblesubstancesaswell，sinceina
　　sensetheinquiryaboutperceptiblesubstancesistheworkofphysics，
　　i。e。ofsecondphilosophy；forthephysicistmustcometoknownot
　　onlyaboutthematter，butalsoaboutthesubstanceexpressedinthe
　　formula，andevenmorethanabouttheother。Andinthecaseof
　　definitions，howtheelementsintheformulaarepartsofthe
　　definition，andwhythedefinitionisoneformulaforclearlythe
　　thingisone，butinvirtueofwhatisthethingone，althoughit
　　hasparts？，-thismustbeconsideredlater。
　　Whattheessenceisandinwhatsenseitisindependent，has
　　beenstateduniversallyinawaywhichistrueofeverycase，andalso
　　whytheformulaoftheessenceofsomethingscontainsthepartsof
　　thethingdefined，whilethatofothersdoesnot。Andwehavestated
　　thatintheformulaofthesubstancethematerialpartswillnotbe
　　presentfortheyarenotevenpartsofthesubstanceinthatsense，
　　butoftheconcretesubstance；butofthisthereisinasensea
　　formula，andinasensethereisnot；forthereisnoformulaofit
　　withitsmatter，forthisisindefinite，butthereisaformulaof
　　itwithreferencetoitsprimarysubstance-e。g。inthecaseofmanthe
　　formulaofthesoul-，forthesubstanceistheindwellingform，from
　　whichandthemattertheso-calledconcretesubstanceisderived；e。g。
　　concavityisaformofthissort，forfromthisandthenosearise
　　’snubnose’and’snubness’；butintheconcretesubstance，e。g。a
　　snubnoseorCallias，thematteralsowillbepresent。Andwehave
　　statedthattheessenceandthethingitselfareinsomecasesthe
　　same；ie。inthecaseofprimarysubstances，e。g。curvatureandthe
　　essenceofcurvatureifthisisprimary。Bya’primary’substanceI
　　meanonewhichdoesnotimplythepresenceofsomethinginsomething
　　else，i。e。insomethingthatunderliesitwhichactsasmatter。But
　　thingswhichareofthenatureofmatter，orofwholesthatinclude
　　matter，arenotthesameastheiressences，norareaccidentalunities
　　likethatof’Socrates’and’musical’；forthesearethesameonly
　　byaccident。
　　Nowletustreatfirstofdefinition，insofaraswehavenot
　　treatedofitintheAnalytics；fortheproblemstatedinthemis
　　usefulforourinquiriesconcerningsubstance。Imeanthis
　　problem:-whereincanconsisttheunityofthat，theformulaofwhich
　　wecalladefinition，asforinstance，inthecaseofman，’two-footed
　　animal’；forletthisbetheformulaofman。Why，then，isthisone，
　　andnotmany，viz。’animal’and’two-footed’？Forinthecaseof’man’
　　and’pale’thereisapluralitywhenonetermdoesnotbelongtothe
　　other，butaunitywhenitdoesbelongandthesubject，man，hasa
　　certainattribute；forthenaunityisproducedandwehave’the
　　paleman’。Inthepresentcase，ontheotherhand，onedoesnot
　　shareintheother；thegenusisnotthoughttoshareinits
　　differentiaeforthenthesamethingwouldshareincontraries；for
　　thedifferentiaebywhichthegenusisdividedarecontrary。Andeven
　　ifthegenusdoesshareinthem，thesameargumentapplies，since
　　thedifferentiaepresentinmanaremany，e。g。endowedwithfeet，
　　two-footed，featherless。Whyaretheseoneandnotmany？Notbecause
　　theyarepresentinonething；foronthisprincipleaunitycanbe
　　madeoutofalltheattributesofathing。Butsurelyallthe
　　attributesinthedefinitionmustbeone；forthedefinitionisa
　　singleformulaandaformulaofsubstance，sothatitmustbea
　　formulaofsomeonething；forsubstancemeansa’one’anda’this’，
　　aswemaintain。
　　Wemustfirstinquireaboutdefinitionsreachedbythemethodof
　　divisions。Thereisnothinginthedefinitionexceptthefirst-named
　　andthedifferentiae。Theothergeneraarethefirstgenusandalong
　　withthisthedifferentiaethataretakenwithit，e。g。thefirst
　　maybe’animal’，thenext’animalwhichistwo-footed’，andagain
　　’animalwhichistwo-footedandfeatherless’，andsimilarlyifthe
　　definitionincludesmoreterms。Andingeneralitmakesno
　　differencewhetheritincludesmanyorfewterms，-nor，therefore，
　　whetheritincludesfeworsimplytwo；andofthetwotheoneis
　　differentiaandtheothergenus；e。g。in’two-footedanimal’
　　’animal’isgenus，andtheotherisdifferentia。
　　Ifthenthegenusabsolutelydoesnotexistapartfromthe
　　species-of-a-genus，orifitexistsbutexistsasmatterforthe
　　voiceisgenusandmatter，butitsdifferentiaemakethespecies，i。e。
　　theletters，outofit，clearlythedefinitionistheformulawhich
　　comprisesthedifferentiae。
　　Butitisalsonecessarythatthedivisionbebythedifferentia
　　ofthediferentia；e。g。’endowedwithfeet’isadifferentiaof
　　’animal’；againthedifferentiaof’animalendowedwithfeet’must
　　beofitquaendowedwithfeet。Thereforewemustnotsay，ifweare
　　tospeakrightly，thatofthatwhichisendowedwithfeetoneparthas
　　feathersandoneisfeatherlessifwedothiswedoitthrough
　　incapacity；wemustdivideitonlyintocloven-footedandnotcloven；
　　forthesearedifferentiaeinthefoot；cloven-footednessisaformof
　　footedness。Andtheprocesswantsalwaystogoonsotillitreaches
　　thespeciesthatcontainnodifferences。Andthentherewillbeas
　　manykindsoffootastherearedifferentiae，andthekindsofanimals
　　endowedwithfeetwillbeequalinnumbertothedifferentiae。Ifthen
　　thisisso，clearlythelastdifferentiawillbethesubstanceof
　　thethinganditsdefinition，sinceitisnotrighttostatethe
　　samethingsmorethanonceinourdefinitions；foritis
　　superfluous。Andthisdoeshappen；forwhenwesay’animalendowed
　　withfeetandtwo-footed’wehavesaidnothingotherthan’animal
　　havingfeet，havingtwofeet’；andifwedividethisbytheproper
　　division，weshallbesayingthesamethingmorethanonce-asmany
　　timesastherearedifferentiae。
　　Ifthenadifferentiaofadifferentiabetakenateachstep，
　　onedifferentia-thelast-willbetheformandthesubstance；butifwe
　　divideaccordingtoaccidentalqualities，e。g。ifweweretodivide
　　thatwhichisendowedwithfeetintothewhiteandtheblack，there
　　willbeasmanydifferentiaeastherearecuts。Thereforeitis
　　plainthatthedefinitionistheformulawhichcontainsthe
　　differentiae，or，accordingtotherightmethod，thelastofthese。
　　Thiswouldbeevident，ifweweretochangetheorderofsuch
　　definitions，e。g。ofthatofman，saying’animalwhichistwo-footed
　　andendowedwithfeet’；for’endowedwithfeet’issuperfluouswhen
　　’two-footed’hasbeensaid。Butthereisnoorderinthesubstance；
　　forhowarewetothinktheoneelementposteriorandtheotherprior？
　　Regardingthedefinitions，then，whicharereachedbythemethodof
　　divisions，letthissufficeasourfirstattemptatstatingtheir
　　Letusreturntothesubjectofourinquiry，whichissubstance。
　　Asthesubstratumandtheessenceandthecompoundofthesearecalled
　　substance，soalsoistheuniversal。Abouttwoofthesewehave
　　spoken；bothabouttheessenceandaboutthesubstratum，ofwhichwe
　　havesaidthatitunderliesintwosenses，eitherbeinga’this’-which
　　isthewayinwhichananimalunderliesitsattributes-orasthe
　　matterunderliesthecompletereality。Theuniversalalsoisthought
　　bysometobeinthefullestsenseacause，andaprinciple；therefore
　　letusattackthediscussionofthispointalso。Foritseems
　　impossiblethatanyuniversaltermshouldbethenameofa
　　substance。Forfirstlythesubstanceofeachthingisthatwhichis
　　peculiartoit，whichdoesnotbelongtoanythingelse；butthe
　　universaliscommon，sincethatiscalleduniversalwhichissuchas
　　tobelongtomorethanonething。Ofwhichindividualthenwillthis
　　bethesubstance？Eitherofallorofnone；butitcannotbethe
　　substanceofall。Andifitistobethesubstanceofone，thisone
　　willbetheothersalso；forthingswhosesubstanceisoneandwhose
　　essenceisonearethemselvesalsoone。
　　Further，substancemeansthatwhichisnotpredicableofa
　　subject，buttheuniversalispredicableofsomesubjectalways。
　　Butperhapstheuniversal，whileitcannotbesubstanceintheway
　　inwhichtheessenceisso，canbepresentinthis；e。g。’animal’
　　canbepresentin’man’and’horse’。Thenclearlyitisaformulaof
　　theessence。Anditmakesnodifferenceevenifitisnotaformulaof
　　everythingthatisinthesubstance；fornonethelesstheuniversal
　　willbethesubstanceofsomething，as’man’isthesubstanceofthe
　　individualmaninwhomitispresent，sothatthesameresultwill
　　followoncemore；fortheuniversal，e。g。’animal’，willbethe
　　substanceofthatinwhichitispresentassomethingpeculiarto
　　it。Andfurtheritisimpossibleandabsurdthatthe’this’，i。e。
　　thesubstance，ifitconsistsofparts，shouldnotconsistof
　　substancesnorofwhatisa’this’，butofquality；forthatwhich
　　isnotsubstance，i。e。thequality，willthenbepriortosubstance
　　andtothe’this’。Whichisimpossible；forneitherinformulanor
　　intimenorincomingtobecanthemodificationsbepriortothe
　　substance；forthentheywillalsobeseparablefromit。Further，
　　Socrateswillcontainasubstancepresentinasubstance，sothatthis
　　willbethesubstanceoftwothings。Andingeneralitfollows，ifman
　　andsuchthingsaresubstance，thatnoneoftheelementsintheir
　　formulaeisthesubstanceofanything，nordoesitexistapartfrom
　　thespeciesorinanythingelse；Imean，forinstance，thatno
　　’animal’existsapartfromtheparticularkindsofanimal，nordoes
　　anyotheroftheelementspresentinformulaeexistapart。
　　If，then，weviewthematterfromthesestandpoints，itisplain
　　thatnouniversalattributeisasubstance，andthisisplainalso
　　fromthefactthatnocommonpredicateindicatesa’this’，but
　　rathera’such’。Ifnot，manydifficultiesfollowandespeciallythe
　　’thirdman’。
　　Theconclusionisevidentalsofromthefollowingconsideration。A
　　substancecannotconsistofsubstancespresentinitincomplete
　　reality；forthingsthatarethusincompleterealitytwoareneverin
　　completerealityone，thoughiftheyarepotentiallytwo，theycan
　　beonee。g。thedoublelineconsistsoftwohalves-potentially；for
　　thecompleterealizationofthehalvesdividesthemfromoneanother；
　　thereforeifthesubstanceisone，itwillnotconsistofsubstances
　　presentinitandpresentinthisway，whichDemocritusdescribes
　　rightly；hesaysonethingcannotbemadeoutoftwonortwooutof
　　one；forheidentifiessubstanceswithhisindivisiblemagnitudes。
　　Itisclearthereforethatthesamewillholdgoodofnumber，if
　　numberisasynthesisofunits，asissaidbysome；fortwois
　　eithernotone，orthereisnounitpresentinitincompletereality。
　　Butourresultinvolvesadifficulty。Ifnosubstancecanconsistof
　　universalsbecauseauniversalindicatesa’such’，nota’this’，and
　　ifnosubstancecanbecomposedofsubstancesexistingincomplete
　　reality，everysubstancewouldbeincomposite，sothattherewouldnot
　　evenbeaformulaofanysubstance。Butitisthoughtbyallandwas
　　statedlongagothatitiseitheronly，orprimarily，substancethat
　　candefined；yetnowitseemsthatnotevensubstancecan。There
　　cannot，then，beadefinitionofanything；orinasensetherecanbe，
　　andinasensetherecannot。Andwhatwearesayingwillbeplainer
　　fromwhatfollows。