composedofthemarealsouniversal，ornon-substancewillbepriorto
　　substance；fortheuniversalisnotasubstance，buttheelementor
　　principleisuniversal，andtheelementorprincipleispriortothe
　　thingsofwhichitistheprincipleorelement。
　　Allthesedifficultiesfollownaturally，whentheymakethe
　　Ideasoutofelementsandatthesametimeclaimthatapartfromthe
　　substanceswhichhavethesameformthereareIdeas，asingleseparate
　　entity。Butif，e。g。inthecaseoftheelementsofspeech，thea’s
　　andtheb’smayquitewellbemanyandthereneedbenoa-itselfand
　　b-itselfbesidesthemany，theremaybe，sofarasthisgoes，an
　　infinitenumberofsimilarsyllables。Thestatementthatan
　　knowledgeisuniversal，sothattheprinciplesofthingsmustalso
　　beuniversalandnotseparatesubstances，presentsindeed，ofall
　　thepointswehavementioned，thegreatestdifficulty，butyetthe
　　statementisinasensetrue，althoughinasenseitisnot。For
　　knowledge，liketheverb’toknow’，meanstwothings，ofwhichone
　　ispotentialandoneactual。Thepotency，being，asmatter，
　　universalandindefinite，dealswiththeuniversalandindefinite；but
　　theactuality，beingdefinite，dealswithadefiniteobject，beinga
　　’this’，itdealswitha’this’。Butperaccidenssightsees
　　universalcolour，becausethisindividualcolourwhichitseesis
　　colour；andthisindividualawhichthegrammarianinvestigatesis
　　ana。Foriftheprinciplesmustbeuniversal，whatisderivedfrom
　　themmustalsobeuniversal，asindemonstrations；andifthisis
　　so，therewillbenothingcapableofseparateexistence-i。e。no
　　substance。Butevidentlyinasenseknowledgeisuniversal，andina
　　senseitisnot。
　　thiskindofsubstance，whatwehavesaidmustbe
　　takenassufficient。Allphilosophersmakethefirstprinciples
　　contraries:asinnaturalthings，soalsointhecaseof
　　unchangeablesubstances。Butsincetherecannotbeanythingpriorto
　　thefirstprincipleofallthings，theprinciplecannotbethe
　　principleandyetbeanattributeofsomethingelse。Tosuggestthis
　　islikesayingthatthewhiteisafirstprinciple，notquaanything
　　elsebutquawhite，butyetthatitispredicableofasubject，i。e。
　　thatitsbeingwhitepresupposesitsbeingsomethingelse；thisis
　　absurd，forthenthatsubjectwillbeprior。Butallthingswhich
　　aregeneratedfromtheircontrariesinvolveanunderlyingsubject；a
　　subject，then，mustbepresentinthecaseofcontraries，ifanywhere。
　　Allcontraries，then，arealwayspredicableofasubject，andnonecan
　　existapart，butjustasappearancessuggestthatthereisnothing
　　contrarytosubstance，argumentconfirmsthis。Nocontrary，then，is
　　thefirstprincipleofallthingsinthefullsense；thefirst
　　principleissomethingdifferent。
　　Butthesethinkersmakeoneofthecontrariesmatter，some
　　makingtheunequalwhichtheytaketobetheessenceof
　　plurality-matterfortheOne，andothersmakingpluralitymatterfor
　　theOne。Theformergeneratenumbersoutofthedyadofthe
　　unequal，i。e。ofthegreatandsmall，andtheotherthinkerwehave
　　referredtogeneratesthemoutofplurality，whileaccordingtoboth
　　itisgeneratedbytheessenceoftheOne。Foreventhephilosopher
　　whosaystheunequalandtheOnearetheelements，andtheunequal
　　isadyadcomposedofthegreatandsmall，treatstheunequal，or
　　thegreatandthesmall，asbeingone，anddoesnotdrawthe
　　distinctionthattheyareoneindefinition，butnotinnumber。But
　　theydonotdescriberightlyeventheprincipleswhichtheycall
　　elements，forsomenamethegreatandthesmallwiththeOneandtreat
　　thesethreeaselementsofnumbers，twobeingmatter，onetheform；
　　whileothersnamethemanyandfew，becausethegreatandthesmall
　　aremoreappropriateintheirnaturetomagnitudethantonumber；
　　andothersnamerathertheuniversalcharactercommontothese-’that
　　whichexceedsandthatwhichisexceeded’。Noneofthesevarieties
　　ofopinionmakesanydifferencetospeakof，inviewofsomeofthe
　　consequences；theyaffectonlytheabstractobjections，whichthese
　　thinkerstakecaretoavoidbecausethedemonstrationstheythemselves
　　offerareabstract，-withthisexception，thatiftheexceedingandthe
　　exceededaretheprinciples，andnotthegreatandthesmall，
　　consistencyrequiresthatnumbershouldcomefromtheelements
　　beforedoes；fornumberismoreuniversalthanastheexceedingand
　　theexceededaremoreuniversalthanthegreatandthesmall。Butas
　　itis，theysayoneofthesethingsbutdonotsaytheother。Others
　　opposethedifferentandtheothertotheOne，andothersoppose
　　pluralitytotheOne。Butif，astheyclaim，thingsconsistof
　　contraries，andtotheOneeitherthereisnothingcontrary，orif
　　thereistobeanythingitisplurality，andtheunequaliscontrary
　　totheequal，andthedifferenttothesame，andtheothertothe
　　thingitself，thosewhoopposetheOnetopluralityhavemostclaimto
　　plausibility，buteventheirviewisinadequate，fortheOnewould
　　ontheirviewbeafew；forpluralityisopposedtofewness，andthe
　　manytothefew。
　　’Theone’evidentlymeansameasure。Andineverycasethereis
　　someunderlyingthingwithadistinctnatureofitsown，e。g。inthe
　　scaleaquarter-tone，inspatialmagnitudeafingerorafootor
　　somethingofthesort，inrhythmsabeatorasyllable；and
　　similarlyingravityitisadefiniteweight；andinthesamewayin
　　allcases，inqualitiesaquality，inquantitiesaquantityandthe
　　measureisindivisible，intheformercaseinkind，andinthe
　　lattertothesense；whichimpliesthattheoneisnotinitself
　　thesubstanceofanything。Andthisisreasonable；for’theone’means
　　themeasureofsomeplurality，and’number’meansameasuredplurality
　　andapluralityofmeasures。Thusitisnaturalthatoneisnota
　　number；forthemeasureisnotmeasures，butboththemeasureand
　　theonearestarting-points。Themeasuremustalwaysbesome
　　identicalthingpredicableofallthethingsitmeasures，e。g。if
　　thethingsarehorses，themeasureis’horse’，andiftheyaremen，
　　’man’。Iftheyareaman，ahorse，andagod，themeasureisperhaps
　　’livingbeing’，andthenumberofthemwillbeanumberofliving
　　beings。Ifthethingsare’man’and’pale’and’walking’，thesewill
　　scarcelyhaveanumber，becauseallbelongtoasubjectwhichisone
　　andthesameinnumber，yetthenumberofthesewillbeanumberof
　　’kinds’orofsomesuchterm。
　　Thosewhotreattheunequalasonething，andthedyadasan
　　indefinitecompoundofgreatandsmall，saywhatisveryfarfrom
　　beingprobableorpossible。Forathesearemodificationsand
　　accidents，ratherthansubstrata，ofnumbersandmagnitudes-themany
　　andfewofnumber，andthegreatandsmallofmagnitude-likeeven
　　andodd，smoothandrough，straightandcurved。Again，bapart
　　fromthismistake，thegreatandthesmall，andsoon，mustbe
　　relativetosomething；butwhatisrelativeisleastofallthingsa
　　kindofentityorsubstance，andisposteriortoqualityandquantity；
　　andtherelativeisanaccidentofquantity，aswassaid，notits
　　matter，sincesomethingwithadistinctnatureofitsownmustserve
　　asmatterbothtotherelativeingeneralandtoitspartsand
　　kinds。Forthereisnothingeithergreatorsmall，manyorfew，or，in
　　general，relativetosomethingelse，whichwithouthavinganature
　　ofitsownismanyorfew，greatorsmall，orrelativetosomething
　　else。Asignthattherelativeisleastofallasubstanceanda
　　realthingisthefactthatitalonehasnopropergenerationor
　　destructionormovement，asinrespectofquantitythereisincrease
　　anddiminution，inrespectofqualityalteration，inrespectof
　　placelocomotion，inrespectofsubstancesimplegenerationand
　　destruction。Inrespectofrelationthereisnoproperchange；for，
　　withoutchanging，athingwillbenowgreaterandnowlessorequal，
　　ifthatwithwhichitiscomparedhaschangedinquantity。Andcthe
　　matterofeachthing，andthereforeofsubstance，mustbethatwhich
　　ispotentiallyofthenatureinquestion；buttherelativeis
　　neitherpotentiallynoractuallysubstance。Itisstrange，then，or
　　ratherimpossible，tomakenot-substanceanelementin，andprior
　　to，substance；forallthecategoriesareposteriortosubstance。
　　Again，delementsarenotpredicatedofthethingsofwhichtheyare
　　elements，butmanyandfewarepredicatedbothapartandtogetherof
　　number，andlongandshortoftheline，andbothbroadandnarrow
　　applytotheplane。Ifthereisaplurality，then，ofwhichtheone
　　term，viz。few，isalwayspredicated，e。g。2whichcannotbemany，
　　forifitweremany，1wouldbefew，theremustbealsoonewhich
　　isabsolutelymany，e。g。10ismanyifthereisnonumberwhichis
　　greaterthan10，or10，000。Howthen，inviewofthis，cannumber
　　consistoffewandmany？Eitherbothoughttobepredicatedofit，
　　orneither；butinfactonlytheoneortheotherispredicated。
　　Wemustinquiregenerally，whethereternalthingscanconsistof
　　elements。Iftheydo，theywillhavematter；foreverythingthat
　　consistsofelementsiscomposite。Since，then，evenifathingexists
　　forever，outofthatofwhichitconsistsitwouldnecessarily
　　also，ifithadcomeintobeing，havecomeintobeing，andsince
　　everythingcomestobewhatitcomestobeoutofthatwhichisit
　　potentiallyforitcouldnothavecometobeoutofthatwhichhad
　　notthiscapacity，norcoulditconsistofsuchelements，andsince
　　thepotentialcanbeeitheractualornot，-thisbeingso，however
　　everlastingnumberoranythingelsethathasmatteris，itmustbe
　　capableofnotexisting，justasthatwhichisanynumberofyearsold
　　isascapableofnotexistingasthatwhichisadayold；ifthisis
　　capableofnotexisting，soisthatwhichhaslastedforatimeso
　　longthatithasnolimit。Theycannot，then，beeternal，sincethat
　　whichiscapableofnotexistingisnoteternal，aswehadoccasionto
　　showinanothercontext。Ifthatwhichwearenowsayingistrue
　　universally-thatnosubstanceiseternalunlessitisactuality-andif
　　theelementsarematterthatunderliessubstance，noeternalsubstance
　　canhaveelementspresentinit，ofwhichitconsists。
　　TherearesomewhodescribetheelementwhichactswiththeOneas
　　anindefinitedyad，andobjectto’theunequal’，reasonablyenough，
　　becauseoftheensuingdifficulties；buttheyhavegotridonlyof
　　thoseobjectionswhichinevitablyarisefromthetreatmentofthe
　　unequal，i。e。therelative，asanelement；thosewhichariseapart
　　fromthisopinionmustconfronteventhesethinkers，whetheritis
　　idealnumber，ormathematical，thattheyconstructoutofthose
　　elements。
　　Therearemanycauseswhichledthemoffintothese
　　explanations，andespeciallythefactthattheyframedthe
　　difficultyinanobsoleteform。Fortheythoughtthatallthings
　　thatarewouldbeoneviz。Beingitself，ifonedidnotjoinissue
　　withandrefutethesayingofParmenides:
　　’Forneverwillthisheproved，thatthingsthatarenotare。’
　　Theythoughtitnecessarytoprovethatthatwhichisnotis；
　　foronlythus-ofthatwhichisandsomethingelse-couldthethings
　　thatarebecomposed，iftheyaremany。
　　But，first，if’being’hasmanysensesforitmeanssometimes
　　substance，sometimesthatitisofacertainquality，sometimesthat
　　itisofacertainquantity，andatothertimestheothercategories，
　　whatsortof’one’，then，areallthethingsthatare，ifnon-beingis
　　tobesupposednottobe？Isitthesubstancesthatareone，orthe
　　affectionsandsimilarlytheothercategoriesaswell，orall
　　together-sothatthe’this’andthe’such’andthe’somuch’andthe
　　othercategoriesthatindicateeachsomeoneclassofbeingwillall
　　beone？Butitisstrange，orratherimpossible，thatthecoming
　　intoplayofasinglethingshouldbringitaboutthatpartofthat
　　whichisisa’this’，parta’such’，parta’somuch’，parta’here’。
　　Secondly，ofwhatsortofnon-beingandbeingdothethingsthat
　　areconsist？For’nonbeing’alsohasmanysenses，since’being’has；
　　and’notbeingaman’meansnotbeingacertainsubstance，’not
　　beingstraight’notbeingofacertainquality，’notbeingthree
　　cubitslong’notbeingofacertainquantity。Whatsortofbeingand
　　non-being，then，bytheirunionpluralizethethingsthatare？This
　　thinkermeansbythenon-beingtheunionofwhichwithbeing
　　pluralizesthethingsthatare，thefalseandthecharacterof