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