第9章

othersthinktheyareofthelattercharacter。Platoandthe

Pythagoreansthoughtbeingandunitywerenothingelse，butthiswas

theirnature，theiressencebeingjustunityandbeing。Butthe

naturalphilosopherstakeadifferentline；e。g。Empedocles-as

thoughreducingtosomethingmoreintelligible-sayswhatunityis；for

hewouldseemtosayitislove:atleast，thisisforallthings

thecauseoftheirbeingone。Otherssaythisunityandbeing，of

whichthingsconsistandhavebeenmade，isfire，andotherssayitis

air。Asimilarviewisexpressedbythosewhomaketheelementsmore

thanone；forthesealsomustsaythatunityandbeingareprecisely

allthethingswhichtheysayareprinciples。

(A)Ifwedonotsupposeunityandbeingtobesubstances，it

followsthatnoneoftheotheruniversalsisasubstance；forthese

aremostuniversalofall，andifthereisnounityitselfor

being-itself，therewillscarcelybeinanyothercaseanything

apartfromwhatarecalledtheindividuals。Further，ifunityisnota

substance，evidentlynumberalsowillnotexistasanentity

separatefromtheindividualthings；fornumberisunits，andtheunit

ispreciselyacertainkindofone。

But(B)ifthereisaunity-itselfandabeingitself，unityand

beingmustbetheirsubstance；foritisnotsomethingelsethatis

predicateduniversallyofthethingsthatareandareone，butjust

unityandbeing。Butifthereistobeabeing-itselfanda

unity-itself，thereismuchdifficultyinseeinghowtherewillbe

anythingelsebesidesthese，-Imean，howthingswillbemorethan

oneinnumber。Forwhatisdifferentfrombeingdoesnotexist，so

thatitnecessarilyfollows，accordingtotheargumentof

Parmenides，thatallthingsthatareareoneandthisisbeing。

Thereareobjectionstobothviews。Forwhetherunityisnota

substanceorthereisaunity-itself，numbercannotbeasubstance。We

havealreadysaidwhythisresultfollowsifunityisnotasubstance；

andifitis，thesamedifficultyarisesasarosewithregardto

being。Forwhenceistheretobeanotheronebesidesunity-itself？

Itmustbenot-one；butallthingsareeitheroneormany，andof

themanyeachisone。

Further，ifunity-itselfisindivisible，accordingtoZeno’s

postulateitwillbenothing。Forthatwhichneitherwhenadded

makesathinggreaternorwhensubtractedmakesitless，heassertsto

havenobeing，evidentlyassumingthatwhateverhasbeingisaspatial

magnitude。Andifitisamagnitude，itiscorporeal；forthe

corporealhasbeingineverydimension，whiletheotherobjectsof

mathematics，e。g。aplaneoraline，addedinonewaywillincrease

whattheyareaddedto，butinanotherwaywillnotdoso，andapoint

oraunitdoessoinnoway。But，sincehistheoryisofalow

order，andanindivisiblethingcanexistinsuchawayastohavea

defenceevenagainsthim(fortheindivisiblewhenaddedwillmakethe

number，thoughnotthesize，greater)，-yethowcanamagnitudeproceed

fromonesuchindivisibleorfrommany？Itislikesayingthatthe

lineismadeoutofpoints。

Buteveniforesupposesthecasetobesuchthat，assomesay，

numberproceedsfromunity-itselfandsomethingelsewhichisnotone，

nonethelesswemustinquirewhyandhowtheproductwillbe

sometimesanumberandsometimesamagnitude，ifthenot-onewas

inequalityandwasthesameprincipleineithercase。Foritisnot

evidenthowmagnitudescouldproceedeitherfromtheoneandthis

principle，orfromsomenumberandthisprinciple。

(14)Aquestionconnectedwiththeseiswhethernumbersandbodies

andplanesandpointsaresubstancesofakind，ornot。Iftheyare

not，itbafflesustosaywhatbeingisandwhatthesubstancesof

thingsare。Formodificationsandmovementsandrelationsand

dispositionsandratiosdonotseemtoindicatethesubstanceof

anything；forallarepredicatedofasubject，andnoneisa’this’。

Andastothethingswhichmightseemmostofalltoindicate

substance，waterandearthandfireandair，ofwhichcompositebodies

consist，heatandcoldandthelikearemodificationsofthese，not

substances，andthebodywhichisthusmodifiedalonepersistsas

somethingrealandasasubstance。But，ontheotherhand，thebodyis

surelylessofasubstancethanthesurface，andthesurfacethan

theline，andthelinethantheunitandthepoint。Forthebodyis

boundedbythese；andtheyarethoughttobecapableofexisting

withoutbody，butbodyincapableofexistingwithoutthese。Thisis

why，whilemostofthephilosophersandtheearlieramongthemthought

thatsubstanceandbeingwereidenticalwithbody，andthatall

otherthingsweremodificationsofthis，sothatthefirst

principlesofthebodieswerethefirstprinciplesofbeing，the

morerecentandthosewhowereheldtobewiserthoughtnumberswere

thefirstprinciples。Aswesaid，then，ifthesearenotsubstance，

thereisnosubstanceandnobeingatall；fortheaccidentsof

theseitcannotberighttocallbeings。

Butifthisisadmitted，thatlinesandpointsaresubstance

morethanbodies，butwedonotseetowhatsortofbodiesthesecould

belong(fortheycannotbeinperceptiblebodies)，therecanbeno

substance-Further，theseareallevidentlydivisionsofbody，-one

inbreadth，anotherindepth，anotherinlength。Besidesthis，nosort

ofshapeispresentinthesolidmorethananyother；sothatifthe

Hermesisnotinthestone，neitheristhehalfofthecubeinthe

cubeassomethingdeterminate；thereforethesurfaceisnotinit

either；forifanysortofsurfacewereinit，thesurfacewhichmarks

offthehalfofthecubewouldbeinittoo。Andthesameaccount

appliestothelineandtothepointandtheunit。Therefore，ifon

theonehandbodyisinthehighestdegreesubstance，andontheother

handthesethingsaresomorethanbody，butthesearenoteven

instancesofsubstance，itbafflesustosaywhatbeingisandwhat

thesubstanceofthingsis-Forbesideswhathasbeensaid，the

questionsofgenerationandinstructionconfrontuswithfurther

paradoxes。Forifsubstance，nothavingexistedbefore，nowexists，or

havingexistedbefore，afterwardsdoesnotexist，thischangeis

thoughttobeaccompaniedbyaprocessofbecomingorperishing；but

pointsandlinesandsurfacescannotbeinprocesseitherof

becomingorofperishing，whentheyatonetimeexistandatanother

donot。Forwhenbodiescomeintocontactoraredivided，their

boundariessimultaneouslybecomeoneintheonecasewhenthey

touch，andtwointheother-whentheyaredivided；sothatwhenthey

havebeenputtogetheroneboundarydoesnotexistbuthasperished，

andwhentheyhavebeendividedtheboundariesexistwhichbefore

didnotexist(foritcannotbesaidthatthepoint，whichis

indivisible，wasdividedintotwo)。Andiftheboundariescomeinto

beingandceasetobe，fromwhatdotheycomeintobeing？Asimilar

accountmayalsobegivenofthe’now’intime；forthisalsocannot

beinprocessofcomingintobeingorofceasingtobe，butyet

seemstobealwaysdifferent，whichshowsthatitisnota

substance。Andevidentlythesameistrueofpointsandlinesand

planes；forthesameargumentapplies，sincetheyareallalikeeither

limitsordivisions。

Ingeneralonemightraisethequestionwhyafterall，besides

perceptiblethingsandtheintermediates，wehavetolookfor

anotherclassofthings，i。e。theFormswhichweposit。Ifitisfor

thisreason，becausetheobjectsofmathematics，whiletheydiffer

fromthethingsinthisworldinsomeotherrespect，differnotatall

inthattherearemanyofthesamekind，sothattheirfirst

principlescannotbelimitedinnumber(justastheelementsofall

thelanguageinthissensibleworldarenotlimitedinnumber，but

inkind，unlessonetakestheelementsofthisindividualsyllable

orofthisindividualarticulatesound-whoseelementswillbe

limitedeveninnumber；soisitalsointhecaseofthe

intermediates；fortherealsothemembersofthesamekindare

infiniteinnumber)，sothatiftherearenot-besidesperceptible

andmathematicalobjects-otherssuchassomemaintaintheFormstobe，

therewillbenosubstancewhichisoneinnumber，butonlyinkind，

norwillthefirstprinciplesofthingsbedeterminateinnumber，

butonlyinkind:-ifthenthismustbeso，theFormsalsomust

thereforebeheldtoexist。Evenifthosewhosupportthisviewdonot

expressitarticulately，stillthisiswhattheymean，andtheymust

bemaintainingtheFormsjustbecauseeachoftheFormsisasubstance

andnoneisbyaccident。

ButifwearetosupposeboththattheFormsexistandthatthe

principlesareoneinnumber，notinkind，wehavementionedthe

impossibleresultsthatnecessarilyfollow。

(13)Closelyconnectedwiththisisthequestionwhetherthe

elementsexistpotentiallyorinsomeothermanner。Ifinsomeother

way，therewillbesomethingelsepriortothefirstprinciples；for

thepotencyispriortotheactualcause，anditisnotnecessary

foreverythingpotentialtobeactual-Butiftheelementsexist

potentially，itispossiblethateverythingthatisshouldnotbe。For

eventhatwhichisnotyetiscapableofbeing；forthatwhichis

notcomestobe，butnothingthatisincapableofbeingcomestobe。

(12)Wemustnotonlyraisethesequestionsaboutthefirst

principles，butalsoaskwhethertheyareuniversalorwhatwecall

individuals。Iftheyareuniversal，theywillnotbesubstances；for

everythingthatiscommonindicatesnota’this’buta’such’，but

substanceisa’this’。Andifwearetobeallowedtolayitdownthat

acommonpredicateisa’this’andasinglething，Socrateswillbe

severalanimals-himselfand’man’and’animal’，ifeachofthese

indicatesa’this’andasinglething。

If，then，theprinciplesareuniversals，theseuniversal。

Thereforeifthereistoberesultsfollow；iftheyarenotuniversals

butofknowledgeoftheprinciplestheremustbethenatureof

individuals，theywillnotbeotherprinciplespriortothem，namely

thoseknowable；fortheknowledgeofanythingisthatare

universallypredicatedofthem。

THEREisasciencewhichinvestigatesbeingasbeingandthe

attributeswhichbelongtothisinvirtueofitsownnature。Now

thisisnotthesameasanyoftheso-calledspecialsciences；for

noneoftheseotherstreatsuniversallyofbeingasbeing。Theycut

offapartofbeingandinvestigatetheattributeofthispart；this

iswhatthemathematicalsciencesforinstancedo。Nowsinceweare

seekingthefirstprinciplesandthehighestcauses，clearlythere

mustbesomethingtowhichthesebelonginvirtueofitsown

nature。Ifthenthosewhosoughttheelementsofexistingthings

wereseekingthesesameprinciples，itisnecessarythatthe

elementsmustbeelementsofbeingnotbyaccidentbutjustbecauseit

isbeing。Thereforeitisofbeingasbeingthatwealsomustgrasp

thefirstcauses。