第7章

Andinthisway,theone,ifithasbeing,hasturnedouttobemany?

True。

Butnow,letusabstracttheonewhich,aswesay,partakesofbeing,andtrytoimagineitapartfromthatofwhich,aswesay,itpartakes—willthisabstractonebeoneonlyormany?

One,Ithink。

Letussee:—Mustnotthebeingofonebeotherthanone?fortheoneisnotbeing,but,consideredasone,onlypartookofbeing?

Certainly。

Ifbeingandtheonebetwodifferentthings,itisnotbecausetheoneisonethatitisotherthanbeing;norbecausebeingisbeingthatitisotherthantheone;buttheydifferfromoneanotherinvirtueofothernessanddifference。

Certainly。

Sothattheotherisnotthesameeitherwiththeoneorwithbeing?

Certainlynot。

Andthereforewhetherwetakebeingandtheother,orbeingandtheone,ortheoneandtheother,ineverysuchcasewetaketwothings,whichmayberightlycalledboth。

Howso。

Inthisway—youmayspeakofbeing?

Yes。

Andalsoofone?

Yes。

Thennowwehavespokenofeitherofthem?

Yes。

Well,andwhenIspeakofbeingandone,Ispeakofthemboth?

Certainly。

AndifIspeakofbeingandtheother,oroftheoneandtheother—inanysuchcasedoInotspeakofboth?

Yes。

Andmustnotthatwhichiscorrectlycalledboth,bealsotwo?

Undoubtedly。

Andoftwothingshowcaneitherbyanypossibilitynotbeone?

Itcannot。

Then,iftheindividualsofthepairaretogethertwo,theymustbeseverallyone?

Clearly。

Andifeachofthemisone,thenbytheadditionofanyonetoanypair,thewholebecomesthree?

Yes。

Andthreeareodd,andtwoareeven?

Ofcourse。

Andiftherearetwotheremustalsobetwice,andiftherearethreetheremustbethrice;thatis,iftwiceonemakestwo,andthriceonethree?

Certainly。

Therearetwo,andtwice,andthereforetheremustbetwicetwo;andtherearethree,andthereisthrice,andthereforetheremustbethricethree?

Ofcourse。

Iftherearethreeandtwice,thereistwicethree;andiftherearetwoandthrice,thereisthricetwo?

Undoubtedly。

Here,then,wehaveeventakeneventimes,andoddtakenoddtimes,andeventakenoddtimes,andoddtakeneventimes。

True。

Andifthisisso,doesanynumberremainwhichhasnonecessitytobe?

Nonewhatever。

Thenifoneis,numbermustalsobe?

Itmust。

Butifthereisnumber,theremustalsobemany,andinfinitemultiplicityofbeing;fornumberisinfiniteinmultiplicity,andpartakesalsoofbeing:amInotright?

Certainly。

Andifallnumberparticipatesinbeing,everypartofnumberwillalsoparticipate?

Yes。

Thenbeingisdistributedoverthewholemultitudeofthings,andnothingthatis,howeversmallorhowevergreat,isdevoidofit?And,indeed,theverysuppositionofthisisabsurd,forhowcanthatwhichis,bedevoidofbeing?

Innoway。

Anditisdividedintothegreatestandintothesmallest,andintobeingofallsizes,andisbrokenupmorethanallthings;thedivisionsofithavenolimit。

True。

Thenithasthegreatestnumberofparts?

Yes,thegreatestnumber。

Isthereanyofthesewhichisapartofbeing,andyetnopart?

Impossible。

Butifitisatallandsolongasitis,itmustbeone,andcannotbenone?

Certainly。

Thentheoneattachestoeverysinglepartofbeing,anddoesnotfailinanypart,whethergreatorsmall,orwhatevermaybethesizeofit?

True。

Butreflect:—anoneinitsentirety,beinmanyplacesatthesametime?

No;Iseetheimpossibilityofthat。

Andifnotinitsentirety,thenitisdivided;foritcannotbepresentwithallthepartsofbeing,unlessdivided。

True。

Andthatwhichhaspartswillbeasmanyasthepartsare?

Certainly。

Thenwewerewronginsayingjustnow,thatbeingwasdistributedintothegreatestnumberofparts。Foritisnotdistributedintopartsmorethantheone,intopartsequaltotheone;theoneisneverwantingtobeing,orbeingtotheone,butbeingtwotheyareco—equalandcoextensive。

Certainlythatistrue。

Theoneitself,then,havingbeenbrokenupintopartsbybeing,ismanyandinfinite?

True。

Thennotonlytheonewhichhasbeingismany,buttheoneitselfdistributedbybeing,mustalsobemany?

Certainly。

Further,inasmuchasthepartsarepartsofawhole,theone,asawhole,willbelimited;forarenotthepartscontainedthewhole?

Certainly。

Andthatwhichcontains,isalimit?

Ofcourse。

Thentheoneifithasbeingisoneandmany,wholeandparts,havinglimitsandyetunlimitedinnumber?

Clearly。

Andbecausehavinglimits,alsohavingextremes?

Certainly。

Andifawhole,havingbeginningandmiddleandend。Forcananythingbeawholewithoutthesethree?Andifanyoneofthemiswantingtoanything,willthatanylongerbeawhole?

No。

Thentheone,asappears,willhavebeginning,middle,andend。

Itwill。

But,again,themiddlewillbeequidistantfromtheextremes;oritwouldnotbeinthemiddle?

Yes。

Thentheonewillpartakeoffigure,eitherrectilinearorround,oraunionofthetwo?

True。

Andifthisisthecase,itwillbebothinitselfandinanothertoo。

How?

Everypartisinthewhole,andnoneisoutsidethewhole。

True。

Andallthepartsarecontainedbythewhole?

Yes。

Andtheoneisallitsparts,andneithermorenorlessthanall?

No。

Andtheoneisthewhole?

Ofcourse。

Butifallthepartsareinthewhole,andtheoneisallofthemandthewhole,andtheyareallcontainedbythewhole,theonewillbecontainedbytheone;andthustheonewillbeinitself。

Thatistrue。

Butthen,again,thewholeisnotintheparts—neitherinalltheparts,norinsomeoneofthem。Forifitisinall,itmustbeinone;foriftherewereanyoneinwhichitwasnot,itcouldnotbeinalltheparts;forthepartinwhichitiswantingisoneofall,andifthewholeisnotinthis,howcanitbeinthemall?

Itcannot。