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。
第7章