第46章

Butthisconsequencealsowemustnotforget，thatitfollowsthat

therearepriorandposterior2andsimilarlywiththeother

numbers。Forletthe2’sinthe4besimultaneous；yettheseareprior

tothoseinthe8andasthe2generatedthem，theygeneratedthe

4’sinthe8-itself。Thereforeifthefirst2isanIdea，these2’s

alsowillbeIdeasofsomekind。Andthesameaccountappliestothe

units；fortheunitsinthefirst2generatethefourin4，sothat

alltheunitscometobeIdeasandanIdeawillbecomposedof

Ideas。Clearlythereforethosethingsalsoofwhichthesehappentobe

theIdeaswillbecomposite，e。g。onemightsaythatanimalsare

composedofanimals，ifthereareIdeasofthem。

Ingeneral，todifferentiatetheunitsinanywayisan

absurdityandafiction；andbyafictionImeanaforcedstatement

madetosuitahypothesis。Forneitherinquantitynorinqualitydo

weseeunitdifferingfromunit，andnumbermustbeeitherequalor

unequal-allnumberbutespeciallythatwhichconsistsofabstract

units-sothatifonenumberisneithergreaternorlessthan

another，itisequaltoit；butthingsthatareequalandinnowise

differentiatedwetaketobethesamewhenwearespeakingofnumbers。

Ifnot，noteventhe2inthe10-itselfwillbeundifferentiated，

thoughtheyareequal；forwhatreasonwillthemanwhoallegesthat

theyarenotdifferentiatedbeabletogive？

Again，ifeveryunit+anotherunitmakestwo，aunitfromthe

2-itselfandonefromthe3-itselfwillmakea2。Now(a)thiswill

consistofdifferentiatedunits；andwillitbepriortothe3or

posterior？Itratherseemsthatitmustbeprior；foroneoftheunits

issimultaneouswiththe3andtheotherissimultaneouswiththe2。

Andwe，forourpart，supposethatingeneral1and1，whetherthe

thingsareequalorunequal，is2，e。g。thegoodandthebad，oraman

andahorse；butthosewhoholdtheseviewssaythatnoteventwo

unitsare2。

Ifthenumberofthe3-itselfisnotgreaterthanthatofthe2，

thisissurprising；andifitisgreater，clearlythereisalsoa

numberinitequaltothe2，sothatthisisnotdifferentfromthe

2-itself。Butthisisnotpossible，ifthereisafirstandasecond

number。

NorwilltheIdeasbenumbers。Forinthisparticularpointthey

arerightwhoclaimthattheunitsmustbedifferent，ifthereare

tobeIdeas；ashasbeensaidbefore。FortheFormisunique；butif

theunitsarenotdifferent，the2’sandthe3’salsowillnotbe

different。Thisisalsothereasonwhytheymustsaythatwhenwe

countthus-’1，2’-wedonotproceedbyaddingtothegivennumber；

forifwedo，neitherwillthenumbersbegeneratedfromthe

indefinitedyad，norcananumberbeanIdea；forthenoneIdeawill

beinanother，andallFormswillbepartsofoneForm。Andsowith

aviewtotheirhypothesistheirstatementsareright，butasa

wholetheyarewrong；fortheirviewisverydestructive，sincethey

willadmitthatthisquestionitselfaffordssome

difficulty-whether，whenwecountandsay-1，2，3-wecountby

additionorbyseparateportions。Butwedoboth；andsoitis

absurdtoreasonbackfromthisproblemtosogreatadifferenceof

essence。

Firstofallitiswelltodeterminewhatisthedifferentiaof

anumber-andofaunit，ifithasadifferentia。Unitsmustdiffer

eitherinquantityorinquality；andneitheroftheseseemstobe

possible。Butnumberquanumberdiffersinquantity。Andifthe

unitsalsodiddifferinquantity，numberwoulddifferfromnumber，

thoughequalinnumberofunits。Again，arethefirstunitsgreateror

smaller，anddothelateronesincreaseordiminish？Alltheseare

irrationalsuppositions。Butneithercantheydifferinquality。For

noattributecanattachtothem；foreventonumbersqualityissaid

tobelongafterquantity。Again，qualitycouldnotcometothemeither

fromthe1orthedyad；fortheformerhasnoquality，andthe

lattergivesquantity；forthisentityiswhatmakesthingstobe

many。Ifthefactsarereallyotherwis