第45章

But，further，allotherthingscannotcomefromtheFormsinany

oftheusualsensesof’from’。Andtosaythattheyarepatternsand

theotherthingsshareinthemistouseemptywordsandpoetical

metaphors。Forwhatisitthatworks，lookingtotheIdeas？Andany

thingcanbothbeandcomeintobeingwithoutbeingcopiedfrom

somethingelse，sothat，whetherSocratesexistsornot，amanlike

Socratesmightcometobe。Andevidentlythismightbesoevenif

Socrateswereeternal。Andtherewillbeseveralpatternsofthe

samething，andthereforeseveralForms；e。g。’animal’and

’two-footed’，andalso’man-himself’，willbeFormsofman。Again，the

Formsarepatternsnotonlyofsensiblethings，butofForms

themselvesalso；i。e。thegenusisthepatternofthevarious

forms-of-a-genus；thereforethesamethingwillbepatternandcopy。

Again，itwouldseemimpossiblethatsubstanceandthatwhose

substanceitisshouldexistapart；how，therefore，couldtheIdeas，

beingthesubstancesofthings，existapart？

InthePhaedothecaseisstatedinthisway-thattheFormsare

causesbothofbeingandofbecoming。YetthoughtheFormsexist，

stillthingsdonotcomeintobeing，unlessthereissomethingto

originatemovement；andmanyotherthingscomeintobeing(e。g。a

houseoraring)ofwhichtheysaytherearenoForms。Clearly

thereforeeventhethingsofwhichtheysaythereareIdeascanboth

beandcomeintobeingowingtosuchcausesasproducethethingsjust

mentioned，andnotowingtotheForms。ButregardingtheIdeasitis

possible，bothinthiswayandbymoreabstractandaccurate

arguments，tocollectmanyobjectionslikethosewehaveconsidered。

Sincewehavediscussedthesepoints，itiswelltoconsideragain

theresultsregardingnumberswhichconfrontthosewhosaythat

numbersareseparablesubstancesandfirstcausesofthings。Ifnumber

isanentityanditssubstanceisnothingotherthanjustnumber，as

somesay，itfollowsthateither(1)thereisafirstinitanda

second，eachbeingdifferentinspecies，-andeither(a)thisistrue

oftheunitswithoutexception，andanyunitisinassociablewith

anyunit，or(b)theyareallwithoutexceptionsuccessive，andanyof

themareassociablewithany，astheysayisthecasewith

mathematicalnumber；forinmathematicalnumbernooneunitisin

anywaydifferentfromanother。Or(c)someunitsmustbeassociable

andsomenot；e。g。supposethat2isfirstafter1，andthencomes3

andthentherestofthenumberseries，andtheunitsineachnumber

areassociable，e。g。thoseinthefirst2areassociablewithone

another，andthoseinthefirst3withoneanother，andsowiththe

othernumbers；buttheunitsinthe’2-itself’areinassociablewith

thoseinthe’3-itself’；andsimilarlyinthecaseoftheother

successivenumbers。Andsowhilemathematicalnumberiscounted

thus-after1，2(whichconsistsofanother1besidestheformer1)，

and3whichconsistsofanother1besidesthesetwo)，andtheother

numberssimilarly，idealnumberiscountedthus-after1，adistinct

2whichdoesnotincludethefirst1，anda3whichdoesnotinclude

the2andtherestofthenumberseriessimilarly。Or(2)onekind

ofnumbermustbelikethefirstthatwasnamed，onelikethatwhich

themathematiciansspeakof，andthatwhichwehavenamedlastmustbe

athirdkind。

Again，thesekindsofnumbersmusteitherbeseparablefrom

things，ornotseparablebutinobjectsofperception(nothowever

inthewaywhichwefirstconsidered，inthesensethatobjectsof

perceptionconsistsofnumberswhicharepresentinthem)-eitherone

kindandnotanother，orallofthem。

Theseareofnecessitytheonlywaysinwhichthenumberscan

exist。Andofthosewhosaythatthe1isthebeginningand

substanceandelementofallthings，andthatnumberisformedfrom

the1andsomethingelse，almosteveryonehasdescribednumberinone

oftheseways；onlynoonehassaidalltheunitsareinassociable。

Andthishashappenedreasonablyenough；fortherecanbenoway