第32章

WEhavesaidpreviously，inourdistinctionofthevarious meaningsofwords，that’one’hasseveralmeanings；thethingsthat aredirectlyandoftheirownnatureandnotaccidentallycalledone maybesummarizedunderfourheads，thoughthewordisusedinmore senses。(1)Thereisthecontinuous，eitheringeneral，or especiallythatwhichiscontinuousbynatureandnotbycontactnor bybeingtogether；andofthese，thathasmoreunityandisprior， whosemovementismoreindivisibleandsimpler。(2)Thatwhichisa wholeandhasacertainshapeandformisoneinastillhigher degree；andespeciallyifathingisofthissortbynature，andnot byforcelikethethingswhichareunifiedbyglueornailsorby beingtiedtogether，i。e。ifithasinitselfthecauseofits continuity。Athingisofthissortbecauseitsmovementisoneand indivisibleinplaceandtime；sothatevidentlyifathinghasby natureaprincipleofmovementthatisofthefirstkind(i。e。local movement)andthefirstinthatkind(i。e。circularmovement)，thisis intheprimarysenseoneextendedthing。Somethings，then，areonein thisway，quacontinuousorwhole，andtheotherthingsthatareone arethosewhosedefinitionisone。Ofthissortarethethingsthe thoughtofwhichisone，i。e。thosethethoughtofwhichis indivisible；anditisindivisibleifthethingisindivisibleinkind orinnumber。(3)Innumber，then，theindividualisindivisible， and(4)inkind，thatwhichinintelligibilityandinknowledgeis indivisible，sothatthatwhichcausessubstancestobeonemustbe oneintheprimarysense。’One’，then，hasallthesemeanings-the naturallycontinuousandthewhole，andtheindividualandthe universal。Andalltheseareonebecauseinsomecasesthemovement， inothersthethoughtorthedefinitionisindivisible。 Butitmustbeobservedthatthequestions，whatsortofthings aresaidtobeone，andwhatitistobeoneandwhatisthe definitionofit，shouldnotbeassumedtobethesame。’One’has allthesemeanings，andeachofthethingstowhichoneofthesekinds ofunitybelongswillbeone；but’tobeone’willsometimesmean beingoneofthesethings，andsometimesbeingsomethingelsewhichis evennearertothemeaningoftheword’one’whiletheseother thingsapproximatetoitsapplication。Thisisalsotrueof ’element’or’cause’，ifonehadbothtospecifythethingsofwhich itispredicableandtorenderthedefinitionoftheword。Forina sensefireisanelement(anddoubtlessalso’theindefinite’or somethingelseofthesortisbyitsownnaturetheelement)，butina senseitisnot；foritisnotthesamethingtobefireandtobe anelement，butwhileasaparticularthingwithanatureofitsown fireisanelement，thename’element’meansthatithasthis attribute，thatthereissomethingwhichismadeofitasaprimary constituent。Andsowith’cause’and’one’andallsuchterms。For thisreason，too，’tobeone’means’tobeindivisible，being essentiallyonemeansa“this“andcapableofbeingisolatedeitherin place，orinformorthought’；orperhaps’tobewholeand indivisible’；butitmeansespecially’tobethefirstmeasureofa kind’，andmoststrictlyofquantity；foritisfromthisthatit hasbeenextendedtotheothercategories。Formeasureisthatby whichquantityisknown；andquantityquaquantityisknowneither bya’one’orbyanumber，andallnumberisknownbya’one’。 Thereforeallquantityquaquantityisknownbytheone，andthatby whichquantitiesareprimarilyknownistheoneitself；andsotheone isthestarting-pointofnumberquanumber。Andhenceintheother classestoo’measure’meansthatbywhicheachisfirstknown，andthe measureofeachisaunit-inlength，inbreadth，indepth，in weight，inspeed。(Thewords’weight’and’speed’arecommontoboth contraries；foreachofthemhastwomeanings-’weight’meansboththat whichhasanyamountofgravityandthatwhichhasanexcessof gravity，and’speed’boththatwhichhasanyamountofmovementand thatwhichhasanexcessofmovement；foreventheslowhasa certainspeedandthecomparativelylightacertainweight。) Inallthese，then，themeasureandstarting-pointissomething oneandindivisible，sinceeveninlineswetreatasindivisiblethe lineafootlong。Foreverywhereweseekasthemeasuresomething oneandindivisible；andthisisthatwhichissimpleeitherin qualityorinquantity。Nowwhereitisthoughtimpossibletotake awayortoadd，therethemeasureisexact(hencethatofnumberis mostexact；forweposittheunitasindivisibleineveryrespect)； butinallothercasesweimitatethissortofmeasure。Forinthe caseofafurlongoratalentorofanythingcomparativelylargeany additionorsubtractionmightmoreeasilyescapeournoticethanin thecaseofsomethingsmaller；sothatthefirstthingfromwhich， asfarasourperceptiongoes，nothingcanbesubtracted，allmenmake themeasure，whetherofliquidsorofsolids，whetherofweightor ofsize；andtheythinktheyknowthequantitywhentheyknowitby meansofthismeasure。Andindeedtheyknowmovementtoobythesimple movementandthequickest；forthisoccupiesleasttime。Andsoin astronomya’one’ofthissortisthestarting-pointandmeasure (fortheyassumethemovementoftheheavenstobeuniformandthe quickest，andjudgetheothersbyreferencetoit)，andinmusicthe quarter-tone(becauseitistheleastinterval)，andinspeechthe letter。Andalltheseareonesinthissense——notthat’one’is somethingpredicableinthesamesenseofallofthese，butinthe sensewehavementioned。 Butthemeasureisnotalwaysoneinnumber——sometimesthereare several；e。g。thequarter-tones(nottotheear，butasdetermined bytheratios)aretwo，andthearticulatesoundsbywhichwe measurearemorethanone，andthediagonalofthesquareanditsside aremeasuredbytwoquantities，andallspatialmagnitudesreveal similarvarietiesofunit。Thus，then，theoneisthemeasureofall things，becausewecometoknowtheelementsinthesubstanceby dividingthethingseitherinrespectofquantityorinrespectof kind。Andtheoneisindivisiblejustbecausethefirstofeach classofthingsisindivisible。Butitisnotinthesamewaythat every’one’isindivisiblee。g。afootandaunit；thelatteris indivisibleineveryrespect，whiletheformermustbeplacedamong thingswhichareundividedtoperception，ashasbeensaid already-onlytoperception，fordoubtlesseverycontinuousthingis divisible。 Themeasureisalwayshomogeneouswiththethingmeasured；the measureofspatialmagnitudesisaspatialmagnitude，andin particularthatoflengthisalength，thatofbreadthabreadth，that ofarticulatesoundanarticulatesound，thatofweightaweight，that ofunitsaunit。(Forwemuststatethematterso，andnotsaythat themeasureofnumbersisanumber；weoughtindeedtosaythisif weweretousethecorrespondingformofwords，buttheclaimdoesnot reallycorrespond-itisasifoneclaimedthatthemeasureofunitsis unitsandnotaunit；numberisapluralityofunits。) Knowledge，also，andperception，wecallthemeasureofthingsfor thesamereason，becausewecometoknowsomethingbythem-whileas amatteroffacttheyaremeasuredratherthanmeasureotherthings。 Butitiswithusasifsomeoneelsemeasuredusandwecameto knowhowbigwearebyseeingthatheappliedthecubit-measureto suchandsuchafractionofus。ButProtagorassays’manisthe measureofallthings’，asifhehadsaid’themanwhoknows’or ’themanwhoperceives’；andthesebecausetheyhaverespectively knowledgeandperception，whichwesayarethemeasuresofobjects。 Suchthinkersaresayingnothing，then，whiletheyappeartobesaying somethingremarkable。 Evidently，then，unityinthestrictestsense，ifwedefineit accordingtothemeaningoftheword，isameasure，andmost properlyofquantity，andsecondlyofquality。Andsomethingswillbe oneiftheyareindivisibleinquantity，andothersiftheyare indivisibleinquality；andsothatwhichisoneisindivisible， eitherabsolutelyorquaone。 Withregardtothesubstanceandnatureoftheonewemustask inwhichoftwowaysitexists。Thisistheveryquestionthatwe reviewedinourdiscussionofproblems，viz。whattheoneisandhow wemustconceiveofit，whetherwemusttaketheoneitselfasbeinga substance(asboththePythagoreanssayinearlierandPlatoin latertimes)，orthereis，rather，anunderlyingnatureandtheone shouldbedescribedmoreintelligiblyandmoreinthemannerofthe physicalphilosophers，ofwhomonesaystheoneislove，another saysitisair，andanothertheindefinite。 If，then，nouniversalcanbeasubstance，ashasbeensaidour discussionofsubstanceandbeing，andifbeingitselfcannotbea substanceinthesenseofaoneapartfromthemany(foritis commontothemany)，butisonlyapredicate，clearlyunityalso cannotbeasubstance；forbeingandunityarethemostuniversalof allpredicates。Therefore，ontheonehand，generaarenotcertain entitiesandsubstancesseparablefromotherthings；andonthe otherhandtheonecannotbeagenus，forthesamereasonsforwhich beingandsubstancecannotbegenera。 Further，thepositionmustbesimilarinallthekindsofunity。 Now’unity’hasjustasmanymeaningsas’being’；sothatsinceinthe sphereofqualitiestheoneissomethingdefinite-someparticularkind ofthing-andsimilarlyinthesphereofquantities，clearlywemustin everycategoryaskwhattheoneis，aswemustaskwhattheexistent is，sinceitisnotenoughtosaythatitsnatureisjusttobeoneor existent。Butincolourstheoneisacolour，e。g。white，andthenthe othercoloursareobservedtobeproducedoutofthisandblack，and blackistheprivationofwhite，asdarknessoflight。Thereforeif allexistentthingswerecolours，existentthingswouldhavebeena number，indeed，butofwhat？Clearlyofcolours；andthe’one’would havebeenaparticular’one’，i。e。white。Andsimilarlyifall existingthingsweretunes，theywouldhavebeenanumber，buta numberofquarter-tones，andtheiressencewouldnothavebeennumber； andtheonewouldhavebeensomethingwhosesubstancewasnottobe onebuttobethequarter-tone。Andsimilarlyifallexistentthings hadbeenarticulatesounds，theywouldhavebeenanumberof letters，andtheonewouldhavebeenavowel。Andifallexistent thingswererectilinearfigures，theywouldhavebeenanumberof figures，andtheonewouldhavebeenthetriangle。Andthesame argumentappliestoallotherclasses。Since，therefore，whilethere arenumbersandaonebothinaffectionsandinqualitiesandin quantitiesandinmovement，inallcasesthenumberisanumberof particularthingsandtheoneisonesomething，anditssubstanceis notjusttobeone，thesamemustbetrueofsubstancesalso；forit istrueofallcasesalike。 Thattheone，then，ineveryclassisadefinitething，andin nocaseisitsnaturejustthis，unity，isevident；butasin colourstheone-itselfwhichwemustseekisonecolour，sotooin substancetheone-itselfisonesubstance。Thatinasenseunitymeans thesameasbeingisclearfromthefactsthatitsmeaningscorrespond tothecategoriesonetoone，anditisnotcomprisedwithinany category(e。g。itiscomprisedneitherin’whatathingis’norin quality，butisrelatedtothemjustasbeingis)；thatin’oneman’ nothingmoreispredicatedthanin’man’(justasbeingisnothing apartfromsubstanceorqualityorquantity)；andthattobeoneis justtobeaparticularthing。