第48章

composedofthemarealsouniversal，ornon-substancewillbepriorto substance；fortheuniversalisnotasubstance，buttheelementor principleisuniversal，andtheelementorprincipleispriortothe thingsofwhichitistheprincipleorelement。 Allthesedifficultiesfollownaturally，whentheymakethe Ideasoutofelementsandatthesametimeclaimthatapartfromthe substanceswhichhavethesameformthereareIdeas，asingleseparate entity。Butif，e。g。inthecaseoftheelementsofspeech，thea’s andtheb’smayquitewellbemanyandthereneedbenoa-itselfand b-itselfbesidesthemany，theremaybe，sofarasthisgoes，an infinitenumberofsimilarsyllables。Thestatementthatan knowledgeisuniversal，sothattheprinciplesofthingsmustalso beuniversalandnotseparatesubstances，presentsindeed，ofall thepointswehavementioned，thegreatestdifficulty，butyetthe statementisinasensetrue，althoughinasenseitisnot。For knowledge，liketheverb’toknow’，meanstwothings，ofwhichone ispotentialandoneactual。Thepotency，being，asmatter， universalandindefinite，dealswiththeuniversalandindefinite；but theactuality，beingdefinite，dealswithadefiniteobject，beinga ’this’，itdealswitha’this’。Butperaccidenssightsees universalcolour，becausethisindividualcolourwhichitseesis colour；andthisindividualawhichthegrammarianinvestigatesis ana。Foriftheprinciplesmustbeuniversal，whatisderivedfrom themmustalsobeuniversal，asindemonstrations；andifthisis so，therewillbenothingcapableofseparateexistence-i。e。no substance。Butevidentlyinasenseknowledgeisuniversal，andina senseitisnot。 thiskindofsubstance，whatwehavesaidmustbe takenassufficient。Allphilosophersmakethefirstprinciples contraries:asinnaturalthings，soalsointhecaseof unchangeablesubstances。Butsincetherecannotbeanythingpriorto thefirstprincipleofallthings，theprinciplecannotbethe principleandyetbeanattributeofsomethingelse。Tosuggestthis islikesayingthatthewhiteisafirstprinciple，notquaanything elsebutquawhite，butyetthatitispredicableofasubject，i。e。 thatitsbeingwhitepresupposesitsbeingsomethingelse；thisis absurd，forthenthatsubjectwillbeprior。Butallthingswhich aregeneratedfromtheircontrariesinvolveanunderlyingsubject；a subject，then，mustbepresentinthecaseofcontraries，ifanywhere。 Allcontraries，then，arealwayspredicableofasubject，andnonecan existapart，butjustasappearancessuggestthatthereisnothing contrarytosubstance，argumentconfirmsthis。Nocontrary，then，is thefirstprincipleofallthingsinthefullsense；thefirst principleissomethingdifferent。 Butthesethinkersmakeoneofthecontrariesmatter，some makingtheunequalwhichtheytaketobetheessenceof plurality-matterfortheOne，andothersmakingpluralitymatterfor theOne。(Theformergeneratenumbersoutofthedyadofthe unequal，i。e。ofthegreatandsmall，andtheotherthinkerwehave referredtogeneratesthemoutofplurality，whileaccordingtoboth itisgeneratedbytheessenceoftheOne。)Foreventhephilosopher whosaystheunequalandtheOnearetheelements，andtheunequal isadyadcomposedofthegreatandsmall，treatstheunequal，or thegreatandthesmall，asbeingone，anddoesnotdrawthe distinctionthattheyareoneindefinition，butnotinnumber。But theydonotdescriberightlyeventheprincipleswhichtheycall elements，forsomenamethegreatandthesmallwiththeOneandtreat thesethreeaselementsofnumbers，twobeingmatter，onetheform； whileothersnamethemanyandfew，becausethegreatandthesmall aremoreappropriateintheirnaturetomagnitudethantonumber； andothersnamerathertheuniversalcharactercommontothese-’that whichexceedsandthatwhichisexceeded’。Noneofthesevarieties ofopinionmakesanydifferencetospeakof，inviewofsomeofthe consequences；theyaffectonlytheabstractobjections，whichthese thinkerstakecaretoavoidbecausethedemonstrationstheythemselves offerareabstract，-withthisexception，thatiftheexceedingandthe exceededaretheprinciples，andnotthegreatandthesmall， consistencyrequiresthatnumbershouldcomefromtheelements beforedoes；fornumberismoreuniversalthanastheexceedingand theexceededaremoreuniversalthanthegreatandthesmall。Butas itis，theysayoneofthesethingsbutdonotsaytheother。Others opposethedifferentandtheothertotheOne，andothersoppose pluralitytotheOne。Butif，astheyclaim，thingsconsistof contraries，andtotheOneeitherthereisnothingcontrary，orif thereistobeanythingitisplurality，andtheunequaliscontrary totheequal，andthedifferenttothesame，andtheothertothe thingitself，thosewhoopposetheOnetopluralityhavemostclaimto plausibility，buteventheirviewisinadequate，fortheOnewould ontheirviewbeafew；forpluralityisopposedtofewness，andthe manytothefew。 ’Theone’evidentlymeansameasure。Andineverycasethereis someunderlyingthingwithadistinctnatureofitsown，e。g。inthe scaleaquarter-tone，inspatialmagnitudeafingerorafootor somethingofthesort，inrhythmsabeatorasyllable；and similarlyingravityitisadefiniteweight；andinthesamewayin allcases，inqualitiesaquality，inquantitiesaquantity(andthe measureisindivisible，intheformercaseinkind，andinthe lattertothesense)；whichimpliesthattheoneisnotinitself thesubstanceofanything。Andthisisreasonable；for’theone’means themeasureofsomeplurality，and’number’meansameasuredplurality andapluralityofmeasures。(Thusitisnaturalthatoneisnota number；forthemeasureisnotmeasures，butboththemeasureand theonearestarting-points。)Themeasuremustalwaysbesome identicalthingpredicableofallthethingsitmeasures，e。g。if thethingsarehorses，themeasureis’horse’，andiftheyaremen， ’man’。Iftheyareaman，ahorse，andagod，themeasureisperhaps ’livingbeing’，andthenumberofthemwillbeanumberofliving beings。Ifthethingsare’man’and’pale’and’walking’，thesewill scarcelyhaveanumber，becauseallbelongtoasubjectwhichisone andthesameinnumber，yetthenumberofthesewillbeanumberof ’kinds’orofsomesuchterm。 Thosewhotreattheunequalasonething，andthedyadasan indefinitecompoundofgreatandsmall，saywhatisveryfarfrom beingprobableorpossible。For(a)thesearemodificationsand accidents，ratherthansubstrata，ofnumbersandmagnitudes-themany andfewofnumber，andthegreatandsmallofmagnitude-likeeven andodd，smoothandrough，straightandcurved。Again，(b)apart fromthismistake，thegreatandthesmall，andsoon，mustbe relativetosomething；butwhatisrelativeisleastofallthingsa kindofentityorsubstance，andisposteriortoqualityandquantity； andtherelativeisanaccidentofquantity，aswassaid，notits matter，sincesomethingwithadistinctnatureofitsownmustserve asmatterbothtotherelativeingeneralandtoitspartsand kinds。Forthereisnothingeithergreatorsmall，manyorfew，or，in general，relativetosomethingelse，whichwithouthavinganature ofitsownismanyorfew，greatorsmall，orrelativetosomething else。Asignthattherelativeisleastofallasubstanceanda realthingisthefactthatitalonehasnopropergenerationor destructionormovement，asinrespectofquantitythereisincrease anddiminution，inrespectofqualityalteration，inrespectof placelocomotion，inrespectofsubstancesimplegenerationand destruction。Inrespectofrelationthereisnoproperchange；for， withoutchanging，athingwillbenowgreaterandnowlessorequal， ifthatwithwhichitiscomparedhaschangedinquantity。And(c)the matterofeachthing，andthereforeofsubstance，mustbethatwhich ispotentiallyofthenatureinquestion；buttherelativeis neitherpotentiallynoractuallysubstance。Itisstrange，then，or ratherimpossible，tomakenot-substanceanelementin，andprior to，substance；forallthecategoriesareposteriortosubstance。 Again，(d)elementsarenotpredicatedofthethingsofwhichtheyare elements，butmanyandfewarepredicatedbothapartandtogetherof number，andlongandshortoftheline，andbothbroadandnarrow applytotheplane。Ifthereisaplurality，then，ofwhichtheone term，viz。few，isalwayspredicated，e。g。2(whichcannotbemany， forifitweremany，1wouldbefew)，theremustbealsoonewhich isabsolutelymany，e。g。10ismany(ifthereisnonumberwhichis greaterthan10)，or10，000。Howthen，inviewofthis，cannumber consistoffewandmany？Eitherbothoughttobepredicatedofit， orneither；butinfactonlytheoneortheotherispredicated。 Wemustinquiregenerally，whethereternalthingscanconsistof elements。Iftheydo，theywillhavematter；foreverythingthat consistsofelementsiscomposite。Since，then，evenifathingexists forever，outofthatofwhichitconsistsitwouldnecessarily also，ifithadcomeintobeing，havecomeintobeing，andsince everythingcomestobewhatitcomestobeoutofthatwhichisit potentially(foritcouldnothavecometobeoutofthatwhichhad notthiscapacity，norcoulditconsistofsuchelements)，andsince thepotentialcanbeeitheractualornot，-thisbeingso，however everlastingnumberoranythingelsethathasmatteris，itmustbe capableofnotexisting，justasthatwhichisanynumberofyearsold isascapableofnotexistingasthatwhichisadayold；ifthisis capableofnotexisting，soisthatwhichhaslastedforatimeso longthatithasnolimit。Theycannot，then，beeternal，sincethat whichiscapableofnotexistingisnoteternal，aswehadoccasionto showinanothercontext。Ifthatwhichwearenowsayingistrue universally-thatnosubstanceiseternalunlessitisactuality-andif theelementsarematterthatunderliessubstance，noeternalsubstance canhaveelementspresentinit，ofwhichitconsists。 TherearesomewhodescribetheelementwhichactswiththeOneas anindefinitedyad，andobjectto’theunequal’，reasonablyenough， becauseoftheensuingdifficulties；buttheyhavegotridonlyof thoseobjectionswhichinevitablyarisefromthetreatmentofthe unequal，i。e。therelative，asanelement；thosewhichariseapart fromthisopinionmustconfronteventhesethinkers，whetheritis idealnumber，ormathematical，thattheyconstructoutofthose elements。 Therearemanycauseswhichledthemoffintothese explanations，andespeciallythefactthattheyframedthe difficultyinanobsoleteform。Fortheythoughtthatallthings thatarewouldbeone(viz。Beingitself)，ifonedidnotjoinissue withandrefutethesayingofParmenides: ’Forneverwillthisheproved，thatthingsthatarenotare。’ Theythoughtitnecessarytoprovethatthatwhichisnotis； foronlythus-ofthatwhichisandsomethingelse-couldthethings thatarebecomposed，iftheyaremany。 But，first，if’being’hasmanysenses(foritmeanssometimes substance，sometimesthatitisofacertainquality，sometimesthat itisofacertainquantity，andatothertimestheothercategories)， whatsortof’one’，then，areallthethingsthatare，ifnon-beingis tobesupposednottobe？Isitthesubstancesthatareone，orthe affectionsandsimilarlytheothercategoriesaswell，orall together-sothatthe’this’andthe’such’andthe’somuch’andthe othercategoriesthatindicateeachsomeoneclassofbeingwillall beone？Butitisstrange，orratherimpossible，thatthecoming intoplayofasinglethingshouldbringitaboutthatpartofthat whichisisa’this’，parta’such’，parta’somuch’，parta’here’。 Secondly，ofwhatsortofnon-beingandbeingdothethingsthat areconsist？For’nonbeing’alsohasmanysenses，since’being’has； and’notbeingaman’meansnotbeingacertainsubstance，’not beingstraight’notbeingofacertainquality，’notbeingthree cubitslong’notbeingofacertainquantity。Whatsortofbeingand non-being，then，bytheirunionpluralizethethingsthatare？This thinkermeansbythenon-beingtheunionofwhichwithbeing pluralizesthethingsthatare，thefalseandthecharacterof