第2章

5 Firstthenweobservethatsomethingsalwayscometopassinthesameway，andothersforthemostpart。Itisclearlyofneitherofthesethatchanceissaidtobethecause，norcanthe\'effectofchance\'beidentifiedwithanyofthethingsthatcometopassbynecessityandalways，orforthemostpart。Butasthereisathirdclassofeventsbesidesthesetwo-eventswhichallsayare\'bychance\'-itisplainthatthereissuchathingaschanceandspontaneity；forweknowthatthingsofthiskindareduetochanceandthatthingsduetochanceareofthiskind。 But，secondly，someeventsareforthesakeofsomething，othersnot。Again，someoftheformerclassareinaccordancewithdeliberateintention，othersnot，butbothareintheclassofthingswhichareforthesakeofsomething。Henceitisclearthatevenamongthethingswhichareoutsidethenecessaryandthenormal，therearesomeinconnexionwithwhichthephrase\'forthesakeofsomething\' isapplicable。(Eventsthatareforthesakeofsomethingincludewhatevermaybedoneasaresultofthoughtorofnature。)Thingsofthiskind，then，whentheycometopassincidentalaresaidtobe\'bychance\'。Forjustasathingissomethingeitherinvirtueofitselforincidentally，somayitbeacause。Forinstance，thehousebuildingfacultyisinvirtueofitselfthecauseofahouse，whereasthepaleorthemusicalistheincidentalcause。Thatwhichispersecauseoftheeffectisdeterminate，buttheincidentalcauseisindeterminable，forthepossibleattributesofanindividualareinnumerable。Toresumethen；whenathingofthiskindcomestopassamongeventswhichareforthesakeofsomething，itissaidtobespontaneousorbychance。(Thedistinctionbetweenthetwomustbemadelater-forthepresentitissufficientifitisplainthatbothareinthesphereofthingsdoneforthesakeofsomething。) Example:Amanisengagedincollectingsubscriptionsforafeast。 Hewouldhavegonetosuchandsuchaplaceforthepurposeofgettingthemoney，ifhehadknown。Heactuallywentthereforanotherpurposeanditwasonlyincidentallythathegothismoneybygoingthere；andthiswasnotduetothefactthathewentthereasaruleornecessarily，noristheendeffected(gettingthemoney)acausepresentinhimself-itbelongstotheclassofthingsthatareintentionalandtheresultofintelligentdeliberation。Itiswhentheseconditionsaresatisfiedthatthemanissaidtohavegone\'bychance\'。Ifhehadgoneofdeliberatepurposeandforthesakeofthis-ifhealwaysornormallywenttherewhenhewascollectingpayments-hewouldnotbesaidtohavegone\'bychance\'。 Itisclearthenthatchanceisanincidentalcauseinthesphereofthoseactionsforthesakeofsomethingwhichinvolvepurpose。 Intelligentreflection，then，andchanceareinthesamesphere，forpurposeimpliesintelligentreflection。 Itisnecessary，nodoubt，thatthecausesofwhatcomestopassbychancebeindefinite；andthatiswhychanceissupposedtobelongtotheclassoftheindefiniteandtobeinscrutabletoman，andwhyitmightbethoughtthat，inaway，nothingoccursbychance。Forallthesestatementsarecorrect，becausetheyarewellgrounded。Thingsdo，inaway，occurbychance，fortheyoccurincidentallyandchanceisanincidentalcause。Butstrictlyitisnotthecause-withoutqualification-ofanything；forinstance，ahousebuilderisthecauseofahouse；incidentally，afluteplayermaybeso。 Andthecausesoftheman\'scomingandgettingthemoney(whenhedidnotcomeforthesakeofthat)areinnumerable。Hemayhavewishedtoseesomebodyorbeenfollowingsomebodyoravoidingsomebody，ormayhavegonetoseeaspectacle。Thustosaythatchanceisathingcontrarytoruleiscorrect。For\'rule\'appliestowhatisalwaystrueortrueforthemostpart，whereaschancebelongstoathirdtypeofevent。Hence，toconclude，sincecausesofthiskindareindefinite，chancetooisindefinite。(Yetinsomecasesonemightraisethequestionwhetheranyincidentalfactmightbethecauseofthechanceoccurrence，e。g。ofhealththefreshairorthesun\'sheatmaybethecause，buthavinghadone\'shaircutcannot；forsomeincidentalcausesaremorerelevanttotheeffectthanothers。) Chanceorfortuneiscalled\'good\'whentheresultisgood，\'evil\' whenitisevil。Theterms\'goodfortune\'and\'illfortune\'areusedwheneitherresultisofconsiderablemagnitude。Thusonewhocomeswithinanaceofsomegreatevilorgreatgoodissaidtobefortunateorunfortunate。Themindaffirmstheessenceoftheattribute，ignoringthehair\'sbreadthofdifference。Further，itiswithreasonthatgoodfortuneisregardedasunstable；forchanceisunstable，asnoneofthethingswhichresultfromitcanbeinvariableornormal。 Botharethen，asIhavesaid，incidentalcauses-bothchanceandspontaneity-inthesphereofthingswhicharecapableofcomingtopassnotnecessarily，nornormally，andwithreferencetosuchoftheseasmightcometopassforthesakeofsomething。 6 Theydifferinthat\'spontaneity\'isthewiderterm。Everyresultofchanceisfromwhatisspontaneous，butnoteverythingthatisfromwhatisspontaneousisfromchance。 Chanceandwhatresultsfromchanceareappropriatetoagentsthatarecapableofgoodfortuneandofmoralactiongenerally。Thereforenecessarilychanceisinthesphereofmoralactions。Thisisindicatedbythefactthatgoodfortuneisthoughttobethesame，ornearlythesame，ashappiness，andhappinesstobeakindofmoralaction，sinceitiswell-doing。Hencewhatisnotcapableofmoralactioncannotdoanythingbychance。Thusaninanimatethingoraloweranimalorachildcannotdoanythingbychance，becauseitisincapableofdeliberateintention；norcan\'goodfortune\'or\'illfortune\'beascribedtothem，exceptmetaphorically，asProtarchus，forexample，saidthatthestonesofwhichaltarsaremadearefortunatebecausetheyareheldinhonour，whiletheirfellowsaretroddenunderfoot。Eventhesethings，however，caninawaybeaffectedbychance，whenonewhoisdealingwiththemdoessomethingtothembychance，butnototherwise。 Thespontaneousontheotherhandisfoundbothintheloweranimalsandinmanyinanimateobjects。Wesay，forexample，thatthehorsecame\'spontaneously\'，because，thoughhiscomingsavedhim，hedidnotcomeforthesakeofsafety。Again，thetripodfell\'ofitself\'，because，thoughwhenitfellitstoodonitsfeetsoastoserveforaseat，itdidnotfallforthesakeofthat。 Henceitisclearthateventswhich(1)belongtothegeneralclassofthingsthatmaycometopassforthesakeofsomething，(2) donotcometopassforthesakeofwhatactuallyresults，and(3) haveanexternalcause，maybedescribedbythephrase\'fromspontaneity\'。These\'spontaneous\'eventsaresaidtobe\'fromchance\'iftheyhavethefurthercharacteristicsofbeingtheobjectsofdeliberateintentionandduetoagentscapableofthatmodeofaction。Thisisindicatedbythephrase\'invain\'，whichisusedwhenAwhichisforthesakeofB，doesnotresultinB。Forinstance，takingawalkisforthesakeofevacuationofthebowels；ifthisdoesnotfollowafterwalking，wesaythatwehavewalked\'invain\' andthatthewalkingwas\'vain\'。Thisimpliesthatwhatisnaturallythemeanstoanendis\'invain\'，whenitdoesnoteffecttheendtowardswhichitwasthenaturalmeans-foritwouldbeabsurdforamantosaythathehadbathedinvainbecausethesunwasnoteclipsed，sincetheonewasnotdonewithaviewtotheother。Thusthespontaneousisevenaccordingtoitsderivationthecaseinwhichthethingitselfhappensinvain。Thestonethatstruckthemandidnotfallforthepurposeofstrikinghim；thereforeitfellspontaneously，becauseitmighthavefallenbytheactionofanagentandforthepurposeofstriking。Thedifferencebetweenspontaneityandwhatresultsbychanceisgreatestinthingsthatcometobebynature；forwhenanythingcomestobecontrarytonature，wedonotsaythatitcametobebychance，butbyspontaneity。Yetstrictlythistooisdifferentfromthespontaneousproper；forthecauseofthelatterisexternal，thatoftheformerinternal。 Wehavenowexplainedwhatchanceisandwhatspontaneityis，andinwhattheydifferfromeachother。Bothbelongtothemodeofcausation\'sourceofchange\'，foreithersomenaturalorsomeintelligentagentisalwaysthecause；butinthissortofcausationthenumberofpossiblecausesisinfinite。 Spontaneityandchancearecausesofeffectswhichthoughtheymightresultfromintelligenceornature，haveinfactbeencausedbysomethingincidentally。Nowsincenothingwhichisincidentalispriortowhatisperse，itisclearthatnoincidentalcausecanbepriortoacauseperse。Spontaneityandchance，therefore，areposteriortointelligenceandnature。Hence，howevertrueitmaybethattheheavensareduetospontaneity，itwillstillbetruethatintelligenceandnaturewillbepriorcausesofthisAllandofmanythingsinitbesides。 7 Itisclearthenthattherearecauses，andthatthenumberofthemiswhatwehavestated。Thenumberisthesameasthatofthethingscomprehendedunderthequestion\'why\'。The\'why\'isreferredultimatelyeither(1)，inthingswhichdonotinvolvemotion，e。g。 inmathematics，tothe\'what\'(tothedefinitionof\'straightline\'or\'commensurable\'，&c。)，or(2)towhatinitiatedamotion，e。g。\'whydidtheygotowar?-becausetherehadbeenaraid\'；or(3)weareinquiring\'forthesakeofwhat?\'-\'thattheymayrule\'；or(4)，inthecaseofthingsthatcomeintobeing，wearelookingforthematter。 Thecauses，therefore，aretheseandsomanyinnumber。 Now，thecausesbeingfour，itisthebusinessofthephysicisttoknowaboutthemall，andifherefershisproblemsbacktoallofthem，hewillassignthe\'why\'inthewaypropertohisscience-thematter，theform，themover，\'thatforthesakeofwhich\'。Thelastthreeoftencoincide；forthe\'what\'and\'thatforthesakeofwhich\'areone，whiletheprimarysourceofmotionisthesameinspeciesasthese(formangeneratesman)，andsotoo，ingeneral，areallthingswhichcausemovementbybeingthemselvesmoved；andsuchasarenotofthiskindarenolongerinsidetheprovinceofphysics，fortheycausemotionnotbypossessingmotionorasourceofmotioninthemselves，butbeingthemselvesincapableofmotion。 Hencetherearethreebranchesofstudy，oneofthingswhichareincapableofmotion，thesecondofthingsinmotion，butindestructible，thethirdofdestructiblethings。 Thequestion\'why\'，then，isansweredbyreferencetothematter，totheform，andtotheprimarymovingcause。Forinrespectofcomingtobeitismostlyinthislastwaythatcausesareinvestigated-\'whatcomestobeafterwhat?whatwastheprimaryagentorpatient?\'andsoateachstepoftheseries。 Nowtheprincipleswhichcausemotioninaphysicalwayaretwo，ofwhichoneisnotphysical，asithasnoprincipleofmotioninitself。Ofthiskindiswhatevercausesmovement，notbeingitselfmoved，suchas(1)thatwhichiscompletelyunchangeable，theprimaryreality，and(2)theessenceofthatwhichiscomingtobe，i。e。theform；forthisistheendor\'thatforthesakeofwhich\'。 Hencesincenatureisforthesakeofsomething，wemustknowthiscausealso。Wemustexplainthe\'why\'inallthesensesoftheterm，namely，(1)thatfromthisthatwillnecessarilyresult(\'fromthis\' eitherwithoutqualificationorinmostcases)；(2)that\'thismustbesoifthatistobeso\'(astheconclusionpresupposesthepremisses)； (3)thatthiswastheessenceofthething；and(4)becauseitisbetterthus(notwithoutqualification，butwithreferencetotheessentialnatureineachcase)。 8 Wemustexplainthen(1)thatNaturebelongstotheclassofcauseswhichactforthesakeofsomething；(2)aboutthenecessaryanditsplaceinphysicalproblems，forallwritersascribethingstothiscause，arguingthatsincethehotandthecold，&c。，areofsuchandsuchakind，thereforecertainthingsnecessarilyareandcometobe-andiftheymentionanyothercause(onehis\'friendshipandstrife\'，anotherhis\'mind\')，itisonlytotouchonit，andthengood-byetoit。 Adifficultypresentsitself:whyshouldnotnaturework，notforthesakeofsomething，norbecauseitisbetterso，butjustastheskyrains，notinordertomakethecorngrow，butofnecessity? Whatisdrawnupmustcool，andwhathasbeencooledmustbecomewateranddescend，theresultofthisbeingthatthecorngrows。Similarlyifaman\'scropisspoiledonthethreshing-floor，theraindidnotfallforthesakeofthis-inorderthatthecropmightbespoiled-butthatresultjustfollowed。Whythenshoulditnotbethesamewiththepartsinnature，e。g。thatourteethshouldcomeupofnecessity-thefrontteethsharp，fittedfortearing，themolarsbroadandusefulforgrindingdownthefood-sincetheydidnotariseforthisend，butitwasmerelyacoincidentresult；andsowithallotherpartsinwhichwesupposethatthereispurpose?Whereverthenallthepartscameaboutjustwhattheywouldhavebeeniftheyhadcomebeforanend，suchthingssurvived，beingorganizedspontaneouslyinafittingway；whereasthosewhichgrewotherwiseperishedandcontinuetoperish，asEmpedoclessayshis\'man-facedox-progeny\'did。 Sucharethearguments(andothersofthekind)whichmaycausedifficultyonthispoint。Yetitisimpossiblethatthisshouldbethetrueview。Forteethandallothernaturalthingseitherinvariablyornormallycomeaboutinagivenway；butofnotoneoftheresultsofchanceorspontaneityisthistrue。Wedonotascribetochanceormerecoincidencethefrequencyofraininwinter，butfrequentraininsummerwedo；norheatinthedog-days，butonlyifwehaveitinwinter。Ifthen，itisagreedthatthingsareeithertheresultofcoincidenceorforanend，andthesecannotbetheresultofcoincidenceorspontaneity，itfollowsthattheymustbeforanend； andthatsuchthingsareallduetonatureeventhechampionsofthetheorywhichisbeforeuswouldagree。Thereforeactionforanendispresentinthingswhichcometobeandarebynature。 Further，whereaserieshasacompletion，alltheprecedingstepsareforthesakeofthat。Nowsurelyasinintelligentaction，soinnature；andasinnature，soitisineachaction，ifnothinginterferes。Nowintelligentactionisforthesakeofanend； thereforethenatureofthingsalsoisso。Thusifahouse，e。g。hadbeenathingmadebynature，itwouldhavebeenmadeinthesamewayasitisnowbyart；andifthingsmadebynatureweremadealsobyart，theywouldcometobeinthesamewayasbynature。Eachstepthenintheseriesisforthesakeofthenext；andgenerallyartpartlycompleteswhatnaturecannotbringtoafinish，andpartlyimitatesher。If，therefore，artificialproductsareforthesakeofanend，soclearlyalsoarenaturalproducts。Therelationofthelatertotheearliertermsoftheseriesisthesameinboth。Thisismostobviousintheanimalsotherthanman:theymakethingsneitherbyartnorafterinquiryordeliberation。Whereforepeoplediscusswhetheritisbyintelligenceorbysomeotherfacultythatthesecreatureswork，spiders，ants，andthelike。Bygradualadvanceinthisdirectionwecometoseeclearlythatinplantstoothatisproducedwhichisconducivetotheend-leaves，e。g。growtoprovideshadeforthefruit。Ifthenitisbothbynatureandforanendthattheswallowmakesitsnestandthespideritsweb，andplantsgrowleavesforthesakeofthefruitandsendtheirrootsdown(notup)forthesakeofnourishment，itisplainthatthiskindofcauseisoperativeinthingswhichcometobeandarebynature。Andsince\'nature\'meanstwothings，thematterandtheform，ofwhichthelatteristheend，andsincealltherestisforthesakeoftheend，theformmustbethecauseinthesenseof\'thatforthesakeofwhich\'。 Nowmistakescometopassevenintheoperationsofart:thegrammarianmakesamistakeinwritingandthedoctorpoursoutthewrongdose。Henceclearlymistakesarepossibleintheoperationsofnaturealso。Iftheninarttherearecasesinwhichwhatisrightlyproducedservesapurpose，andifwheremistakesoccurtherewasapurposeinwhatwasattempted，onlyitwasnotattained，somustitbealsoinnaturalproducts，andmonstrositieswillbefailuresinthepurposiveeffort。Thusintheoriginalcombinationsthe\'ox-progeny\' iftheyfailedtoreachadeterminateendmusthavearisenthroughthecorruptionofsomeprinciplecorrespondingtowhatisnowtheseed。 Further，seedmusthavecomeintobeingfirst，andnotstraightwaytheanimals:thewords\'whole-naturedfirst……\'musthavemeantseed。 Again，inplantstoowefindtherelationofmeanstoend，thoughthedegreeoforganizationisless。Weretheretheninplantsalso\'olive-headedvine-progeny\'，likethe\'man-headedox-progeny\'，ornot? Anabsurdsuggestion；yettheremusthavebeen，ifthereweresuchthingsamonganimals。 Moreover，amongtheseedsanythingmusthavecometobeatrandom。 Butthepersonwhoassertsthisentirelydoesawaywith\'nature\'andwhatexists\'bynature\'。Forthosethingsarenaturalwhich，byacontinuousmovementoriginatedfromaninternalprinciple，arriveatsomecompletion:thesamecompletionisnotreachedfromeveryprinciple；noranychancecompletion，butalwaysthetendencyineachistowardsthesameend，ifthereisnoimpediment。 Theendandthemeanstowardsitmaycomeaboutbychance。Wesay，forinstance，thatastrangerhascomebychance，paidtheransom，andgoneaway，whenhedoessoasifhehadcomeforthatpurpose，thoughitwasnotforthatthathecame。Thisisincidental，forchanceisanincidentalcause，asIremarkedbefore。Butwhenaneventtakesplacealwaysorforthemostpart，itisnotincidentalorbychance。Innaturalproductsthesequenceisinvariable，ifthereisnoimpediment。 Itisabsurdtosupposethatpurposeisnotpresentbecausewedonotobservetheagentdeliberating。Artdoesnotdeliberate。Iftheship-buildingartwereinthewood，itwouldproducethesameresultsbynature。If，therefore，purposeispresentinart，itispresentalsoinnature。Thebestillustrationisadoctordoctoringhimself:natureislikethat。 Itisplainthenthatnatureisacause，acausethatoperatesforapurpose。 9 Asregardswhatis\'ofnecessity\'，wemustaskwhetherthenecessityis\'hypothetical\'，or\'simple\'aswell。Thecurrentviewplaceswhatisofnecessityintheprocessofproduction，justasifoneweretosupposethatthewallofahousenecessarilycomestobebecausewhatisheavyisnaturallycarrieddownwardsandwhatislighttothetop，whereforethestonesandfoundationstakethelowestplace，withearthabovebecauseitislighter，andwoodatthetopofallasbeingthelightest。Whereas，thoughthewalldoesnotcometobewithoutthese，itisnotduetothese，exceptasitsmaterialcause: itcomestobeforthesakeofshelteringandguardingcertainthings。 Similarlyinallotherthingswhichinvolveproductionforanend；theproductcannotcometobewithoutthingswhichhaveanecessarynature，butitisnotduetothese(exceptasitsmaterial)；itcomestobeforanend。Forinstance，whyisasawsuchasitis?Toeffectso-and-soandforthesakeofso-and-so。Thisend，however，cannotberealizedunlessthesawismadeofiron。Itis，therefore，necessaryforittobeofiron，itwearetohaveasawandperformtheoperationofsawing。Whatisnecessarythen，isnecessaryonahypothesis；itisnotaresultnecessarilydeterminedbyantecedents。Necessityisinthematter，while\'thatforthesakeofwhich\'isinthedefinition。 Necessityinmathematicsisinawaysimilartonecessityinthingswhichcometobethroughtheoperationofnature。Sinceastraightlineiswhatitis，itisnecessarythattheanglesofatriangleshouldequaltworightangles。Butnotconversely；thoughiftheanglesarenotequaltotworightangles，thenthestraightlineisnotwhatitiseither。Butinthingswhichcometobeforanend，thereverseistrue。Iftheendistoexistordoesexist，thatalsowhichprecedesitwillexistordoesexist；otherwisejustasthere，if-theconclusionisnottrue，thepremisswillnotbetrue，soheretheendor\'thatforthesakeofwhich\'willnotexist。Forthistooisitselfastarting-point，butofthereasoning，notoftheaction；whileinmathematicsthestarting-pointisthestarting-pointofthereasoningonly，asthereisnoaction。Ifthenthereistobeahouse，such-and-suchthingsmustbemadeorbetherealreadyorexist，orgenerallythematterrelativetotheend，bricksandstonesifitisahouse。Buttheendisnotduetotheseexceptasthematter，norwillitcometoexistbecauseofthem。Yetiftheydonotexistatall，neitherwillthehouse，orthesaw-theformerintheabsenceofstones，thelatterintheabsenceofiron-justasintheothercasethepremisseswillnotbetrue，iftheanglesofthetrianglearenotequaltotworightangles。 Thenecessaryinnature，then，isplainlywhatwecallbythenameofmatter，andthechangesinit。Bothcausesmustbestatedbythephysicist，butespeciallytheend；forthatisthecauseofthematter，notviceversa；andtheendis\'thatforthesakeofwhich\'，andthebeginningstartsfromthedefinitionoressence；asinartificialproducts，sinceahouseisofsuch-and-suchakind，certainthingsmustnecessarilycometobeorbetherealready，orsincehealthisthis，thesethingsmustnecessarilycometobeorbetherealready。Similarlyifmanisthis，thenthese；ifthese，thenthose。 Perhapsthenecessaryispresentalsointhedefinition。Forifonedefinestheoperationofsawingasbeingacertainkindofdividing，thenthiscannotcomeaboutunlessthesawhasteethofacertainkind；andthesecannotbeunlessitisofiron。Forinthedefinitiontootherearesomepartsthatare，asitwere，itsmatter。 BookIII 1 NATUREhasbeendefinedasa\'principleofmotionandchange\'，anditisthesubjectofourinquiry。Wemustthereforeseethatweunderstandthemeaningof\'motion\'；forifitwereunknown，themeaningof\'nature\'toowouldbeunknown。 Whenwehavedeterminedthenatureofmotion，ournexttaskwillbetoattackinthesamewaythetermswhichareinvolvedinit。Nowmotionissupposedtobelongtotheclassofthingswhicharecontinuous；andtheinfinitepresentsitselffirstinthecontinuous-thatishowitcomesaboutthat\'infinite\'isoftenusedindefinitionsofthecontinuous(\'whatisinfinitelydivisibleiscontinuous\')。Besidesthese，place，void，andtimearethoughttobenecessaryconditionsofmotion。 Clearly，then，forthesereasonsandalsobecausetheattributesmentionedarecommonto，andcoextensivewith，alltheobjectsofourscience，wemustfirsttakeeachoftheminhandanddiscussit。 Fortheinvestigationofspecialattributescomesafterthatofthecommonattributes。 Tobeginthen，aswesaid，withmotion。 Wemaystartbydistinguishing(1)whatexistsinastateoffulfilmentonly，(2)whatexistsaspotential，(3)whatexistsaspotentialandalsoinfulfilment-onebeinga\'this\'，another\'somuch\'，athird\'such\'，andsimilarlyineachoftheothermodesofthepredicationofbeing。 Further，theword\'relative\'isusedwithreferenceto(1)excessanddefect，(2)agentandpatientandgenerallywhatcanmoveandwhatcanbemoved。For\'whatcancausemovement\'isrelativeto\'whatcanbemoved\'，andviceversa。 Again，thereisnosuchthingasmotionoverandabovethethings。 Itisalwayswithrespecttosubstanceortoquantityortoqualityortoplacethatwhatchangeschanges。Butitisimpossible，asweassert，tofindanythingcommontothesewhichisneither\'this\'norquantumnorqualenoranyoftheotherpredicates。Henceneitherwillmotionandchangehavereferencetosomethingoverandabovethethingsmentioned，forthereisnothingoverandabovethem。 Noweachofthesebelongstoallitssubjectsineitheroftwoways: namely(1)substance-theoneispositiveform，theotherprivation； (2)inquality，whiteandblack；(3)inquantity，completeandincomplete；(4)inrespectoflocomotion，upwardsanddownwardsorlightandheavy。Hencethereareasmanytypesofmotionorchangeastherearemeaningsoftheword\'is\'。 Wehavenowbeforeusthedistinctionsinthevariousclassesofbeingbetweenwhatisfullrealandwhatispotential。 Def。Thefulfilmentofwhatexistspotentially，insofarasitexistspotentially，ismotion-namely，ofwhatisalterablequaalterable，alteration:ofwhatcanbeincreasedanditsoppositewhatcanbedecreased(thereisnocommonname)，increaseanddecrease:ofwhatcancometobeandcanpassaway，comingtoheandpassingaway:ofwhatcanbecarriedalong，locomotion。 Exampleswillelucidatethisdefinitionofmotion。Whenthebuildable，insofarasitisjustthat，isfullyreal，itisbeingbuilt，andthisisbuilding。Similarly，learning，doctoring，rolling，leaping，ripening，ageing。 Thesamething，ifitisofacertainkind，canbebothpotentialandfullyreal，notindeedatthesametimeornotinthesamerespect，bute。g。potentiallyhotandactuallycold。Henceatoncesuchthingswillactandbeactedonbyoneanotherinmanyways:eachofthemwillbecapableatthesametimeofcausingalterationandofbeingaltered。Hence，too，whateffectsmotionasaphysicalagentcanbemoved:whenathingofthiskindcausesmotion，itisitselfalsomoved。This，indeed，hasledsomepeopletosupposethateverymoverismoved。Butthisquestiondependsonanothersetofarguments，andthetruthwillbemadeclearlater。ispossibleforathingtocausemotion，thoughitisitselfincapableofbeingmoved。 Itisthefulfilmentofwhatispotentialwhenitisalreadyfullyrealandoperatesnotasitselfbutasmovable，thatismotion。WhatI meanby\'as\'isthis:Bronzeispotentiallyastatue。Butitisnotthefulfilmentofbronzeasbronzewhichismotion。For\'tobebronze\' and\'tobeacertainpotentiality\'arenotthesame。 Iftheywereidenticalwithoutqualification，i。e。indefinition，thefulfilmentofbronzeasbronzewouldhavebeenmotion。Buttheyarenotthesame，ashasbeensaid。(Thisisobviousincontraries。 \'Tobecapableofhealth\'and\'tobecapableofillness\'arenotthesame，foriftheyweretherewouldbenodifferencebetweenbeingillandbeingwell。Yetthesubjectbothofhealthandofsickness-whetheritishumourorblood-isoneandthesame。) Wecandistinguish，then，betweenthetwo-justas，togiveanotherexample，\'colour\'andvisible\'aredifferent-andclearlyitisthefulfilmentofwhatispotentialaspotentialthatismotion。Sothis，precisely，ismotion。 Furtheritisevidentthatmotionisanattributeofathingjustwhenitisfullyrealinthisway，andneitherbeforenorafter。Foreachthingofthiskindiscapableofbeingatonetimeactual，atanothernot。Takeforinstancethebuildableasbuildable。Theactualityofthebuildableasbuildableistheprocessofbuilding。 Fortheactualityofthebuildablemustbeeitherthisorthehouse。 Butwhenthereisahouse，thebuildableisnolongerbuildable。Ontheotherhand，itisthebuildablewhichisbeingbuilt。TheprocessthenofbeingbuiltmustbethekindofactualityrequiredButbuildingisakindofmotion，andthesameaccountwillapplytotheotherkindsalso。 2 Thesoundnessofthisdefinitionisevidentbothwhenweconsidertheaccountsofmotionthattheothershavegiven，andalsofromthedifficultyofdefiningitotherwise。 Onecouldnoteasilyputmotionandchangeinanothergenus-thisisplainifweconsiderwheresomepeopleputit；theyidentifymotionwithor\'inequality\'or\'notbeing\'；butsuchthingsarenotnecessarilymoved，whethertheyare\'different\'or\'unequal\'or\'non-existent\'；Norischangeeithertoorfromtheseratherthantoorfromtheiropposites。 Thereasonwhytheyputmotionintothesegeneraisthatitisthoughttobesomethingindefinite，andtheprinciplesinthesecondcolumnareindefinitebecausetheyareprivative:noneofthemiseither\'this\'or\'such\'orcomesunderanyoftheothermodesofpredication。Thereasoninturnwhymotionisthoughttobeindefiniteisthatitcannotbeclassedsimplyasapotentialityorasanactuality-athingthatismerelycapableofhavingacertainsizeisnotundergoingchange，noryetathingthatisactuallyofacertainsize，andmotionisthoughttobeasortofactuality，butincomplete，thereasonforthisviewbeingthatthepotentialwhoseactualityitisisincomplete。Thisiswhyitishardtograspwhatmotionis。Itisnecessarytoclassitwithprivationorwithpotentialityorwithsheeractuality，yetnoneoftheseseemspossible。Thereremainsthenthesuggestedmodeofdefinition，namelythatitisasortofactuality，oractualityofthekinddescribed，hardtograsp，butnotincapableofexisting。 Themovertooismoved，ashasbeensaid-everymover，thatis，whichiscapableofmotion，andwhoseimmobilityisrest-whenathingissubjecttomotionitsimmobilityisrest。Fortoactonthemovableassuchisjusttomoveit。Butthisitdoesbycontact，sothatatthesametimeitisalsoactedon。Hencewecandefinemotionasthefulfilmentofthemovablequamovable，thecauseoftheattributebeingcontactwithwhatcanmovesothatthemoverisalsoactedon。 Themoveroragentwillalwaysbethevehicleofaform，eithera\'this\'or\'such\'，which，whenitacts，willbethesourceandcauseofthechange，e。g。thefull-formedmanbegetsmanfromwhatispotentiallyman。 3 Thesolutionofthedifficultythatisraisedaboutthemotion-whetheritisinthemovable-isplain。Itisthefulfilmentofthispotentiality，andbytheactionofthatwhichhasthepowerofcausingmotion；andtheactualityofthatwhichhasthepowerofcausingmotionisnototherthantheactualityofthemovable，foritmustbethefulfilmentofboth。Athingiscapableofcausingmotionbecauseitcandothis，itisamoverbecauseitactuallydoesit。Butitisonthemovablethatitiscapableofacting。 Hencethereisasingleactualityofbothalike，justasonetotwoandtwotoonearethesameinterval，andthesteepascentandthesteepdescentareone-fortheseareoneandthesame，althoughtheycanbedescribedindifferentways。Soitiswiththemoverandthemoved。 Thisviewhasadialecticaldifficulty。Perhapsitisnecessarythattheactualityoftheagentandthatofthepatientshouldnotbethesame。Theoneis\'agency\'andtheother\'patiency\'；andtheoutcomeandcompletionoftheoneisan\'action\'，thatoftheothera\'passion\'。Sincethentheyarebothmotions，wemayask:inwhatarethey，iftheyaredifferent?Either(a)bothareinwhatisactedonandmoved，or(b)theagencyisintheagentandthepatiencyinthepatient。(Ifweoughttocallthelatteralso\'agency\'，thewordwouldbeusedintwosenses。) Now，inalternative(b)，themotionwillbeinthemover，forthesamestatementwillholdof\'mover\'and\'moved\'。Henceeithereverymoverwillbemoved，or，thoughhavingmotion，itwillnotbemoved。 Ifontheotherhand(a)bothareinwhatismovedandactedon-boththeagencyandthepatiency(e。g。bothteachingandlearning，thoughtheyaretwo，inthelearner)，then，first，theactualityofeachwillnotbepresentineach，and，asecondabsurdity，athingwillhavetwomotionsatthesametime。Howwilltherebetwoalterationsofqualityinonesubjecttowardsonedefinitequality?Thethingisimpossible:theactualizationwillbeone。 But(someonewillsay)itiscontrarytoreasontosupposethatthereshouldbeoneidenticalactualizationoftwothingswhicharedifferentinkind。Yettherewillbe，ifteachingandlearningarethesame，andagencyandpatiency。Toteachwillbethesameastolearn，andtoactthesameastobeactedon-theteacherwillnecessarilybelearningeverythingthatheteaches，andtheagentwillbeactedon。Onemayreply: (1)Itisnotabsurdthattheactualizationofonethingshouldbeinanother。Teachingistheactivityofapersonwhocanteach，yettheoperationisperformedonsomepatient-itisnotcutadriftfromasubject，butisofAonB。 (2)Thereisnothingtopreventtwothingshavingoneandthesameactualization，providedtheactualizationsarenotdescribedinthesameway，butarerelatedaswhatcanacttowhatisacting。 (3)Norisitnecessarythattheteachershouldlearn，eveniftoactandtobeactedonareoneandthesame，providedtheyarenotthesameindefinition(as\'raiment\'and\'dress\')，butarethesamemerelyinthesenseinwhichtheroadfromThebestoAthensandtheroadfromAthenstoThebesarethesame，ashasbeenexplainedabove。Foritisnotthingswhichareinawaythesamethathavealltheirattributesthesame，butonlysuchashavethesamedefinition。Butindeeditbynomeansfollowsfromthefactthatteachingisthesameaslearning，thattolearnisthesameastoteach，anymorethanitfollowsfromthefactthatthereisonedistancebetweentwothingswhichareatadistancefromeachother，thatthetwovectorsABandBA，areoneandthesame。Togeneralize，teachingisnotthesameaslearning，oragencyaspatiency，inthefullsense，thoughtheybelongtothesamesubject，themotion；forthe\'actualizationofXinY\'andthe\'actualizationofYthroughtheactionofX\'differindefinition。 WhatthenMotionis，hasbeenstatedbothgenerallyandparticularly。Itisnotdifficulttoseehoweachofitstypeswillbedefined-alterationisthefulfillmentofthealterablequaalterable(or，morescientifically，thefulfilmentofwhatcanactandwhatcanbeactedon，assuch)-generallyandagainineachparticularcase，building，healing，&c。Asimilardefinitionwillapplytoeachoftheotherkindsofmotion。 4 Thescienceofnatureisconcernedwithspatialmagnitudesandmotionandtime，andeachoftheseatleastisnecessarilyinfiniteorfinite，evenifsomethingsdealtwithbythesciencearenot，e。g。 aqualityorapoint-itisnotnecessaryperhapsthatsuchthingsshouldbeputundereitherhead。Henceitisincumbentonthepersonwhospecializesinphysicstodiscusstheinfiniteandtoinquirewhetherthereissuchathingornot，and，ifthereis，whatitis。 Theappropriatenesstothescienceofthisproblemisclearlyindicated。Allwhohavetouchedonthiskindofscienceinawayworthconsideringhaveformulatedviewsabouttheinfinite，andindeed，toaman，makeitaprincipleofthings。 (1)Some，asthePythagoreansandPlato，maketheinfiniteaprincipleinthesenseofaself-subsistentsubstance，andnotasamereattributeofsomeotherthing。OnlythePythagoreansplacetheinfiniteamongtheobjectsofsense(theydonotregardnumberasseparablefromthese)，andassertthatwhatisoutsidetheheavenisinfinite。Plato，ontheotherhand，holdsthatthereisnobodyoutside(theFormsarenotoutsidebecausetheyarenowhere)，yetthattheinfiniteispresentnotonlyintheobjectsofsensebutintheFormsalso。 Further，thePythagoreansidentifytheinfinitewiththeeven。Forthis，theysay，whenitiscutoffandshutinbytheodd，providesthingswiththeelementofinfinity。Anindicationofthisiswhathappenswithnumbers。Ifthegnomonsareplacedroundtheone，andwithouttheone，intheoneconstructionthefigurethatresultsisalwaysdifferent，intheotheritisalwaysthesame。ButPlatohastwoinfinites，theGreatandtheSmall。 Thephysicists，ontheotherhand，allofthem，alwaysregardtheinfiniteasanattributeofasubstancewhichisdifferentfromitandbelongstotheclassoftheso-calledelements-waterorairorwhatisintermediatebetweenthem。Thosewhomakethemlimitedinnumbernevermaketheminfiniteinamount。Butthosewhomaketheelementsinfiniteinnumber，asAnaxagorasandDemocritusdo，saythattheinfiniteiscontinuousbycontact-compoundedofthehomogeneouspartsaccordingtotheone，oftheseed-massoftheatomicshapesaccordingtotheother。 Further，AnaxagorasheldthatanypartisamixtureinthesamewayastheAll，onthegroundoftheobservedfactthatanythingcomesoutofanything。Foritisprobablyforthisreasonthathemaintainsthatonceuponatimeallthingsweretogether。(Thisfleshandthisboneweretogether，andsoofanything:thereforeallthings:andatthesametimetoo。)Forthereisabeginningofseparation，notonlyforeachthing，butforall。Eachthingthatcomestobecomesfromasimilarbody，andthereisacomingtobeofallthings，thoughnot，itistrue，atthesametime。Hencetheremustalsobeanoriginofcomingtobe。OnesuchsourcethereiswhichhecallsMind，andMindbeginsitsworkofthinkingfromsomestarting-point。Sonecessarilyallthingsmusthavebeentogetheratacertaintime，andmusthavebeguntobemovedatacertaintime。 Democritus，forhispart，assertsthecontrary，namelythatnoelementarisesfromanotherelement。Neverthelessforhimthecommonbodyisasourceofallthings，differingfromparttopartinsizeandinshape。 Itisclearthenfromtheseconsiderationsthattheinquiryconcernsthephysicist。Norisitwithoutreasonthattheyallmakeitaprincipleorsource。Wecannotsaythattheinfinitehasnoeffect，andtheonlyeffectivenesswhichwecanascribetoitisthatofaprinciple。Everythingiseitherasourceorderivedfromasource。Buttherecannotbeasourceoftheinfiniteorlimitless，forthatwouldbealimitofit。Further，asitisabeginning，itisbothuncreatableandindestructible。Fortheremustbeapointatwhichwhathascometobereachescompletion，andalsoaterminationofallpassingaway。Thatiswhy，aswesay，thereisnoprincipleofthis，butitisthiswhichisheldtobetheprincipleofotherthings，andtoencompassallandtosteerall，asthoseassertwhodonotrecognize，alongsidetheinfinite，othercauses，suchasMindorFriendship。FurthertheyidentifyitwiththeDivine，foritis\'deathlessandimperishable\'asAnaximandersays，withthemajorityofthephysicists。 Beliefintheexistenceoftheinfinitecomesmainlyfromfiveconsiderations: (1)Fromthenatureoftime-foritisinfinite。 (2)Fromthedivisionofmagnitudes-forthemathematiciansalsousethenotionoftheinfinite。 (3)Ifcomingtobeandpassingawaydonotgiveout，itisonlybecausethatfromwhichthingscometobeisinfinite。 (4)Becausethelimitedalwaysfindsitslimitinsomething，sothattheremustbenolimit，ifeverythingisalwayslimitedbysomethingdifferentfromitself。 (5)Mostofall，areasonwhichispeculiarlyappropriateandpresentsthedifficultythatisfeltbyeverybody-notonlynumberbutalsomathematicalmagnitudesandwhatisoutsidetheheavenaresupposedtobeinfinitebecausetheynevergiveoutinourthought。 Thelastfact(thatwhatisoutsideisinfinite)leadspeopletosupposethatbodyalsoisinfinite，andthatthereisaninfinitenumberofworlds。Whyshouldtherebebodyinonepartofthevoidratherthaninanother?Grantonlythatmassisanywhereanditfollowsthatitmustbeeverywhere。Also，ifvoidandplaceareinfinite，theremustbeinfinitebodytoo，forinthecaseofeternalthingswhatmaybemustbe。Buttheproblemoftheinfiniteisdifficult:manycontradictionsresultwhetherwesupposeittoexistornottoexist。Ifitexists，wehavestilltoaskhowitexists； asasubstanceorastheessentialattributeofsomeentity?Orinneitherway，yetnonethelessistheresomethingwhichisinfiniteorsomethingswhichareinfinitelymany? Theproblem，however，whichspeciallybelongstothephysicististoinvestigatewhetherthereisasensiblemagnitudewhichisinfinite。 Wemustbeginbydistinguishingthevarioussensesinwhichtheterm\'infinite\'isused。 (1)Whatisincapableofbeinggonethrough，becauseitisnotinitsnaturetobegonethrough(thesenseinwhichthevoiceis\'invisible\')。 (2)Whatadmitsofbeinggonethrough，theprocesshoweverhavingnotermination，orwhatscarcelyadmitsofbeinggonethrough。 (3)Whatnaturallyadmitsofbeinggonethrough，butisnotactuallygonethroughordoesnotactuallyreachanend。 Further，everythingthatisinfinitemaybesoinrespectofadditionordivisionorboth。 5 Nowitisimpossiblethattheinfiniteshouldbeathingwhichisitselfinfinite，separablefromsensibleobjects。Iftheinfiniteisneitheramagnitudenoranaggregate，butisitselfasubstanceandnotanattribute，itwillbeindivisible；forthedivisiblemustbeeitheramagnitudeoranaggregate。Butifindivisible，thennotinfinite，exceptinthesense(1)inwhichthevoiceis\'invisible\'。 Butthisisnotthesenseinwhichitisusedbythosewhosaythattheinfiniteexists，northatinwhichweareinvestigatingit，namelyas(2)\'thatwhichcannotbegonethrough\'。Butiftheinfiniteexistsasanattribute，itwouldnotbe，quainfiniteanelementinsubstances，anymorethantheinvisiblewouldbeanelementofspeech，thoughthevoiceisinvisible。 Further，howcantheinfinitebeitselfanything，unlessbothnumberandmagnitude，ofwhichitisanessentialattribute，existinthatway?Iftheyarenotsubstances，afortioritheinfiniteisnot。 Itisplain，too，thattheinfinitecannotbeanactualthingandasubstanceandprinciple。Foranypartofitthatistakenwillbeinfinite，ifithasparts:for\'tobeinfinite\'and\'theinfinite\'arethesame，ifitisasubstanceandnotpredicatedofasubject。 Henceitwillbeeitherindivisibleordivisibleintoinfinites。Butthesamethingcannotbemanyinfinites。(Yetjustaspartofairisair，soapartoftheinfinitewouldbeinfinite，ifitissupposedtobeasubstanceandprinciple。)Thereforetheinfinitemustbewithoutpartsandindivisible。Butthiscannotbetrueofwhatisinfiniteinfullcompletion:foritmustbeadefinitequantity。 Supposethenthatinfinitybelongstosubstanceasanattribute。 But，ifso，itcannot，aswehavesaid，bedescribedasaprinciple，butratherthatofwhichitisanattribute-theairortheevennumber。 ThustheviewofthosewhospeakafterthemannerofthePythagoreansisabsurd。Withthesamebreaththeytreattheinfiniteassubstance，anddivideitintoparts。 Thisdiscussion，however，involvesthemoregeneralquestionwhethertheinfinitecanbepresentinmathematicalobjectsandthingswhichareintelligibleanddonothaveextension，aswellasamongsensibleobjects。Ourinquiry(asphysicists)islimitedtoitsspecialsubject-matter，theobjectsofsense，andwehavetoaskwhetherthereisorisnotamongthemabodywhichisinfiniteinthedirectionofincrease。 Wemaybeginwithadialecticalargumentandshowasfollowsthatthereisnosuchthing。If\'boundedbyasurface\'isthedefinitionofbodytherecannotbeaninfinitebodyeitherintelligibleorsensible。 Norcannumbertakeninabstractionbeinfinite，fornumberorthatwhichhasnumberisnumerable。Ifthenthenumerablecanbenumbered，itwouldalsobepossibletogothroughtheinfinite。 If，ontheotherhand，weinvestigatethequestionmoreinaccordancewithprinciplesappropriatetophysics，weareledasfollowstothesameresult。 Theinfinitebodymustbeeither(1)compound，or(2)simple；yetneitheralternativeispossible。 (1)Compoundtheinfinitebodywillnotbe，iftheelementsarefiniteinnumber。Fortheymustbemorethanone，andthecontrariesmustalwaysbalance，andnooneofthemcanbeinfinite。Ifoneofthebodiesfallsinanydegreeshortoftheotherinpotency-supposefireisfiniteinamountwhileairisinfiniteandagivenquantityoffireexceedsinpowerthesameamountofairinanyratioprovideditisnumericallydefinite-theinfinitebodywillobviouslyprevailoverandannihilatethefinitebody。Ontheotherhand，itisimpossiblethateachshouldbeinfinite。\'Body\'iswhathasextensioninalldirectionsandtheinfiniteiswhatisboundlesslyextended，sothattheinfinitebodywouldbeextendedinalldirectionsadinfinitum。 Nor(2)cantheinfinitebodybeoneandsimple，whetheritis，assomehold，athingoverandabovetheelements(fromwhichtheygeneratetheelements)orisnotthusqualified。 (a)Wemustconsidertheformeralternative；fortherearesomepeoplewhomakethistheinfinite，andnotairorwater，inorderthattheotherelementsmaynotbeannihilatedbytheelementwhichisinfinite。Theyhavecontrarietywitheachother-airiscold，watermoist，firehot；ifonewereinfinite，theothersbynowwouldhaveceasedtobe。Asitis，theysay，theinfiniteisdifferentfromthemandistheirsource。 Itisimpossible，however，thatthereshouldbesuchabody；notbecauseitisinfiniteonthatpointageneralproofcanbegivenwhichappliesequallytoall，air，water，oranythingelse-butsimplybecausethereis，asamatteroffact，nosuchsensiblebody，alongsidetheso-calledelements。Everythingcanberesolvedintotheelementsofwhichitiscomposed。Hencethebodyinquestionwouldhavebeenpresentinourworldhere，alongsideairandfireandearthandwater:butnothingofthekindisobserved。 (b)Norcanfireoranyotheroftheelementsbeinfinite。Forgenerally，andapartfromthequestionofhowanyofthemcouldbeinfinite，theAll，evenifitwerelimited，cannoteitherbeorbecomeoneofthem，asHeraclitussaysthatatsometimeallthingsbecomefire。(Thesameargumentappliesalsototheonewhichthephysicistssupposetoexistalongsidetheelements:foreverythingchangesfromcontrarytocontrary，e。g。fromhottocold)。 Theprecedingconsiderationofthevariouscasesservestoshowuswhetheritisorisnotpossiblethatthereshouldbeaninfinitesensiblebody。Thefollowingargumentsgiveageneraldemonstrationthatitisnotpossible。 Itisthenatureofeverykindofsensiblebodytobesomewhere，andthereisaplaceappropriatetoeach，thesameforthepartandforthewhole，e。g。forthewholeearthandforasingleclod，andforfireandforaspark。 Suppose(a)thattheinfinitesensiblebodyishomogeneous。Theneachpartwillbeeitherimmovableoralwaysbeingcarriedalong。 Yetneitherispossible。Forwhydownwardsratherthanupwardsorinanyotherdirection?Imean，e。g，ifyoutakeaclod，wherewillitbemovedorwherewillitbeatrest?Forexhypothesitheplaceofthebodyakintoitisinfinite。Willitoccupythewholeplace，then?Andhow?Whatthenwillbethenatureofitsrestandofitsmovement，orwherewilltheybe?Itwilleitherbeathomeeverywhere-thenitwillnotbemoved；oritwillbemovedeverywhere-thenitwillnotcometorest。 Butif(b)theAllhasdissimilarparts，theproperplacesofthepartswillbedissimilaralso，andthebodyoftheAllwillhavenounityexceptthatofcontact。Then，further，thepartswillbeeitherfiniteorinfiniteinvarietyofkind。(i)Finitetheycannotbe，foriftheAllistobeinfinite，someofthemwouldhavetobeinfinite，whiletheotherswerenot，e。g。fireorwaterwillbeinfinite。But，aswehaveseenbefore，suchanelementwoulddestroywhatiscontrarytoit。(Thisindeedisthereasonwhynoneofthephysicistsmadefireorearththeoneinfinitebody，buteitherwaterorairorwhatisintermediatebetweenthem，becausetheabodeofeachofthetwowasplainlydeterminate，whiletheothershaveanambiguousplacebetweenupanddown。) But(ii)ifthepartsareinfiniteinnumberandsimple，theirproperplacestoowillbeinfiniteinnumber，andthesamewillbetrueoftheelementsthemselves。Ifthatisimpossible，andtheplacesarefinite，thewholetoomustbefinite；fortheplaceandthebodycannotbutfiteachother。Neitheristhewholeplacelargerthanwhatcanbefilledbythebody(andthenthebodywouldnolongerbeinfinite)，noristhebodylargerthantheplace；foreithertherewouldbeanemptyspaceorabodywhosenatureitistobenowhere。 Anaxagorasgivesanabsurdaccountofwhytheinfiniteisatrest。 Hesaysthattheinfiniteitselfisthecauseofitsbeingfixed。Thisbecauseitisinitself，sincenothingelsecontainsit-ontheassumptionthatwhereveranythingis，itistherebyitsownnature。 Butthisisnottrue:athingcouldbesomewherebycompulsion，andnotwhereitisitsnaturetobe。 Evenifitistrueastruecanbethatthewholeisnotmoved(forwhatisfixedbyitselfandisinitselfmustbeimmovable)，yetwemustexplainwhyitisnotitsnaturetobemoved。Itisnotenoughjusttomakethisstatementandthendecamp。Anythingelsemightbeinastateofrest，butthereisnoreasonwhyitshouldnotbeitsnaturetobemoved。Theearthisnotcarriedalong，andwouldnotbecarriedalongifitwereinfinite，provideditisheldtogetherbythecentre。Butitwouldnotbebecausetherewasnootherregioninwhichitcouldbecarriedalongthatitwouldremainatthecentre，butbecausethisisitsnature。Yetinthiscasealsowemaysaythatitfixesitself。Iftheninthecaseoftheearth，supposedtobeinfinite，itisatrest，notbecauseitisinfinite，butbecauseithasweightandwhatisheavyrestsatthecentreandtheearthisatthecentre，similarlytheinfinitealsowouldrestinitself，notbecauseitisinfiniteandfixesitself，butowingtosomeothercause。 Anotherdifficultyemergesatthesametime。Anypartoftheinfinitebodyoughttoremainatrest。Justastheinfiniteremainsatrestinitselfbecauseitfixesitself，sotooanypartofityoumaytakewillremaininitself。Theappropriateplacesofthewholeandofthepartarealike，e。g。ofthewholeearthandofaclodtheappropriateplaceisthelowerregion；offireasawholeandofaspark，theupperregion。If，therefore，tobeinitselfistheplaceoftheinfinite，thatalsowillbeappropriatetothepart。 Thereforeitwillremaininitself。 Ingeneral，theviewthatthereisaninfinitebodyisplainlyincompatiblewiththedoctrinethatthereisnecessarilyaproperplaceforeachkindofbody，ifeverysensiblebodyhaseitherweightorlightness，andifabodyhasanaturallocomotiontowardsthecentreifitisheavy，andupwardsifitislight。Thiswouldneedtobetrueoftheinfinitealso。Butneithercharactercanbelongtoit:itcannotbeeitherasawhole，norcanitbehalftheoneandhalftheother。Forhowshouldyoudivideit?orhowcantheinfinitehavetheonepartupandtheotherdown，oranextremityandacentre? Further，everysensiblebodyisinplace，andthekindsordifferencesofplaceareup-down，before-behind，right-left；andthesedistinctionsholdnotonlyinrelationtousandbyarbitraryagreement，butalsointhewholeitself。Butintheinfinitebodytheycannotexist。Ingeneral，ifitisimpossiblethatthereshouldbeaninfiniteplace，andifeverybodyisinplace，therecannotbeaninfinitebody。 Surelywhatisinaspecialplaceisinplace，andwhatisinplaceisinaspecialplace。Just，then，astheinfinitecannotbequantity-thatwouldimplythatithasaparticularquantity，e，g，twoorthreecubits；quantityjustmeansthese-soathing\'sbeinginplacemeansthatitissomewhere，andthatiseitherupordownorinsomeotherofthesixdifferencesofposition:buteachoftheseisalimit。 Itisplainfromtheseargumentsthatthereisnobodywhichisactuallyinfinite。 6 Butontheotherhandtosupposethattheinfinitedoesnotexistinanywayleadsobviouslytomanyimpossibleconsequences:therewillbeabeginningandanendoftime，amagnitudewillnotbedivisibleintomagnitudes，numberwillnotbeinfinite。If，then，inviewoftheaboveconsiderations，neitheralternativeseemspossible，anarbitermustbecalledin；andclearlythereisasenseinwhichtheinfiniteexistsandanotherinwhichitdoesnot。 Wemustkeepinmindthattheword\'is\'meanseitherwhatpotentiallyisorwhatfullyis。Further，athingisinfiniteeitherbyadditionorbydivision。 Now，aswehaveseen，magnitudeisnotactuallyinfinite。Butbydivisionitisinfinite。(Thereisnodifficultyinrefutingthetheoryofindivisiblelines。)Thealternativethenremainsthattheinfinitehasapotentialexistence。 Butthephrase\'potentialexistence\'isambiguous。Whenwespeakofthepotentialexistenceofastatuewemeanthattherewillbeanactualstatue。Itisnotsowiththeinfinite。Therewillnotbeanactualinfinite。Theword\'is\'hasmanysenses，andwesaythattheinfinite\'is\'inthesenseinwhichwesay\'itisday\'or\'itisthegames\'，becauseonethingafteranotherisalwayscomingintoexistence。Forofthesethingstoothedistinctionbetweenpotentialandactualexistenceholds。WesaythatthereareOlympicgames，bothinthesensethattheymayoccurandthattheyareactuallyoccurring。 Theinfiniteexhibitsitselfindifferentways-intime，inthegenerationsofman，andinthedivisionofmagnitudes。Forgenerallytheinfinitehasthismodeofexistence:onethingisalwaysbeingtakenafteranother，andeachthingthatistakenisalwaysfinite，butalwaysdifferent。Again，\'being\'hasmorethanonesense，sothatwemustnotregardtheinfiniteasa\'this\'，suchasamanorahorse，butmustsupposeittoexistinthesenseinwhichwespeakofthedayorthegamesasexistingthingswhosebeinghasnotcometothemlikethatofasubstance，butconsistsinaprocessofcomingtobeorpassingaway；definiteifyoulikeateachstage，yetalwaysdifferent。 Butwhenthistakesplaceinspatialmagnitudes，whatistakenperists，whileinthesuccessionoftimeandofmenittakesplacebythepassingawayoftheseinsuchawaythatthesourceofsupplynevergivesout。 Inawaytheinfinitebyadditionisthesamethingastheinfinitebydivision。Inafinitemagnitude，theinfinitebyadditioncomesaboutinawayinversetothatoftheother。Forinproportionasweseedivisiongoingon，inthesameproportionweseeadditionbeingmadetowhatisalreadymarkedoff。Forifwetakeadeterminatepartofafinitemagnitudeandaddanotherpartdeterminedbythesameratio(nottakinginthesameamountoftheoriginalwhole)，andsoon，weshallnottraversethegivenmagnitude。 Butifweincreasetheratioofthepart，soasalwaystotakeinthesameamount，weshalltraversethemagnitude，foreveryfinitemagnitudeisexhaustedbymeansofanydeterminatequantityhoweversmall。 Theinfinite，then，existsinnootherway，butinthiswayitdoesexist，potentiallyandbyreduction。Itexistsfullyinthesenseinwhichwesay\'itisday\'or\'itisthegames\'；andpotentiallyasmatterexists，notindependentlyaswhatisfinitedoes。 Byadditionthen，also，thereispotentiallyaninfinite，namely，whatwehavedescribedasbeinginasensethesameastheinfiniteinrespectofdivision。Foritwillalwaysbepossibletotakesomethingahextra。Yetthesumofthepartstakenwillnotexceedeverydeterminatemagnitude，justasinthedirectionofdivisioneverydeterminatemagnitudeissurpassedinsmallnessandtherewillbeasmallerpart。 Butinrespectofadditiontherecannotbeaninfinitewhichevenpotentiallyexceedseveryassignablemagnitude，unlessithastheattributeofbeingactuallyinfinite，asthephysicistsholdtobetrueofthebodywhichisoutsidetheworld，whoseessentialnatureisairorsomethingofthekind。Butiftherecannotbeinthiswayasensiblebodywhichisinfiniteinthefullsense，evidentlytherecannomorebeabodywhichispotentiallyinfiniteinrespectofaddition，exceptastheinverseoftheinfinitebydivision，aswehavesaid。ItisforthisreasonthatPlatoalsomadetheinfinitestwoinnumber，becauseitissupposedtobepossibletoexceedalllimitsandtoproceedadinfinituminthedirectionbothofincreaseandofreduction。Yetthoughhemakestheinfinitestwo，hedoesnotusethem。Forinthenumberstheinfiniteinthedirectionofreductionisnotpresent，asthemonadisthesmallest；noristheinfiniteinthedirectionofincrease，forthepartsnumberonlyuptothedecad。 Theinfiniteturnsouttobethecontraryofwhatitissaidtobe。Itisnotwhathasnothingoutsideitthatisinfinite，butwhatalwayshassomethingoutsideit。Thisisindicatedbythefactthatringsalsothathavenobezelaredescribedas\'endless\'，becauseitisalwayspossibletotakeapartwhichisoutsideagivenpart。Thedescriptiondependsonacertainsimilarity，butitisnottrueinthefullsenseoftheword。Thisconditionaloneisnotsufficient:itisnecessaryalsothatthenextpartwhichistakenshouldneverbethesame。Inthecircle，thelatterconditionisnotsatisfied:itisonlytheadjacentpartfromwhichthenewpartisdifferent。 Ourdefinitionthenisasfollows: Aquantityisinfiniteifitissuchthatwecanalwaystakeapartoutsidewhathasbeenalreadytaken。Ontheotherhand，whathasnothingoutsideitiscompleteandwhole。Forthuswedefinethewhole-thatfromwhichnothingiswanting，asawholemanorawholebox。Whatistrueofeachparticularistrueofthewholeassuch-thewholeisthatofwhichnothingisoutside。Ontheotherhandthatfromwhichsomethingisabsentandoutside，howeversmallthatmaybe，isnot\'all\'。\'Whole\'and\'complete\'areeitherquiteidenticalorcloselyakin。Nothingiscomplete(teleion)whichhasnoend(telos)；andtheendisalimit。 HenceParmenidesmustbethoughttohavespokenbetterthanMelissus。Thelattersaysthatthewholeisinfinite，buttheformerdescribesitaslimited，\'equallybalancedfromthemiddle\'。Fortoconnecttheinfinitewiththeallandthewholeisnotlikejoiningtwopiecesofstring；foritisfromthistheygetthedignitytheyascribetotheinfinite-itscontainingallthingsandholdingtheallinitself-fromitshavingacertainsimilaritytothewhole。Itisinfactthematterofthecompletenesswhichbelongstosize，andwhatispotentiallyawhole，thoughnotinthefullsense。Itisdivisiblebothinthedirectionofreductionandoftheinverseaddition。Itisawholeandlimited；not，however，invirtueofitsownnature，butinvirtueofwhatisotherthanit。Itdoesnotcontain，but，insofarasitisinfinite，iscontained。Consequently，also，itisunknowable，quainfinite；forthematterhasnoform。 (Henceitisplainthattheinfinitestandsintherelationofpartratherthanofwhole。Forthematterispartofthewhole，asthebronzeisofthebronzestatue。)Ifitcontainsinthecaseofsensiblethings，inthecaseofintelligiblethingsthegreatandthesmalloughttocontainthem。Butitisabsurdandimpossibletosupposethattheunknowableandindeterminateshouldcontainanddetermine。 7 Itisreasonablethatthereshouldnotbeheldtobeaninfiniteinrespectofadditionsuchastosurpasseverymagnitude，butthatthereshouldbethoughttobesuchaninfiniteinthedirectionofdivision。Forthematterandtheinfinitearecontainedinsidewhatcontainsthem，whileitistheformwhichcontains。Itisnaturaltootosupposethatinnumberthereisalimitinthedirectionoftheminimum，andthatintheotherdirectioneveryassignednumberissurpassed。Inmagnitude，onthecontrary，everyassignedmagnitudeissurpassedinthedirectionofsmallness，whileintheotherdirectionthereisnoinfinitemagnitude。Thereasonisthatwhatisoneisindivisiblewhateveritmaybe，e。g。amanisoneman，notmany。Numberontheotherhandisapluralityof\'ones\'andacertainquantityofthem。Hencenumbermuststopattheindivisible: for\'two\'and\'three\'aremerelyderivativeterms，andsowitheachoftheothernumbers。Butinthedirectionoflargenessitisalwayspossibletothinkofalargernumber:forthenumberoftimesamagnitudecanbebisectedisinfinite。Hencethisinfiniteispotential，neveractual:thenumberofpartsthatcanbetakenalwayssurpassesanyassignednumber。Butthisnumberisnotseparablefromtheprocessofbisection，anditsinfinityisnotapermanentactualitybutconsistsinaprocessofcomingtobe，liketimeandthenumberoftime。 Withmagnitudesthecontraryholds。Whatiscontinuousisdividedadinfinitum，butthereisnoinfiniteinthedirectionofincrease。 Forthesizewhichitcanpotentiallybe，itcanalsoactuallybe。 Hencesincenosensiblemagnitudeisinfinite，itisimpossibletoexceedeveryassignedmagnitude；forifitwerepossibletherewouldbesomethingbiggerthantheheavens。 Theinfiniteisnotthesameinmagnitudeandmovementandtime，inthesenseofasinglenature，butitssecondarysensedependsonitsprimarysense，i。e。movementiscalledinfiniteinvirtueofthemagnitudecoveredbythemovement(oralterationorgrowth)，andtimebecauseofthemovement。(Iusethesetermsforthemoment。LaterIshallexplainwhateachofthemmeans，andalsowhyeverymagnitudeisdivisibleintomagnitudes。) Ouraccountdoesnotrobthemathematiciansoftheirscience，bydisprovingtheactualexistenceoftheinfiniteinthedirectionofincrease，inthesenseoftheuntraversable。Inpointoffacttheydonotneedtheinfiniteanddonotuseit。Theypostulateonlythatthefinitestraightlinemaybeproducedasfarastheywish。Itispossibletohavedividedinthesameratioasthelargestquantityanothermagnitudeofanysizeyoulike。Hence，forthepurposesofproof，itwillmakenodifferencetothemtohavesuchaninfiniteinstead，whileitsexistencewillbeinthesphereofrealmagnitudes。 Inthefourfoldschemeofcauses，itisplainthattheinfiniteisacauseinthesenseofmatter，andthatitsessenceisprivation，thesubjectassuchbeingwhatiscontinuousandsensible。Alltheotherthinkers，too，evidentlytreattheinfiniteasmatter-thatiswhyitisinconsistentinthemtomakeitwhatcontains，andnotwhatiscontained。 8 Itremainstodisposeoftheargumentswhicharesupposedtosupporttheviewthattheinfiniteexistsnotonlypotentiallybutasaseparatething。Somehavenocogency；otherscanbemetbyfreshobjectionsthatarevalid。 (1)Inorderthatcomingtobeshouldnotfail，itisnotnecessarythatthereshouldbeasensiblebodywhichisactuallyinfinite。Thepassingawayofonethingmaybethecomingtobeofanother，theAllbeinglimited。 (2)Thereisadifferencebetweentouchingandbeinglimited。Theformerisrelativetosomethingandisthetouchingofsomething(foreverythingthattouchestouchessomething)，andfurtherisanattributeofsomeoneofthethingswhicharelimited。Ontheotherhand，whatislimitedisnotlimitedinrelationtoanything。Again，contactisnotnecessarilypossiblebetweenanytwothingstakenatrandom。 (3)Torelyonmerethinkingisabsurd，forthentheexcessordefectisnotinthethingbutinthethought。Onemightthinkthatoneofusisbiggerthanheisandmagnifyhimadinfinitum。Butitdoesnotfollowthatheisbiggerthanthesizeweare，justbecausesomeonethinksheis，butonlybecauseheisthesizeheis。Thethoughtisanaccident。 (a)Timeindeedandmovementareinfinite，andalsothinking，inthesensethateachpartthatistakenpassesinsuccessionoutofexistence。 (b)Magnitudeisnotinfiniteeitherinthewayofreductionorofmagnificationinthought。 Thisconcludesmyaccountofthewayinwhichtheinfiniteexists，andofthewayinwhichitdoesnotexist，andofwhatitis。 BookIV 1 THEphysicistmusthaveaknowledgeofPlace，too，aswellasoftheinfinite-namely，whetherthereissuchathingornot，andthemannerofitsexistenceandwhatitis-bothbecauseallsupposethatthingswhichexistaresomewhere(thenon-existentisnowhere——whereisthegoat-stagorthesphinx?)，andbecause\'motion\'initsmostgeneralandprimarysenseischangeofplace，whichwecall\'locomotion\'。 Thequestion，whatisplace?presentsmanydifficulties。Anexaminationofalltherelevantfactsseemstoleadtodivergentconclusions。Moreover，wehaveinheritednothingfrompreviousthinkers，whetherinthewayofastatementofdifficultiesorofasolution。 Theexistenceofplaceisheldtobeobviousfromthefactofmutualreplacement。Wherewaternowis，thereinturn，whenthewaterhasgoneoutasfromavessel，airispresent。Whenthereforeanotherbodyoccupiesthissameplace，theplaceisthoughttobedifferentfromallthebodieswhichcometobeinitandreplaceoneanother。Whatnowcontainsairformerlycontainedwater，sothatclearlytheplaceorspaceintowhichandoutofwhichtheypassedwassomethingdifferentfromboth。 Further，thetypicallocomotionsoftheelementarynaturalbodies-namely，fire，earth，andthelike-shownotonlythatplaceissomething，butalsothatitexertsacertaininfluence。Eachiscarriedtoitsownplace，ifitisnothindered，theoneup，theotherdown。Nowtheseareregionsorkindsofplace-upanddownandtherestofthesixdirections。Nordosuchdistinctions(upanddownandrightandleft，&c。)holdonlyinrelationtous。Toustheyarenotalwaysthesamebutchangewiththedirectioninwhichweareturned:thatiswhythesamethingmaybebothrightandleft，upanddown，beforeandbehind。Butinnatureeachisdistinct，takenapartbyitself。Itisnoteverychancedirectionwhichis\'up\'，butwherefireandwhatislightarecarried；similarly，too，\'down\'isnotanychancedirectionbutwherewhathasweightandwhatismadeofeartharecarried-theimplicationbeingthattheseplacesdonotdiffermerelyinrelativeposition，butalsoaspossessingdistinctpotencies。Thisismadeplainalsobytheobjectsstudiedbymathematics。Thoughtheyhavenorealplace，theynevertheless，inrespectoftheirpositionrelativelytous，havearightandleftasattributesascribedtothemonlyinconsequenceoftheirrelativeposition，nothavingbynaturethesevariouscharacteristics。Again，thetheorythatthevoidexistsinvolvestheexistenceofplace:foronewoulddefinevoidasplacebereftofbody。 Theseconsiderationsthenwouldleadustosupposethatplaceissomethingdistinctfrombodies，andthateverysensiblebodyisinplace。Hesiodtoomightbeheldtohavegivenacorrectaccountofitwhenhemadechaosfirst。Atleasthesays: \'Firstofallthingscamechaostobeing，thenbroad-breastedearth，\' implyingthatthingsneedtohavespacefirst，becausehethought，withmostpeople，thateverythingissomewhereandinplace。Ifthisisitsnature，thepotencyofplacemustbeamarvellousthing，andtakeprecedenceofallotherthings。Forthatwithoutwhichnothingelsecanexist，whileitcanexistwithouttheothers，mustneedsbefirst；forplacedoesnotpassoutofexistencewhenthethingsinitareannihilated。 True，butevenifwesupposeitsexistencesettled，thequestionofitsnaturepresentsdifficulty-whetheritissomesortof\'bulk\'ofbodyorsomeentityotherthanthat，forwemustfirstdetermineitsgenus。 (1)Nowithasthreedimensions，length，breadth，depth，thedimensionsbywhichallbodyalsoisbounded。Buttheplacecannotbebody；forifitweretherewouldbetwobodiesinthesameplace。 (2)Further，ifbodyhasaplaceandspace，clearlysotoohavesurfaceandtheotherlimitsofbody；forthesamestatementwillapplytothem:wheretheboundingplanesofthewaterwere，thereinturnwillbethoseoftheair。Butwhenwecometoapointwecannotmakeadistinctionbetweenitanditsplace。Henceiftheplaceofapointisnotdifferentfromthepoint，nomorewillthatofanyoftheothersbedifferent，andplacewillnotbesomethingdifferentfromeachofthem。 (3)Whatintheworldthenarewetosupposeplacetobe?Ifithasthesortofnaturedescribed，itcannotbeanelementorcomposedofelements，whetherthesebecorporealorincorporeal:forwhileithassize，ithasnotbody。Buttheelementsofsensiblebodiesarebodies，whilenothingthathassizeresultsfromacombinationofintelligibleelements。 (4)Alsowemayask:ofwhatinthingsisspacethecause?Noneofthefourmodesofcausationcanbeascribedtoit。Itisneitherinthesenseofthematterofexistents(fornothingiscomposedofit)，norastheformanddefinitionofthings，norasend，nordoesitmoveexistents。 (5)Further，too，ifitisitselfanexistent，wherewillitbe? Zeno\'sdifficultydemandsanexplanation:forifeverythingthatexistshasaplace，placetoowillhaveaplace，andsoonadinfinitum。 (6)Again，justaseverybodyisinplace，so，too，everyplacehasabodyinit。Whatthenshallwesayaboutgrowingthings?Itfollowsfromthesepremissesthattheirplacemustgrowwiththem，iftheirplaceisneitherlessnorgreaterthantheyare。 Byaskingthesequestions，then，wemustraisethewholeproblemaboutplace-notonlyastowhatitis，butevenwhetherthereissuchathing。