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，noristheendeffectedgettingthemoneyacausepresentinhimself-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'scomingandgettingthemoneywhenhedidnotcomeforthesakeofthatareinnumerable。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。
　　Henceitisclearthateventswhich1belongtothegeneralclassofthingsthatmaycometopassforthesakeofsomething，2
　　donotcometopassforthesakeofwhatactuallyresults，and3
　　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'isreferredultimatelyeither1，inthingswhichdonotinvolvemotion，e。g。
　　inmathematics，tothe'what'tothedefinitionof'straightline'or'commensurable'，&c。，or2towhatinitiatedamotion，e。g。'whydidtheygotowar?-becausetherehadbeenaraid'；or3weareinquiring'forthesakeofwhat?'-'thattheymayrule'；or4，inthecaseofthingsthatcomeintobeing，wearelookingforthematter。
　　Thecauses，therefore，aretheseandsomanyinnumber。
　　Now，thecausesbeingfour，itisthebusinessofthephysicisttoknowaboutthemall，andifherefershisproblemsbacktoallofthem，hewillassignthe'why'inthewaypropertohisscience-thematter，theform，themover，'thatforthesakeofwhich'。Thelastthreeoftencoincide；forthe'what'and'thatforthesakeofwhich'areone，whiletheprimarysourceofmotionisthesameinspeciesastheseformangeneratesman，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，suchas1thatwhichiscompletelyunchangeable，theprimaryreality，and2theessenceofthatwhichiscomingtobe，i。e。theform；forthisistheendor'thatforthesakeofwhich'。
　　Hencesincenatureisforthesakeofsomething，wemustknowthiscausealso。Wemustexplainthe'why'inallthesensesoftheterm，namely，1thatfromthisthatwillnecessarilyresult'fromthis'
　　eitherwithoutqualificationorinmostcases；2that'thismustbesoifthatistobeso'astheconclusionpresupposesthepremisses；
　　3thatthiswastheessenceofthething；and4becauseitisbetterthusnotwithoutqualification，butwithreferencetotheessentialnatureineachcase。
　　8
　　Wemustexplainthen1thatNaturebelongstotheclassofcauseswhichactforthesakeofsomething；2aboutthenecessaryanditsplaceinphysicalproblems，forallwritersascribethingstothiscause，arguingthatsincethehotandthecold，&c。，areofsuchandsuchakind，thereforecertainthingsnecessarilyareandcometobe-andiftheymentionanyothercauseonehis'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。
　　Sucharetheargumentsandothersofthekindwhichmaycausedifficultyonthispoint。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，andplantsgrowleavesforthesakeofthefruitandsendtheirrootsdownnotupforthesakeofnourishment，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，butitisnotduetotheseexceptasitsmaterial；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。
　　Wemaystartbydistinguishing1whatexistsinastateoffulfilmentonly，2whatexistsaspotential，3whatexistsaspotentialandalsoinfulfilment-onebeinga'this'，another'somuch'，athird'such'，andsimilarlyineachoftheothermodesofthepredicationofbeing。
　　Further，theword'relative'isusedwithreferenceto1excessanddefect，2agentandpatientandgenerallywhatcanmoveandwhatcanbemoved。For'whatcancausemovement'isrelativeto'whatcanbemoved'，andviceversa。
　　Again，thereisnosuchthingasmotionoverandabovethethings。
　　Itisalwayswithrespecttosubstanceortoquantityortoqualityortoplacethatwhatchangeschanges。Butitisimpossible，asweassert，tofindanythingcommontothesewhichisneither'this'norquantumnorqualenoranyoftheotherpredicates。Henceneitherwillmotionandchangehavereferencetosomethingoverandabovethethingsmentioned，forthereisnothingoverandabovethem。
　　Noweachofthesebelongstoallitssubjectsineitheroftwoways:
　　namely1substance-theoneispositiveform，theotherprivation；
　　2inquality，whiteandblack；3inquantity，completeandincomplete；4inrespectoflocomotion，upwardsanddownwardsorlightandheavy。Hencethereareasmanytypesofmotionorchangeastherearemeaningsoftheword'is'。
　　Wehavenowbeforeusthedistinctionsinthevariousclassesofbeingbetweenwhatisfullrealandwhatispotential。
　　Def。Thefulfilmentofwhatexistspotentially，insofarasitexistspotentially，ismotion-namely，ofwhatisalterablequaalterable，alteration:ofwhatcanbeincreasedanditsoppositewhatcanbedecreasedthereisnocommonname，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?Eitherabothareinwhatisactedonandmoved，orbtheagencyisintheagentandthepatiencyinthepatient。Ifweoughttocallthelatteralso'agency'，thewordwouldbeusedintwosenses。
　　Now，inalternativeb，themotionwillbeinthemover，forthesamestatementwillholdof'mover'and'moved'。Henceeithereverymoverwillbemoved，or，thoughhavingmotion，itwillnotbemoved。
　　Ifontheotherhandabothareinwhatismovedandactedon-boththeagencyandthepatiencye。g。bothteachingandlearning，thoughtheyaretwo，inthelearner，then，first，theactualityofeachwillnotbepresentineach，and，asecondabsurdity，athingwillhavetwomotionsatthesametime。Howwilltherebetwoalterationsofqualityinonesubjecttowardsonedefinitequality?Thethingisimpossible:theactualizationwillbeone。
　　Butsomeonewillsayitiscontrarytoreasontosupposethatthereshouldbeoneidenticalactualizationoftwothingswhicharedifferentinkind。Yettherewillbe，ifteachingandlearningarethesame，andagencyandpatiency。Toteachwillbethesameastolearn，andtoactthesameastobeactedon-theteacherwillnecessarilybelearningeverythingthatheteaches，andtheagentwillbeactedon。Onemayreply:
　　1Itisnotabsurdthattheactualizationofonethingshouldbeinanother。Teachingistheactivityofapersonwhocanteach，yettheoperationisperformedonsomepatient-itisnotcutadriftfromasubject，butisofAonB。
　　2Thereisnothingtopreventtwothingshavingoneandthesameactualization，providedtheactualizationsarenotdescribedinthesameway，butarerelatedaswhatcanacttowhatisacting。
　　3Norisitnecessarythattheteachershouldlearn，eveniftoactandtobeactedonareoneandthesame，providedtheyarenotthesameindefinitionas'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-alterationisthefulfillmentofthealterablequaalterableor，morescientifically，thefulfilmentofwhatcanactandwhatcanbeactedon，assuch-generallyandagainineachparticularcase，building，healing，&c。Asimilardefinitionwillapplytoeachoftheotherkindsofmotion。
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　　Thescienceofnatureisconcernedwithspatialmagnitudesandmotionandtime，andeachoftheseatleastisnecessarilyinfiniteorfinite，evenifsomethingsdealtwithbythesciencearenot，e。g。
　　aqualityorapoint-itisnotnecessaryperhapsthatsuchthingsshouldbeputundereitherhead。Henceitisincumbentonthepersonwhospecializesinphysicstodiscusstheinfiniteandtoinquirewhetherthereissuchathingornot，and，ifthereis，whatitis。
　　Theappropriatenesstothescienceofthisproblemisclearlyindicated。Allwhohavetouchedonthiskindofscienceinawayworthconsideringhaveformulatedviewsabouttheinfinite，andindeed，toaman，makeitaprincipleofthings。
　　1Some，asthePythagoreansandPlato，maketheinfiniteaprincipleinthesenseofaself-subsistentsubstance，andnotasamereattributeofsomeotherthing。OnlythePythagoreansplacetheinfiniteamongtheobjectsofsensetheydonotregardnumberasseparablefromthese，andassertthatwhatisoutsidetheheavenisinfinite。Plato，ontheotherhand，holdsthatthereisnobodyoutsidetheFormsarenotoutsidebecausetheyarenowhere，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:
　　1Fromthenatureoftime-foritisinfinite。
　　2Fromthedivisionofmagnitudes-forthemathematiciansalsousethenotionoftheinfinite。
　　3Ifcomingtobeandpassingawaydonotgiveout，itisonlybecausethatfromwhichthingscometobeisinfinite。
　　4Becausethelimitedalwaysfindsitslimitinsomething，sothattheremustbenolimit，ifeverythingisalwayslimitedbysomethingdifferentfromitself。
　　5Mostofall，areasonwhichispeculiarlyappropriateandpresentsthedifficultythatisfeltbyeverybody-notonlynumberbutalsomathematicalmagnitudesandwhatisoutsidetheheavenaresupposedtobeinfinitebecausetheynevergiveoutinourthought。
　　Thelastfactthatwhatisoutsideisinfiniteleadspeopletosupposethatbodyalsoisinfinite，andthatthereisaninfinitenumberofworlds。Whyshouldtherebebodyinonepartofthevoidratherthaninanother?Grantonlythatmassisanywhereanditfollowsthatitmustbeeverywhere。Also，ifvoidandplaceareinfinite，theremustbeinfinitebodytoo，forinthecaseofeternalthingswhatmaybemustbe。Buttheproblemoftheinfiniteisdifficult:manycontradictionsresultwhetherwesupposeittoexistornottoexist。Ifitexists，wehavestilltoaskhowitexists；
　　asasubstanceorastheessentialattributeofsomeentity?Orinneitherway，yetnonethelessistheresomethingwhichisinfiniteorsomethingswhichareinfinitelymany?
　　Theproblem，however，whichspeciallybelongstothephysicististoinvestigatewhetherthereisasensiblemagnitudewhichisinfinite。
　　Wemustbeginbydistinguishingthevarioussensesinwhichtheterm'infinite'isused。
　　1Whatisincapableofbeinggonethrough，becauseitisnotinitsnaturetobegonethroughthesenseinwhichthevoiceis'invisible'。
　　2Whatadmitsofbeinggonethrough，theprocesshoweverhavingnotermination，orwhatscarcelyadmitsofbeinggonethrough。
　　3Whatnaturallyadmitsofbeinggonethrough，butisnotactuallygonethroughordoesnotactuallyreachanend。
　　Further，everythingthatisinfinitemaybesoinrespectofadditionordivisionorboth。
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　　Nowitisimpossiblethattheinfiniteshouldbeathingwhichisitselfinfinite，separablefromsensibleobjects。Iftheinfiniteisneitheramagnitudenoranaggregate，butisitselfasubstanceandnotanattribute，itwillbeindivisible；forthedivisiblemustbeeitheramagnitudeoranaggregate。Butifindivisible，thennotinfinite，exceptinthesense1inwhichthevoiceis'invisible'。
　　Butthisisnotthesenseinwhichitisusedbythosewhosaythattheinfiniteexists，northatinwhichweareinvestigatingit，namelyas2'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。Ourinquiryasphysicistsislimitedtoitsspecialsubject-matter，theobjectsofsense，andwehavetoaskwhetherthereisorisnotamongthemabodywhichisinfiniteinthedirectionofincrease。
　　Wemaybeginwithadialecticalargumentandshowasfollowsthatthereisnosuchthing。If'boundedbyasurface'isthedefinitionofbodytherecannotbeaninfinitebodyeitherintelligibleorsensible。
　　Norcannumbertakeninabstractionbeinfinite，fornumberorthatwhichhasnumberisnumerable。Ifthenthenumerablecanbenumbered，itwouldalsobepossibletogothroughtheinfinite。
　　If，ontheotherhand，weinvestigatethequestionmoreinaccordancewithprinciplesappropriatetophysics，weareledasfollowstothesameresult。
　　Theinfinitebodymustbeeither1compound，or2simple；yetneitheralternativeispossible。
　　1Compoundtheinfinitebodywillnotbe，iftheelementsarefiniteinnumber。Fortheymustbemorethanone，andthecontrariesmustalwaysbalance，andnooneofthemcanbeinfinite。Ifoneofthebodiesfallsinanydegreeshortoftheotherinpotency-supposefireisfiniteinamountwhileairisinfiniteandagivenquantityoffireexceedsinpowerthesameamountofairinanyratioprovideditisnumericallydefinite-theinfinitebodywillobviouslyprevailoverandannihilatethefinitebody。Ontheotherhand，itisimpossiblethateachshouldbeinfinite。'Body'iswhathasextensioninalldirectionsandtheinfiniteiswhatisboundlesslyextended，sothattheinfinitebodywouldbeextendedinalldirectionsadinfinitum。
　　Nor2cantheinfinitebodybeoneandsimple，whetheritis，assomehold，athingoverandabovetheelementsfromwhichtheygeneratetheelementsorisnotthusqualified。
　　aWemustconsidertheformeralternative；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。
　　bNorcanfireoranyotheroftheelementsbeinfinite。Forgenerally，andapartfromthequestionofhowanyofthemcouldbeinfinite，theAll，evenifitwerelimited，cannoteitherbeorbecomeoneofthem，asHeraclitussaysthatatsometimeallthingsbecomefire。Thesameargumentappliesalsototheonewhichthephysicistssupposetoexistalongsidetheelements:foreverythingchangesfromcontrarytocontrary，e。g。fromhottocold。
　　Theprecedingconsiderationofthevariouscasesservestoshowuswhetheritisorisnotpossiblethatthereshouldbeaninfinitesensiblebody。Thefollowingargumentsgiveageneraldemonstrationthatitisnotpossible。
　　Itisthenatureofeverykindofsensiblebodytobesomewhere，andthereisaplaceappropriatetoeach，thesameforthepartandforthewhole，e。g。forthewholeearthandforasingleclod，andforfireandforaspark。
　　Supposeathattheinfinitesensiblebodyishomogeneous。Theneachpartwillbeeitherimmovableoralwaysbeingcarriedalong。
　　Yetneitherispossible。Forwhydownwardsratherthanupwardsorinanyotherdirection?Imean，e。g，ifyoutakeaclod，wherewillitbemovedorwherewillitbeatrest?Forexhypothesitheplaceofthebodyakintoitisinfinite。Willitoccupythewholeplace，then?Andhow?Whatthenwillbethenatureofitsrestandofitsmovement，orwherewilltheybe?Itwilleitherbeathomeeverywhere-thenitwillnotbemoved；oritwillbemovedeverywhere-thenitwillnotcometorest。
　　ButifbtheAllhasdissimilarparts，theproperplacesofthepartswillbedissimilaralso，andthebodyoftheAllwillhavenounityexceptthatofcontact。Then，further，thepartswillbeeitherfiniteorinfiniteinvarietyofkind。iFinitetheycannotbe，foriftheAllistobeinfinite，someofthemwouldhavetobeinfinite，whiletheotherswerenot，e。g。fireorwaterwillbeinfinite。But，aswehaveseenbefore，suchanelementwoulddestroywhatiscontrarytoit。Thisindeedisthereasonwhynoneofthephysicistsmadefireorearththeoneinfinitebody，buteitherwaterorairorwhatisintermediatebetweenthem，becausetheabodeofeachofthetwowasplainlydeterminate，whiletheothershaveanambiguousplacebetweenupanddown。
　　Butiiifthepartsareinfiniteinnumberandsimple，theirproperplacestoowillbeinfiniteinnumber，andthesamewillbetrueoftheelementsthemselves。Ifthatisimpossible，andtheplacesarefinite，thewholetoomustbefinite；fortheplaceandthebodycannotbutfiteachother。Neitheristhewholeplacelargerthanwhatcanbefilledbythebodyandthenthebodywouldnolongerbeinfinite，noristhebodylargerthantheplace；foreithertherewouldbeanemptyspaceorabodywhosenatureitistobenowhere。
　　Anaxagorasgivesanabsurdaccountofwhytheinfiniteisatrest。
　　Hesaysthattheinfiniteitselfisthecauseofitsbeingfixed。Thisbecauseitisinitself，sincenothingelsecontainsit-ontheassumptionthatwhereveranythingis，itistherebyitsownnature。
　　Butthisisnottrue:athingcouldbesomewherebycompulsion，andnotwhereitisitsnaturetobe。
　　Evenifitistrueastruecanbethatthewholeisnotmovedforwhatisfixedbyitselfandisinitselfmustbeimmovable，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。
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　　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。Forifwetakeadeterminatepartofafinitemagnitudeandaddanotherpartdeterminedbythesamerationottakinginthesameamountoftheoriginalwhole，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。Nothingiscompleteteleionwhichhasnoendtelos；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。movementiscalledinfiniteinvirtueofthemagnitudecoveredbythemovementoralterationorgrowth，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。
　　1Inorderthatcomingtobeshouldnotfail，itisnotnecessarythatthereshouldbeasensiblebodywhichisactuallyinfinite。Thepassingawayofonethingmaybethecomingtobeofanother，theAllbeinglimited。
　　2Thereisadifferencebetweentouchingandbeinglimited。Theformerisrelativetosomethingandisthetouchingofsomethingforeverythingthattouchestouchessomething，andfurtherisanattributeofsomeoneofthethingswhicharelimited。Ontheotherhand，whatislimitedisnotlimitedinrelationtoanything。Again，contactisnotnecessarilypossiblebetweenanytwothingstakenatrandom。
　　3Torelyonmerethinkingisabsurd，forthentheexcessordefectisnotinthethingbutinthethought。Onemightthinkthatoneofusisbiggerthanheisandmagnifyhimadinfinitum。Butitdoesnotfollowthatheisbiggerthanthesizeweare，justbecausesomeonethinksheis，butonlybecauseheisthesizeheis。Thethoughtisanaccident。
　　aTimeindeedandmovementareinfinite，andalsothinking，inthesensethateachpartthatistakenpassesinsuccessionoutofexistence。
　　bMagnitudeisnotinfiniteeitherinthewayofreductionorofmagnificationinthought。
　　Thisconcludesmyaccountofthewayinwhichtheinfiniteexists，andofthewayinwhichitdoesnotexist，andofwhatitis。
　　BookIV
　　1
　　THEphysicistmusthaveaknowledgeofPlace，too，aswellasoftheinfinite-namely，whetherthereissuchathingornot，andthemannerofitsexistenceandwhatitis-bothbecauseallsupposethatthingswhichexistaresomewherethenon-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。Nordosuchdistinctionsupanddownandrightandleft，&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。
　　1Nowithasthreedimensions，length，breadth，depth，thedimensionsbywhichallbodyalsoisbounded。Buttheplacecannotbebody；forifitweretherewouldbetwobodiesinthesameplace。
　　2Further，ifbodyhasaplaceandspace，clearlysotoohavesurfaceandtheotherlimitsofbody；forthesamestatementwillapplytothem:wheretheboundingplanesofthewaterwere，thereinturnwillbethoseoftheair。Butwhenwecometoapointwecannotmakeadistinctionbetweenitanditsplace。Henceiftheplaceofapointisnotdifferentfromthepoint，nomorewillthatofanyoftheothersbedifferent，andplacewillnotbesomethingdifferentfromeachofthem。
　　3Whatintheworldthenarewetosupposeplacetobe?Ifithasthesortofnaturedescribed，itcannotbeanelementorcomposedofelements，whetherthesebecorporealorincorporeal:forwhileithassize，ithasnotbody。Buttheelementsofsensiblebodiesarebodies，whilenothingthathassizeresultsfromacombinationofintelligibleelements。
　　4Alsowemayask:ofwhatinthingsisspacethecause?Noneofthefourmodesofcausationcanbeascribedtoit。Itisneitherinthesenseofthematterofexistentsfornothingiscomposedofit，norastheformanddefinitionofthings，norasend，nordoesitmoveexistents。
　　5Further，too，ifitisitselfanexistent，wherewillitbe?
　　Zeno'sdifficultydemandsanexplanation:forifeverythingthatexistshasaplace，placetoowillhaveaplace，andsoonadinfinitum。
　　6Again，justaseverybodyisinplace，so，too，everyplacehasabodyinit。Whatthenshallwesayaboutgrowingthings?Itfollowsfromthesepremissesthattheirplacemustgrowwiththem，iftheirplaceisneitherlessnorgreaterthantheyare。
　　Byaskingthesequestions，then，wemustraisethewholeproblemaboutplace-notonlyastowhatitis，butevenwhetherthereissuchathing。