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。

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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。

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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。

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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。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。

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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。