第4章

14 Thesedistinctionshavingbeendrawn，itisevidentthateverychangeandeverythingthatmovesisintime；forthedistinctionoffasterandslowerexistsinreferencetoallchange，sinceitisfoundineveryinstance。Inthephrase\'movingfaster\'Irefertothatwhichchangesbeforeanotherintotheconditioninquestion，whenitmovesoverthesameintervalandwitharegularmovement；e。g。inthecaseoflocomotion，ifboththingsmovealongthecircumferenceofacircle，orbothalongastraightline；andsimilarlyinallothercases。Butwhatisbeforeisintime；forwesay\'before\'and\'after\'withreferencetothedistancefromthe\'now\'，andthe\'now\' istheboundaryofthepastandthefuture；sothatsince\'nows\'areintime，thebeforeandtheafterwillbeintimetoo；forinthatinwhichthe\'now\'is，thedistancefromthe\'now\'willalsobe。But\'before\'isusedcontrariwisewithreferencetopastandtofuturetime；forinthepastwecall\'before\'whatisfartherfromthe\'now\'，and\'after\'whatisnearer，butinthefuturewecallthenearer\'before\'andthefarther\'after\'。Sothatsincethe\'before\'isintime，andeverymovementinvolvesa\'before\'，evidentlyeverychangeandeverymovementisintime。 Itisalsoworthconsideringhowtimecanberelatedtothesoul； andwhytimeisthoughttobeineverything，bothinearthandinseaandinheaven。Isbecauseitisanattribute，orstate，ormovement(sinceitisthenumberofmovement)andallthesethingsaremovable(fortheyareallinplace)，andtimeandmovementaretogether，bothinrespectofpotentialityandinrespectofactuality? Whetherifsouldidnotexisttimewouldexistornot，isaquestionthatmayfairlybeasked；foriftherecannotbesomeonetocounttherecannotbeanythingthatcanbecounted，sothatevidentlytherecannotbenumber；fornumberiseitherwhathasbeen，orwhatcanbe，counted。Butifnothingbutsoul，orinsoulreason，isqualifiedtocount，therewouldnotbetimeunlessthereweresoul，butonlythatofwhichtimeisanattribute，i。e。ifmovementcanexistwithoutsoul，andthebeforeandafterareattributesofmovement，andtimeisthesequanumerable。 Onemightalsoraisethequestionwhatsortofmovementtimeisthenumberof。Mustwenotsay\'ofanykind\'?Forthingsbothcomeintobeingintimeandpassaway，andgrow，andarealteredintime，andaremovedlocally；thusitisofeachmovementquamovementthattimeisthenumber。Andsoitissimplythenumberofcontinuousmovement，notofanyparticularkindofit。 Butotherthingsaswellmayhavebeenmovednow，andtherewouldbeanumberofeachofthetwomovements。Isthereanothertime，then，andwilltherebetwoequaltimesatonce?Surelynot。Foratimethatisbothequalandsimultaneousisoneandthesametime，andeventhosethatarenotsimultaneousareoneinkind；forifthereweredogs，andhorses，andsevenofeach，itwouldbethesamenumber。 So，too，movementsthathavesimultaneouslimitshavethesametime，yettheonemayinfactbefastandtheothernot，andonemaybelocomotionandtheotheralteration；stillthetimeofthetwochangesisthesameiftheirnumberalsoisequalandsimultaneous；andforthisreason，whilethemovementsaredifferentandseparate，thetimeiseverywherethesame，becausethenumberofequalandsimultaneousmovementsiseverywhereoneandthesame。 Nowthereissuchathingaslocomotion，andinlocomotionthereisincludedcircularmovement，andeverythingismeasuredbysomeonethinghomogeneouswithit，unitsbyaunit，horsesbyahorse，andsimilarlytimesbysomedefinitetime，and，aswesaid，timeismeasuredbymotionaswellasmotionbytime(thisbeingsobecausebyamotiondefiniteintimethequantitybothofthemotionandofthetimeismeasured):if，then，whatisfirstisthemeasureofeverythinghomogeneouswithit，regularcircularmotionisaboveallelsethemeasure，becausethenumberofthisisthebestknown。Nowneitheralterationnorincreasenorcomingintobeingcanberegular，butlocomotioncanbe。Thisalsoiswhytimeisthoughttobethemovementofthesphere，viz。becausetheothermovementsaremeasuredbythis，andtimebythismovement。 Thisalsoexplainsthecommonsayingthathumanaffairsformacircle，andthatthereisacircleinallotherthingsthathaveanaturalmovementandcomingintobeingandpassingaway。Thisisbecauseallotherthingsarediscriminatedbytime，andendandbeginasthoughconformingtoacycle；foreventimeitselfisthoughttobeacircle。Andthisopinionagainisheldbecausetimeisthemeasureofthiskindoflocomotionandisitselfmeasuredbysuch。 Sothattosaythatthethingsthatcomeintobeingformacircleistosaythatthereisacircleoftime；andthisistosaythatitismeasuredbythecircularmovement；forapartfromthemeasurenothingelsetobemeasuredisobserved；thewholeisjustapluralityofmeasures。 Itissaidrightly，too，thatthenumberofthesheepandofthedogsisthesamenumberifthetwonumbersareequal，butnotthesamedecadorthesameten；justastheequilateralandthescalenearenotthesametriangle，yettheyarethesamefigure，becausetheyarebothtriangles。Forthingsarecalledthesameso-and-soiftheydonotdifferbyadifferentiaofthatthing，butnotiftheydo；e。g。 trianglediffersfromtrianglebyadifferentiaoftriangle，thereforetheyaredifferenttriangles；buttheydonotdifferbyadifferentiaoffigure，butareinoneandthesamedivisionofit。Forafigureoftheonekindisacircleandafigureofanotherkindoftriangle，andatriangleofonekindisequilateralandatriangleofanotherkindscalene。Theyarethesamefigure，then，that，triangle，butnotthesametriangle。Thereforethenumberoftwogroupsalso-isthesamenumber(fortheirnumberdoesnotdifferbyadifferentiaofnumber)，butitisnotthesamedecad；forthethingsofwhichitisasserteddiffer；onegrouparedogs，andtheotherhorses。 Wehavenowdiscussedtime-bothtimeitselfandthemattersappropriatetotheconsiderationofit。 BookV 1 EVERYTHINGwhichchangesdoessoinoneofthreesenses。Itmaychange(1)accidentally，asforinstancewhenwesaythatsomethingmusicalwalks，thatwhichwalksbeingsomethinginwhichaptitudeformusicisanaccident。Again(2)athingissaidwithoutqualificationtochangebecausesomethingbelongingtoitchanges，i。e。instatementswhichrefertopartofthethinginquestion: thusthebodyisrestoredtohealthbecausetheeyeorthechest，thatistosayapartofthewholebody，isrestoredtohealth。Andaboveallthereis(3)thecaseofathingwhichisinmotionneitheraccidentallynorinrespectofsomethingelsebelongingtoit，butinvirtueofbeingitselfdirectlyinmotion。Herewehaveathingwhichisessentiallymovable:andthatwhichissoisadifferentthingaccordingtotheparticularvarietyofmotion:forinstanceitmaybeathingcapableofalteration:andwithinthesphereofalterationitisagainadifferentthingaccordingasitiscapableofbeingrestoredtohealthorcapableofbeingheated。Andtherearethesamedistinctionsinthecaseofthemover:(1)onethingcausesmotionaccidentally，(2)anotherpartially(becausesomethingbelongingtoitcausesmotion)，(3)anotherofitselfdirectly，as，forinstance，thephysicianheals，thehandstrikes。Wehave，then，thefollowingfactors:(a)ontheonehandthatwhichdirectlycausesmotion，and(b)ontheotherhandthatwhichisinmotion: further，wehave(c)thatinwhichmotiontakesplace，namelytime，and(distinctfromthesethree)(d)thatfromwhichand(e)thattowhichitproceeds:foreverymotionproceedsfromsomethingandtosomething，thatwhichisdirectlyinmotionbeingdistinctfromthattowhichitisinmotionandthatfromwhichitisinmotion:forinstance，wemaytakethethreethings\'wood\'，\'hot\'，and\'cold\'，ofwhichthefirstisthatwhichisinmotion，thesecondisthattowhichthemotionproceeds，andthethirdisthatfromwhichitproceeds。Thisbeingso，itisclearthatthemotionisinthewood，notinitsform:forthemotionisneithercausednorexperiencedbytheformortheplaceorthequantity。Soweareleftwithamover，amoved，andagoalofmotion。Idonotincludethestarting-pointofmotion:foritisthegoalratherthanthestarting-pointofmotionthatgivesitsnametoaparticularprocessofchange。Thus\'perishing\'ischangetonot-being，thoughitisalsotruethatthatthatwhichperisheschangesfrombeing:and\'becoming\'ischangetobeing，thoughitisalsochangefromnot-being。 Nowadefinitionofmotionhasbeengivenabove，fromwhichitwillbeseenthateverygoalofmotion，whetheritbeaform，anaffection，oraplace，isimmovable，as，forinstance，knowledgeandheat。Here，however，adifficultymayberaised。Affections，itmaybesaid，aremotions，andwhitenessisanaffection:thustheremaybechangetoamotion。Tothiswemayreplythatitisnotwhitenessbutwhiteningthatisamotion。Herealsothesamedistinctionsaretobeobserved:agoalofmotionmaybesoaccidentally，orpartiallyandwithreferencetosomethingotherthanitself，ordirectlyandwithnoreferencetoanythingelse:forinstance，athingwhichisbecomingwhitechangesaccidentallytoanobjectofthought，thecolourbeingonlyaccidentallytheobjectofthought；itchangestocolour，becausewhiteisapartofcolour，ortoEurope，becauseAthensisapartofEurope；butitchangesessentiallytowhitecolour。Itisnowclearinwhatsenseathingisinmotionessentially，accidentally，orinrespectofsomethingotherthanitself，andinwhatsensethephrase\'itselfdirectly\'isusedinthecasebothofthemoverandofthemoved:anditisalsoclearthatthemotionisnotintheformbutinthatwhichisinmotion，thatistosay\'themovableinactivity\'。Nowaccidentalchangewemayleaveoutofaccount:foritistobefoundineverything，atanytime，andinanyrespect。 Changewhichisnotaccidentalontheotherhandisnottobefoundineverything，butonlyincontraries，inthingsintermediatecontraries，andincontradictories，asmaybeprovedbyinduction。Anintermediatemaybeastarting-pointofchange，sinceforthepurposesofthechangeitservesascontrarytoeitheroftwocontraries:fortheintermediateisinasensetheextremes。Hencewespeakoftheintermediateasinasenseacontraryrelativelytotheextremesandofeitherextremeasacontraryrelativelytotheintermediate:forinstance，thecentralnoteislowrelatively-tothehighestandhighrelativelytothelowest，andgreyislightrelativelytoblackanddarkrelativelytowhite。 Andsinceeverychangeisfromsomethingtosomething-astheworditself(metabole)indicates，implyingsomething\'after\'(meta) somethingelse，thatistosaysomethingearlierandsomethinglater-thatwhichchangesmustchangeinoneoffourways:fromsubjecttosubject，fromsubjecttononsubject，fromnon-subjecttosubject，orfromnon-subjecttonon-subject，whereby\'subject\'Imeanwhatisaffirmativelyexpressed。Soitfollowsnecessarilyfromwhathasbeensaidabovethatthereareonlythreekindsofchange，thatfromsubjecttosubject，thatfromsubjecttonon-subject，andthatfromnon-subjecttosubject:forthefourthconceivablekind，thatfromnon-subjecttononsubject，isnotchange，asinthatcasethereisnooppositioneitherofcontrariesorofcontradictories。 Nowchangefromnon-subjecttosubject，therelationbeingthatofcontradiction，is\'comingtobe\'-\'unqualifiedcomingtobe\'whenthechangetakesplaceinanunqualifiedway，\'particularcomingtobe\' whenthechangeischangeinaparticularcharacter:forinstance，achangefromnot-whitetowhiteisacomingtobeoftheparticularthing，white，whilechangefromunqualifiednot-beingtobeingiscomingtobeinanunqualifiedway，inrespectofwhichwesaythatathing\'comestobe\'withoutqualification，notthatit\'comestobe\' someparticularthing。Changefromsubjecttonon-subjectis\'perishing\'-\'unqualifiedperishing\'whenthechangeisfrombeingtonot-being，\'particularperishing\'whenthechangeistotheoppositenegation，thedistinctionbeingthesameasthatmadeinthecaseofcomingtobe。 Nowtheexpression\'not-being\'isusedinseveralsenses:andtherecanbemotionneitherofthatwhich\'isnot\'inrespectoftheaffirmationornegationofapredicate，norofthatwhich\'isnot\' inthesensethatitonlypotentially\'is\'，thatistosaytheoppositeofthatwhichactually\'is\'inanunqualifiedsense:foralthoughthatwhichis\'not-white\'or\'not-good\'mayneverthelessheinmotionaccidentally(forexamplethatwhichis\'not-white\'mightbeaman)，yetthatwhichiswithoutqualification\'not-so-and-so\'cannotinanysensebeinmotion:thereforeitisimpossibleforthatwhichisnottobeinmotion。Thisbeingso，itfollowsthat\'becoming\' cannotbeamotion:foritisthatwhich\'isnot\'that\'becomes\'。 Forhowevertrueitmaybethatitaccidentally\'becomes\'，itisneverthelesscorrecttosaythatitisthatwhich\'isnot\'thatinanunqualifiedsense\'becomes\'。Andsimilarlyitisimpossibleforthatwhich\'isnot\'tobeatrest。 Therearethesedifficulties，then，inthewayoftheassumptionthatthatwhich\'isnot\'canbeinmotion:anditmaybefurtherobjectedthat，whereaseverythingwhichisinmotionisinspace，thatwhich\'isnot\'isnotinspace:forthenitwouldbesomewhere。 So，too，\'perishing\'isnotamotion:foramotionhasforitscontraryeitheranothermotionorrest，whereas\'perishing\'isthecontraryof\'becoming\'。 Since，then，everymotionisakindofchange，andthereareonlythethreekindsofchangementionedabove，andsinceofthesethreethosewhichtaketheformof\'becoming\'and\'perishing\'，thatistosaythosewhichimplyarelationofcontradiction，arenotmotions:itnecessarilyfollowsthatonlychangefromsubjecttosubjectismotion。Andeverysuchsubjectiseitheracontraryoranintermediate(foraprivationmaybeallowedtorankasacontrary)andcanbeaffirmativelyexpressed，asnaked，toothless，orblack。If，then，thecategoriesareseverallydistinguishedasBeing，Quality，Place，Time，Relation，Quantity，andActivityorPassivity，itnecessarilyfollowsthattherearethreekindsofmotion-qualitative，quantitative，andlocal。 2 InrespectofSubstancethereisnomotion，becauseSubstancehasnocontraryamongthingsthatare。NoristheremotioninrespectofRelation:foritmayhappenthatwhenonecorrelativechanges，theother，althoughthisdoesnotitselfchange，isnolongerapplicable，sothatinthesecasesthemotionisaccidental。NoristheremotioninrespectofAgentandPatient-infacttherecanneverbemotionofmoverandmoved，becausetherecannotbemotionofmotionorbecomingofbecomingoringeneralchangeofchange。 Forinthefirstplacetherearetwosensesinwhichmotionofmotionisconceivable。(1)Themotionofwhichthereismotionmightbeconceivedassubject；e。g。amanisinmotionbecausehechangesfromfairtodark。Canitbethatinthissensemotiongrowshotorcold，orchangesplace，orincreasesordecreases?Impossible:forchangeisnotasubject。Or(2)cantherebemotionofmotioninthesensethatsomeothersubjectchangesfromachangetoanothermodeofbeing，ase。g。amanchangesfromfallingilltogettingwell?Eventhisispossibleonlyinanaccidentalsense。For，whateverthesubjectmaybe，movementischangefromoneformtoanother。(Andthesameholdsgoodofbecomingandperishing，exceptthatintheseprocesseswehaveachangetoaparticularkindofopposite，whiletheother，motion，isachangetoadifferentkind。)So，ifthereistobemotionofmotion，thatwhichischangingfromhealthtosicknessmustsimultaneouslybechangingfromthisverychangetoanother。Itisclear，then，thatbythetimethatithasbecomesick，itmustalsohavechangedtowhatevermaybetheotherchangeconcerned(forthatitshouldbeatrest，thoughlogicallypossible，isexcludedbythetheory)。Moreoverthisothercanneverbeanycasualchange，butmustbeachangefromsomethingdefinitetosomeotherdefinitething。 Sointhiscaseitmustbetheoppositechange，viz。convalescence。Itisonlyaccidentallythattherecanbechangeofchange，e。g。thereisachangefromrememberingtoforgettingonlybecausethesubjectofthischangechangesatonetimetoknowledge，atanothertoignorance。 Inthesecondplace，ifthereistobechangeofchangeandbecomingofbecoming，weshallhaveaninfiniteregress。Thusifoneofaseriesofchangesistobeachangeofchange，theprecedingchangemustalsobeso:e。g。ifsimplebecomingwaseverinprocessofbecoming，thenthatwhichwasbecomingsimplebecomingwasalsoinprocessofbecoming，sothatweshouldnotyethavearrivedatwhatwasinprocessofsimplebecomingbutonlyatwhatwasalreadyinprocessofbecominginprocessofbecoming。Andthisagainwassometimeinprocessofbecoming，sothateventhenweshouldnothavearrivedatwhatwasinprocessofsimplebecoming。Andsinceinaninfiniteseriesthereisnofirstterm，heretherewillbenofirststageandthereforenofollowingstageeither。Onthishypothesis，then，nothingcanbecomeorbemovedorchange。 Thirdly，ifathingiscapableofanyparticularmotion，itisalsocapableofthecorrespondingcontrarymotionorthecorrespondingcomingtorest，andathingthatiscapableofbecomingisalsocapableofperishing:consequently，iftherebebecomingofbecoming，thatwhichisinprocessofbecomingisinprocessofperishingattheverymomentwhenithasreachedthestageofbecoming:sinceitcannotbeinprocessofperishingwhenitisjustbeginningtobecomeorafterithasceasedtobecome:forthatwhichisinprocessofperishingmustbeinexistence。 Fourthly，theremustbeasubstrateunderlyingallprocessesofbecomingandchanging。Whatcanthisbeinthepresentcase?Itiseitherthebodyorthesoulthatundergoesalteration:whatisitthatcorrespondinglybecomesmotionorbecoming?Andagainwhatisthegoaloftheirmotion?Itmustbethemotionorbecomingofsomethingfromsomethingtosomethingelse。Butinwhatsensecanthisbeso?Forthebecomingoflearningcannotbelearning:soneithercanthebecomingofbecomingbebecoming，norcanthebecomingofanyprocessbethatprocess。 Finally，sincetherearethreekindsofmotion，thesubstratumandthegoalofmotionmustbeoneorotherofthese，e。g。locomotionwillhavetobealteredortobelocallymoved。 Tosumup，then，sinceeverythingthatismovedismovedinoneofthreeways，eitheraccidentally，orpartially，oressentially，changecanchangeonlyaccidentally，ase。g。whenamanwhoisbeingrestoredtohealthrunsorlearns:andaccidentalchangewehavelongagodecidedtoleaveoutofaccount。 Since，then，motioncanbelongneithertoBeingnortoRelationnortoAgentandPatient，itremainsthattherecanbemotiononlyinrespectofQuality，Quantity，andPlace:forwitheachofthesewehaveapairofcontraries。MotioninrespectofQualityletuscallalteration，ageneraldesignationthatisusedtoincludebothcontraries:andbyQualityIdonotheremeanapropertyofsubstance(inthatsensethatwhichconstitutesaspecificdistinctionisaquality)butapassivequalityinvirtueofwhichathingissaidtobeactedonortobeincapableofbeingactedon。MotioninrespectofQuantityhasnonamethatincludesbothcontraries，butitiscalledincreaseordecreaseaccordingasoneortheotherisdesignated:thatistosaymotioninthedirectionofcompletemagnitudeisincrease，motioninthecontrarydirectionisdecrease。 MotioninrespectofPlacehasnonameeithergeneralorparticular: butwemaydesignateitbythegeneralnameoflocomotion，thoughstrictlytheterm\'locomotion\'isapplicabletothingsthatchangetheirplaceonlywhentheyhavenotthepowertocometoastand，andtothingsthatdonotmovethemselveslocally。 Changewithinthesamekindfromalessertoagreaterorfromagreatertoalesserdegreeisalteration:foritismotioneitherfromacontraryortoacontrary，whetherinanunqualifiedorinaqualifiedsense:forchangetoalesserdegreeofaqualitywillbecalledchangetothecontraryofthatquality，andchangetoagreaterdegreeofaqualitywillberegardedaschangefromthecontraryofthatqualitytothequalityitself。Itmakesnodifferencewhetherthechangebequalifiedorunqualified，exceptthatintheformercasethecontrarieswillhavetobecontrarytooneanotheronlyinaqualifiedsense:andathing\'spossessingaqualityinagreaterorinalesserdegreemeansthepresenceorabsenceinitofmoreorlessoftheoppositequality。Itisnowclear，then，thatthereareonlythesethreekindsofmotion。 Theterm\'immovable\'weapplyinthefirstplacetothatwhichisabsolutelyincapableofbeingmoved(justaswecorrespondinglyapplytheterminvisibletosound)；inthesecondplacetothatwhichismovedwithdifficultyafteralongtimeorwhosemovementisslowatthestart-infact，whatwedescribeashardtomove；andinthethirdplacetothatwhichisnaturallydesignedforandcapableofmotion，butisnotinmotionwhen，where，andasitnaturallywouldbeso。ThislastistheonlykindofimmovablethingofwhichIusetheterm\'beingatrest\':forrestiscontrarytomotion，sothatrestwillbenegationofmotioninthatwhichiscapableofadmittingmotion。 Theforegoingremarksaresufficienttoexplaintheessentialnatureofmotionandrest，thenumberofkindsofchange，andthedifferentvarietiesofmotion。 3 Letusnowproceedtodefinetheterms\'together\'and\'apart\'，\'incontact\'，\'between\'，\'insuccession\'，\'contiguous\'，and\'continuous\'，andtoshowinwhatcircumstanceseachofthesetermsisnaturallyapplicable。 Thingsaresaidtobetogetherinplacewhentheyareinoneplace(inthestrictestsenseoftheword\'place\')andtobeapartwhentheyareindifferentplaces。 Thingsaresaidtobeincontactwhentheirextremitiesaretogether。 Thatwhichachangingthing，ifitchangescontinuouslyinanaturalmanner，naturallyreachesbeforeitreachesthattowhichitchangeslast，isbetween。Thus\'between\'impliesthepresenceofatleastthreethings:forinaprocessofchangeitisthecontrarythatis\'last\':andathingismovedcontinuouslyifitleavesnogaporonlythesmallestpossiblegapinthematerial-notinthetime(foragapinthetimedoesnotpreventthingshavinga\'between\'，while，ontheotherhand，thereisnothingtopreventthehighestnotesoundingimmediatelyafterthelowest)butinthematerialinwhichthemotiontakesplace。Thisismanifestlytruenotonlyinlocalchangesbutineveryotherkindaswell。(Noweverychangeimpliesapairofopposites，andoppositesmaybeeithercontrariesorcontradictories；sincethencontradictionadmitsofnomeanterm，itisobviousthat\'between\'mustimplyapairofcontraries)Thatislocallycontrarywhichismostdistantinastraightline:fortheshortestlineisdefinitelylimited，andthatwhichisdefinitelylimitedconstitutesameasure。 Athingis\'insuccession\'whenitisafterthebeginninginpositionorinformorinsomeotherrespectinwhichitisdefinitelysoregarded，andwhenfurtherthereisnothingofthesamekindasitselfbetweenitandthattowhichitisinsuccession，e。g。alineorlinesifitisaline，aunitorunitsifitisaunit，ahouseifitisahouse(thereisnothingtopreventsomethingofadifferentkindbeingbetween)。Forthatwhichisinsuccessionisinsuccessiontoaparticularthing，andissomethingposterior:foroneisnot\'insuccession\'totwo，noristhefirstdayofthemonthtobesecond:ineachcasethelatteris\'insuccession\'totheformer。 Athingthatisinsuccessionandtouchesis\'contiguous\'。The\'continuous\'isasubdivisionofthecontiguous:thingsarecalledcontinuouswhenthetouchinglimitsofeachbecomeoneandthesameandare，asthewordimplies，containedineachother:continuityisimpossibleiftheseextremitiesaretwo。Thisdefinitionmakesitplainthatcontinuitybelongstothingsthatnaturallyinvirtueoftheirmutualcontactformaunity。Andinwhateverwaythatwhichholdsthemtogetherisone，sotoowillthewholebeone，e。g。byarivetorglueorcontactororganicunion。 Itisobviousthatoftheseterms\'insuccession\'isfirstinorderofanalysis:forthatwhichtouchesisnecessarilyinsuccession，butnoteverythingthatisinsuccessiontouches:andsosuccessionisapropertyofthingspriorindefinition，e。g。 numbers，whilecontactisnot。Andifthereiscontinuitythereisnecessarilycontact，butifthereiscontact，thatalonedoesnotimplycontinuity:fortheextremitiesofthingsmaybe\'together\' withoutnecessarilybeingone:buttheycannotbeonewithoutbeingnecessarilytogether。Sonaturaljunctionislastincomingtobe:fortheextremitiesmustnecessarilycomeintocontactiftheyaretobenaturallyjoined:butthingsthatareincontactarenotallnaturallyjoined，whilethereisnocontactclearlythereisnonaturaljunctioneither。Hence，ifassomesay\'point\'and\'unit\'haveanindependentexistenceoftheirown，itisimpossibleforthetwotobeidentical:forpointscantouchwhileunitscanonlybeinsuccession。 Moreover，therecanalwaysbesomethingbetweenpoints(foralllinesareintermediatebetweenpoints)，whereasitisnotnecessarythatthereshouldpossiblybeanythingbetweenunits:fortherecanbenothingbetweenthenumbersoneandtwo。 Wehavenowdefinedwhatismeantby\'together\'and\'apart\'，\'contact\'，\'between\'and\'insuccession\'，\'contiguous\'and\'continuous\':andwehaveshowninwhatcircumstanceseachofthesetermsisapplicable。 4 Therearemanysensesinwhichmotionissaidtobe\'one\':forweusetheterm\'one\'inmanysenses。 Motionisonegenericallyaccordingtothedifferentcategoriestowhichitmaybeassigned:thusanylocomotionisonegenericallywithanyotherlocomotion，whereasalterationisdifferentgenericallyfromlocomotion。 Motionisonespecificallywhenbesidesbeingonegenericallyitalsotakesplaceinaspeciesincapableofsubdivision:e。g。colourhasspecificdifferences:thereforeblackeningandwhiteningdifferspecifically；butatalleventseverywhiteningwillbespecificallythesamewitheveryotherwhiteningandeveryblackeningwitheveryotherblackening。Butwhiteisnotfurthersubdividedbyspecificdifferences:henceanywhiteningisspecificallyonewithanyotherwhitening。Whereithappensthatthegenusisatthesametimeaspecies，itisclearthatthemotionwilltheninasensebeonespecificallythoughnotinanunqualifiedsense:learningisanexampleofthis，knowledgebeingontheonehandaspeciesofapprehensionandontheotherhandagenusincludingthevariousknowledges。Adifficulty，however，mayberaisedastowhetheramotionisspecificallyonewhenthesamethingchangesfromthesametothesame，e。g。whenonepointchangesagainandagainfromaparticularplacetoaparticularplace:ifthismotionisspecificallyone，circularmotionwillbethesameasrectilinearmotion，androllingthesameaswalking。Butisnotthisdifficultyremovedbytheprinciplealreadylaiddownthatifthatinwhichthemotiontakesplaceisspecificallydifferent(asinthepresentinstancethecircularpathisspecificallydifferentfromthestraight)themotionitselfisalsodifferent?Wehaveexplained，then，whatismeantbysayingthatmotionisonegenericallyoronespecifically。 Motionisoneinanunqualifiedsensewhenitisoneessentiallyornumerically:andthefollowingdistinctionswillmakeclearwhatthiskindofmotionis。Therearethreeclassesofthingsinconnexionwithwhichwespeakofmotion，the\'thatwhich\'，the\'thatinwhich\'，andthe\'thatduringwhich\'。Imeanthattheremusthesomethingthatisinmotion，e。g。amanorgold，anditmustbeinmotioninsomething，e。g。aplaceoranaffection，andduringsomething，forallmotiontakesplaceduringatime。Ofthesethreeitisthethinginwhichthemotiontakesplacethatmakesitonegenericallyorspecifically，itisthethingmovedthatmakesthemotiononeinsubject，anditisthetimethatmakesitconsecutive: butitisthethreetogetherthatmakeitonewithoutqualification: toeffectthis，thatinwhichthemotiontakesplace(thespecies) mustbeoneandincapableofsubdivision，thatduringwhichittakesplace(thetime)mustbeoneandunintermittent，andthatwhichisinmotionmustbeone-notinanaccidentalsense(i。e。itmustbeoneasthewhitethatblackensisoneorCoriscuswhowalksisone，notintheaccidentalsenseinwhichCoriscusandwhitemaybeone)，normerelyinvirtueofcommunityofnature(fortheremightbeacaseoftwomenbeingrestoredtohealthatthesametimeinthesameway，e。g。frominflammationoftheeye，yetthismotionisnotreallyone，butonlyspecificallyone)。 Suppose，however，thatSocratesundergoesanalterationspecificallythesamebutatonetimeandagainatanother:inthiscaseifitispossibleforthatwhichceasedtobeagaintocomeintobeingandremainnumericallythesame，thenthismotiontoowillbeone: otherwiseitwillbethesamebutnotone。Andakintothisdifficultythereisanother；viz。ishealthone?andgenerallyarethestatesandaffectionsinbodiesseverallyoneinessencealthough(asisclear) thethingsthatcontainthemareobviouslyinmotionandinflux?Thusifaperson\'shealthatdaybreakandatthepresentmomentisoneandthesame，whyshouldnotthishealthbenumericallyonewiththatwhichherecoversafteraninterval?Thesameargumentappliesineachcase。Thereis，however，wemayanswer，thisdifference:thatifthestatesaretwothenitfollowssimplyfromthisfactthattheactivitiesmustalsoinpointofnumberbetwo(foronlythatwhichisnumericallyonecangiverisetoanactivitythatisnumericallyone)，butifthestateisone，thisisnotinitselfenoughtomakeusregardtheactivityalsoasone:forwhenamanceaseswalking，thewalkingnolongeris，butitwillagainbeifhebeginstowalkagain。 But，bethisasitmay，ifintheaboveinstancethehealthisoneandthesame，thenitmustbepossibleforthatwhichisoneandthesametocometobeandtoceasetobemanytimes。However，thesedifficultieslieoutsideourpresentinquiry。 Sinceeverymotioniscontinuous，amotionthatisoneinanunqualifiedsensemust(sinceeverymotionisdivisible)becontinuous，andacontinuousmotionmustbeone。Therewillnotbecontinuitybetweenanymotionandanyotherindiscriminatelyanymorethanthereisbetweenanytwothingschosenatrandominanyothersphere:therecanbecontinuityonlywhentheextremitiesofthetwothingsareone。Nowsomethingshavenoextremitiesatall:andtheextremitiesofothersdifferspecificallyalthoughwegivethemthesamenameof\'end\':howshoulde。g。the\'end\'ofalineandthe\'end\'ofwalkingtouchorcometobeone?Motionsthatarenotthesameeitherspecificallyorgenericallymay，itistrue，beconsecutive(e。g。amanmayrunandthenatoncefallillofafever)，andagain，inthetorch-racewehaveconsecutivebutnotcontinuouslocomotion:foraccordingtoourdefinitiontherecanbecontinuityonlywhentheendsofthetwothingsareone。Hencemotionsmaybeconsecutiveorsuccessiveinvirtueofthetimebeingcontinuous，buttherecanbecontinuityonlyinvirtueofthemotionsthemselvesbeingcontinuous，thatiswhentheendofeachisonewiththeendoftheother。Motion，therefore，thatisinanunqualifiedsensecontinuousandonemustbespecificallythesame，ofonething，andinonetime。Unityisrequiredinrespectoftimeinorderthattheremaybenointervalofimmobility，forwherethereisintermissionofmotiontheremustberest，andamotionthatincludesintervalsofrestwillbenotonebutmany，sothatamotionthatisinterruptedbystationarinessisnotoneorcontinuous，anditissointerruptedifthereisanintervaloftime。Andthoughofamotionthatisnotspecificallyone(evenifthetimeisunintermittent)thetimeisone，themotionisspecificallydifferent，andsocannotreallybeone，formotionthatisonemustbespecificallyone，thoughmotionthatisspecificallyoneisnotnecessarilyoneinanunqualifiedsense。Wehavenowexplainedwhatwemeanwhenwecallamotiononewithoutqualification。 Further，amotionisalsosaidtobeonegenerically，specifically，oressentiallywhenitiscomplete，justasinothercasescompletenessandwholenessarecharacteristicsofwhatisone: andsometimesamotionevenifincompleteissaidtobeone，providedonlythatitiscontinuous。 Andbesidesthecasesalreadymentionedthereisanotherinwhichamotionissaidtobeone，viz。whenitisregular:forinasenseamotionthatisirregularisnotregardedasone，thattitlebelongingrathertothatwhichisregular，asastraightlineisregular，theirregularbeingassuchdivisible。Butthedifferencewouldseemtobeoneofdegree。Ineverykindofmotionwemayhaveregularityorirregularity:thustheremayberegularalteration，andlocomotioninaregularpath，e。g。inacircleoronastraightline，anditisthesamewithregardtoincreaseanddecrease。Thedifferencethatmakesamotionirregularissometimestobefoundinitspath:thusamotioncannotberegularifitspathisanirregularmagnitude，e。g。abrokenline，aspiral，oranyothermagnitudethatisnotsuchthatanypartofittakenatrandomfitsontoanyotherthatmaybechosen。Sometimesitisfoundneitherintheplacenorinthetimenorinthegoalbutinthemannerofthemotion:forinsomecasesthemotionisdifferentiatedbyquicknessandslowness:thusifitsvelocityisuniformamotionisregular，ifnotitisirregular。Soquicknessandslownessarenotspeciesofmotionnordotheyconstitutespecificdifferencesofmotion，becausethisdistinctionoccursinconnexionwithallthedistinctspeciesofmotion。Thesameistrueofheavinessandlightnesswhentheyrefertothesamething:e。g。theydonotspecificallydistinguishearthfromitselforfirefromitself。Irregularmotion，therefore，whileinvirtueofbeingcontinuousitisone，issoinalesserdegree，asisthecasewithlocomotioninabrokenline:andalesserdegreeofsomethingalwaysmeansanadmixtureofitscontrary。Andsinceeverymotionthatisonecanbebothregularandirregular，motionsthatareconsecutivebutnotspecificallythesamecannotbeoneandcontinuous:forhowshouldamotioncomposedofalterationandlocomotionberegular?Ifamotionistoberegularitspartsoughttofitoneanother。 5 Wehavefurthertodeterminewhatmotionsarecontrarytoeachother，andtodeterminesimilarlyhowitiswithrest。Andwehavefirsttodecidewhethercontrarymotionsaremotionsrespectivelyfromandtothesamething，e。g。amotionfromhealthandamotiontohealth(wheretheopposition，itwouldseem，isofthesamekindasthatbetweencomingtobeandceasingtobe)；ormotionsrespectivelyfromcontraries，e。g。amotionfromhealthandamotionfromdisease；ormotionsrespectivelytocontraries，e。g。amotiontohealthandamotiontodisease；ormotionsrespectivelyfromacontraryandtotheoppositecontrary，e。g。amotionfromhealthandamotiontodisease；ormotionsrespectivelyfromacontrarytotheoppositecontraryandfromthelattertotheformer，e。g。amotionfromhealthtodiseaseandamotionfromdiseasetohealth:formotionsmustbecontrarytooneanotherinoneormoreoftheseways，asthereisnootherwayinwhichtheycanbeopposed。 Nowmotionsrespectivelyfromacontraryandtotheoppositecontrary，e。g。amotionfromhealthandamotiontodisease，arenotcontrarymotions:fortheyareoneandthesame。(Yettheiressenceisnotthesame，justaschangingfromhealthisdifferentfromchangingtodisease。)Noraremotionrespectivelyfromacontraryandfromtheoppositecontrarycontrarymotions，foramotionfromacontraryisatthesametimeamotiontoacontraryortoanintermediate(ofthis，however，weshallspeaklater)，butchangingtoacontraryratherthanchangingfromacontrarywouldseemtobethecauseofthecontrarietyofmotions，thelatterbeingtheloss，theformerthegain，ofcontrariness。Moreover，eachseveralmotiontakesitsnameratherfromthegoalthanfromthestarting-pointofchange，e。g。motiontohealthwecallconvalescence，motiontodiseasesickening。Thusweareleftwithmotionsrespectivelytocontraries，andmotionsrespectivelytocontrariesfromtheoppositecontraries。 Nowitwouldseemthatmotionstocontrariesareatthesametimemotionsfromcontraries(thoughtheiressencemaynotbethesame；\'tohealth\'isdistinct，Imean，from\'fromdisease\'，and\'fromhealth\' from\'todisease\')。 Sincethenchangediffersfrommotion(motionbeingchangefromaparticularsubjecttoaparticularsubject)，itfollowsthatcontrarymotionsaremotionsrespectivelyfromacontrarytotheoppositecontraryandfromthelattertotheformer，e。g。amotionfromhealthtodiseaseandamotionfromdiseasetohealth。 Moreover，theconsiderationofparticularexampleswillalsoshowwhatkindsofprocessesaregenerallyrecognizedascontrary:thusfallingillisregardedascontrarytorecoveringone\'shealth，theseprocesseshavingcontrarygoals，andbeingtaughtascontrarytobeingledintoerrorbyanother，itbeingpossibletoacquireerror，likeknowledge，eitherbyone\'sownagencyorbythatofanother。 Similarlywehaveupwardlocomotionanddownwardlocomotion，whicharecontrarylengthwise，locomotiontotherightandlocomotiontotheleft，whicharecontrarybreadthwise，andforwardlocomotionandbackwardlocomotion，whichtooarecontraries。Ontheotherhand，aprocesssimplytoacontrary，e。g。thatdenotedbytheexpression\'becomingwhite\'，wherenostarting-pointisspecified，isachangebutnotamotion。Andinallcasesofathingthathasnocontrarywehaveascontrarieschangefromandchangetothesamething。Thuscomingtobeiscontrarytoceasingtobe，andlosingtogaining。 Butthesearechangesandnotmotions。Andwhereverapairofcontrariesadmitofanintermediate，motionstothatintermediatemustbeheldtobeinasensemotionstooneorotherofthecontraries: fortheintermediateservesasacontraryforthepurposesofthemotion，inwhicheverdirectionthechangemaybe，e。g。greyinamotionfromgreytowhitetakestheplaceofblackasstarting-point，inamotionfromwhitetogreyittakestheplaceofblackasgoal，andinamotionfromblacktogreyittakestheplaceofwhiteasgoal:forthemiddleisopposedinasensetoeitheroftheextremes，ashasbeensaidabove。Thusweseethattwomotionsarecontrarytoeachotheronlywhenoneisamotionfromacontrarytotheoppositecontraryandtheotherisamotionfromthelattertotheformer。 6 Butsinceamotionappearstohavecontrarytoitnotonlyanothermotionbutalsoastateofrest，wemustdeterminehowthisisso。A motionhasforitscontraryinthestrictsenseofthetermanothermotion，butitalsohasforanoppositeastateofrest(forrestistheprivationofmotionandtheprivationofanythingmaybecalleditscontrary)，andmotionofonekindhasforitsoppositerestofthatkind，e。g。localmotionhaslocalrest。Thisstatement，however，needsfurtherqualification:thereremainsthequestion，istheoppositeofremainingataparticularplacemotionfromormotiontothatplace?Itissurelyclearthatsincetherearetwosubjectsbetweenwhichmotiontakesplace，motionfromoneofthese(A)toitscontrary(B)hasforitsoppositeremaininginAwhilethereversemotionhasforitsoppositeremaininginB。Atthesametimethesetwoarealsocontrarytoeachother:foritwouldbeabsurdtosupposethattherearecontrarymotionsandnotoppositestatesofrest。Statesofrestincontrariesareopposed。Totakeanexample，astateofrestinhealthis(1)contrarytoastateofrestindisease，and(2)themotiontowhichitiscontraryisthatfromhealthtodisease。For(2)itwouldbeabsurdthatitscontrarymotionshouldbethatfromdiseasetohealth，sincemotiontothatinwhichathingisatrestisratheracomingtorest，thecomingtorestbeingfoundtocomeintobeingsimultaneouslywiththemotion；andoneofthesetwomotionsitmustbe。And(1)restinwhitenessisofcoursenotcontrarytorestinhealth。 Ofallthingsthathavenocontrariesthereareoppositechanges(viz。changefromthethingandchangetothething，e。g。changefrombeingandchangetobeing)，butnomotion。So，too，ofsuchthingsthereisnoremainingthoughthereisabsenceofchange。Shouldtherebeaparticularsubject，absenceofchangeinitsbeingwillbecontrarytoabsenceofchangeinitsnot-being。Andhereadifficultymayberaised:ifnot-beingisnotaparticularsomething，whatisit，itmaybeasked，thatiscontrarytoabsenceofchangeinathing\'sbeing?andisthisabsenceofchangeastateofrest?Ifitis，theneitheritisnottruethateverystateofrestiscontrarytoamotionorelsecomingtobeandceasingtobearemotion。Itisclearthenthat，sinceweexcludethesefromamongmotions，wemustnotsaythatthisabsenceofchangeisastateofrest:wemustsaythatitissimilartoastateofrestandcallitabsenceofchange。Anditwillhaveforitscontraryeithernothingorabsenceofchangeinthething\'snot-being，ortheceasingtobeofthething:forsuchceasingtobeischangefromitandthething\'scomingtobeischangetoit。 Again，afurtherdifficultymayberaised。Howisit，itmaybeasked，thatwhereasinlocalchangebothremainingandmovingmaybenaturalorunnatural，intheotherchangesthisisnotso?e。g。 alterationisnotnownaturalandnowunnatural，forconvalescenceisnomorenaturalorunnaturalthanfallingill，whiteningnomorenaturalorunnaturalthanblackening；so，too，withincreaseanddecrease:thesearenotcontrarytoeachotherinthesensethateitherofthemisnaturalwhiletheotherisunnatural，norisoneincreasecontrarytoanotherinthissense；andthesameaccountmaybegivenofbecomingandperishing:itisnottruethatbecomingisnaturalandperishingunnatural(forgrowingoldisnatural)，nordoweobserveonebecomingtobenaturalandanotherunnatural。Weanswerthatifwhathappensunderviolenceisunnatural，thenviolentperishingisunnaturalandassuchcontrarytonaturalperishing。 Aretherethenalsosomebecomingsthatareviolentandnottheresultofnaturalnecessity，andarethereforecontrarytonaturalbecomings，andviolentincreasesanddecreases，e。g。therapidgrowthtomaturityofprofligatesandtherapidripeningofseedsevenwhennotpackedcloseintheearth?Andhowisitwithalterations?Surelyjustthesame:wemaysaythatsomealterationsareviolentwhileothersarenatural，e。g。patientsalternaturallyorunnaturallyaccordingastheythrowofffeversonthecriticaldaysornot。But，itmaybeobjected，thenweshallhaveperishingscontrarytooneanother，nottobecoming。Certainly:andwhyshouldnotthisinasensebeso?Thusitissoifoneperishingispleasantandanotherpainful:andsooneperishingwillbecontrarytoanothernotinanunqualifiedsense，butinsofarasonehasthisqualityandtheotherthat。 Nowmotionsandstatesofrestuniversallyexhibitcontrarietyinthemannerdescribedabove，e。g。upwardmotionandrestabovearerespectivelycontrarytodownwardmotionandrestbelow，thesebeinginstancesoflocalcontrariety；andupwardlocomotionbelongsnaturallytofireanddownwardtoearth，i。e。thelocomotionsofthetwoarecontrarytoeachother。Andagain，firemovesupnaturallyanddownunnaturally:anditsnaturalmotioniscertainlycontrarytoitsunnaturalmotion。Similarlywithremaining:remainingaboveiscontrarytomotionfromabovedownwards，andtoearththisremainingcomesunnaturally，thismotionnaturally。Sotheunnaturalremainingofathingiscontrarytoitsnaturalmotion，justaswefindasimilarcontrarietyinthemotionofthesamething:oneofitsmotions，theupwardorthedownward，willbenatural，theotherunnatural。 Here，however，thequestionarises，haseverystateofrestthatisnotpermanentabecoming，andisthisbecomingacomingtoastandstill?Ifso，theremustbeabecomingofthatwhichisatrestunnaturally，e。g。ofearthatrestabove:andthereforethisearthduringthetimethatitwasbeingcarriedviolentlyupwardwascomingtoastandstill。Butwhereasthevelocityofthatwhichcomestoastandstillseemsalwaystoincrease，thevelocityofthatwhichiscarriedviolentlyseemsalwaystodecrease:soitwillheinastateofrestwithouthavingbecomeso。Moreover\'comingtoastandstill\'isgenerallyrecognizedtobeidenticaloratleastconcomitantwiththelocomotionofathingtoitsproperplace。 Thereisalsoanotherdifficultyinvolvedintheviewthatremaininginaparticularplaceiscontrarytomotionfromthatplace。Forwhenathingismovingfromordiscardingsomething，itstillappearstohavethatwhichisbeingdiscarded，sothatifastateofrestisitselfcontrarytothemotionfromthestateofresttoitscontrary，thecontrariesrestandmotionwillbesimultaneouslypredicableofthesamething。Maywenotsay，however，thatinsofarasthethingisstillstationaryitisinastateofrestinaqualifiedsense?For，infact，wheneverathingisinmotion，partofitisatthestarting-pointwhilepartisatthegoaltowhichitischanging:andconsequentlyamotionfindsitstruecontraryratherinanothermotionthaninastateofrest。 Withregardtomotionandrest，then，wehavenowexplainedinwhatsenseeachofthemisoneandunderwhatconditionstheyexhibitcontrariety。 [Withregardtocomingtoastandstillthequestionmayberaisedwhetherthereisanoppositestateofresttounnaturalaswellastonaturalmotions。Itwouldbeabsurdifthiswerenotthecase: forathingmayremainstillmerelyunderviolence:thusweshallhaveathingbeinginanon-permanentstateofrestwithouthavingbecomeso。Butitisclearthatitmustbethecase:forjustasthereisunnaturalmotion，so，too，athingmaybeinanunnaturalstateofrest。Further，somethingshaveanaturalandanunnaturalmotion，e。g。firehasanaturalupwardmotionandanunnaturaldownwardmotion:isit，then，thisunnaturaldownwardmotionorisitthenaturaldownwardmotionofearththatiscontrarytothenaturalupwardmotion?Surelyitisclearthatbotharecontrarytoitthoughnotinthesamesense:thenaturalmotionofearthiscontraryinasmuchasthemotionoffireisalsonatural，whereastheupwardmotionoffireasbeingnaturaliscontrarytothedownwardmotionoffireasbeingunnatural。Thesameistrueofthecorrespondingcasesofremaining。Buttherewouldseemtobeasenseinwhichastateofrestandamotionareopposites。] BookVI 1 Nowiftheterms\'continuous\'，\'incontact\'，and\'insuccession\'areunderstoodasdefinedabovethingsbeing\'continuous\'iftheirextremitiesareone，\'incontact\'iftheirextremitiesaretogether，and\'insuccession\'ifthereisnothingoftheirownkindintermediatebetweenthem-nothingthatiscontinuouscanbecomposed\'ofindivisibles\':e。g。alinecannotbecomposedofpoints，thelinebeingcontinuousandthepointindivisible。Fortheextremitiesoftwopointscanneitherbeone(sinceofanindivisibletherecanbenoextremityasdistinctfromsomeotherpart)nortogether(sincethatwhichhasnopartscanhavenoextremity，theextremityandthethingofwhichitistheextremitybeingdistinct)。 Moreover，ifthatwhichiscontinuousiscomposedofpoints，thesepointsmustbeeithercontinuousorincontactwithoneanother:andthesamereasoningappliesinthecaseofallindivisibles。Nowforthereasongivenabovetheycannotbecontinuous:andonethingcanbeincontactwithanotheronlyifwholeisincontactwithwholeorpartwithpartorpartwithwhole。Butsinceindivisibleshavenoparts，theymustbeincontactwithoneanotheraswholewithwhole。Andiftheyareincontactwithoneanotheraswholewithwhole，theywillnotbecontinuous:forthatwhichiscontinuoushasdistinctparts: andthesepartsintowhichitisdivisiblearedifferentinthisway，i。e。spatiallyseparate。 Nor，again，canapointbeinsuccessiontoapointoramomenttoamomentinsuchawaythatlengthcanbecomposedofpointsortimeofmoments:forthingsareinsuccessionifthereisnothingoftheirownkindintermediatebetweenthem，whereasthatwhichisintermediatebetweenpointsisalwaysalineandthatwhichisintermediatebetweenmomentsisalwaysaperiodoftime。 Again，iflengthandtimecouldthusbecomposedofindivisibles，theycouldbedividedintoindivisibles，sinceeachisdivisibleintothepartsofwhichitiscomposed。But，aswesaw，nocontinuousthingisdivisibleintothingswithoutparts。Norcantherebeanythingofanyotherkindintermediatebetweenthepartsorbetweenthemoments:foriftherecouldbeanysuchthingitisclearthatitmustbeeitherindivisibleordivisible，andifitisdivisible，itmustbedivisibleeitherintoindivisiblesorintodivisiblesthatareinfinitelydivisible，inwhichcaseitiscontinuous。 Moreover，itisplainthateverythingcontinuousisdivisibleintodivisiblesthatareinfinitelydivisible:forifitweredivisibleintoindivisibles，weshouldhaveanindivisibleincontactwithanindivisible，sincetheextremitiesofthingsthatarecontinuouswithoneanotherareoneandareincontact。 Thesamereasoningappliesequallytomagnitude，totime，andtomotion:eitherallofthesearecomposedofindivisiblesandaredivisibleintoindivisibles，ornone。Thismaybemadeclearasfollows。Ifamagnitudeiscomposedofindivisibles，themotionoverthatmagnitudemustbecomposedofcorrespondingindivisiblemotions:e。g。ifthemagnitudeABGiscomposedoftheindivisiblesA，B，G，eachcorrespondingpartofthemotionDEZofOoverABGisindivisible。Therefore，sincewherethereismotiontheremustbesomethingthatisinmotion，andwherethereissomethinginmotiontheremustbemotion，thereforethebeing-movedwillalsobecomposedofindivisibles。SoOtraversedAwhenitsmotionwasD，B whenitsmotionwasE，andGsimilarlywhenitsmotionwasZ。Nowathingthatisinmotionfromoneplacetoanothercannotatthemomentwhenitwasinmotionbothbeinmotionandatthesametimehavecompleteditsmotionattheplacetowhichitwasinmotion:e。g。ifamaniswalkingtoThebes，hecannotbewalkingtoThebesandatthesametimehavecompletedhiswalktoThebes:and，aswesaw，O traversesathepartlesssectionAinvirtueofthepresenceofthemotionD。Consequently，ifOactuallypassedthroughAafterbeinginprocessofpassingthrough，themotionmustbedivisible:foratthetimewhenOwaspassingthrough，itneitherwasatrestnorhadcompleteditspassagebutwasinanintermediatestate:whileifitispassingthroughandhascompleteditspassageatthesamemoment，thenthatwhichiswalkingwillatthemomentwhenitiswalkinghavecompleteditswalkandwillbeintheplacetowhichitiswalking； thatistosay，itwillhavecompleteditsmotionattheplacetowhichitisinmotion。AndifathingisinmotionoverthewholeKBGanditsmotionisthethreeD，E，andZ，andifitisnotinmotionatalloverthepartlesssectionAbuthascompleteditsmotionoverit，thenthemotionwillconsistnotofmotionsbutofstarts，andwilltakeplacebyathing\'shavingcompletedamotionwithoutbeinginmotion:foronthisassumptionithascompleteditspassagethroughAwithoutpassingthroughit。Soitwillbepossibleforathingtohavecompletedawalkwithouteverwalking:foronthisassumptionithascompletedawalkoveraparticulardistancewithoutwalkingoverthatdistance。Since，then，everythingmustbeeitheratrestorinmotion，andOisthereforeatrestineachofthesectionsA，B，andG，itfollowsthatathingcanbecontinuouslyatrestandatthesametimeinmotion:for，aswesaw，OisinmotionoverthewholeABGandatrestinanypart(andconsequentlyinthewhole)ofit。Moreover，iftheindivisiblescomposingDEZaremotions，itwouldbepossibleforathinginspiteofthepresenceinitofmotiontobenotinmotionbutatrest，whileiftheyarenotmotions，itwouldbepossibleformotiontobecomposedofsomethingotherthanmotions。 Andiflengthandmotionarethusindivisible，itisneithermorenorlessnecessarythattimealsobesimilarlyindivisible，thatistosaybecomposedofindivisiblemoments:forifthewholedistanceisdivisibleandanequalvelocitywillcauseathingtopassthroughlessofitinlesstime，thetimemustalsobedivisible，andconversely，ifthetimeinwhichathingiscarriedoverthesectionA isdivisible，thissectionAmustalsobedivisible。 2 Andsinceeverymagnitudeisdivisibleintomagnitudes-forwehaveshownthatitisimpossibleforanythingcontinuoustobecomposedofindivisibleparts，andeverymagnitudeiscontinuous-itnecessarilyfollowsthatthequickeroftwothingstraversesagreatermagnitudeinanequaltime，anequalmagnitudeinlesstime，andagreatermagnitudeinlesstime，inconformitywiththedefinitionsometimesgivenof\'thequicker\'。SupposethatAisquickerthanB。Nowsinceoftwothingsthatwhichchangessoonerisquicker，inthetimeZH，inwhichAhaschangedfromGtoD，BwillnotyethavearrivedatD butwillbeshortofit:sothatinanequaltimethequickerwillpassoveragreatermagnitude。Morethanthis，itwillpassoveragreatermagnitudeinlesstime:forinthetimeinwhichAhasarrivedatD，Bbeingtheslowerhasarrived，letussay，atE。ThensinceA hasoccupiedthewholetimeZHinarrivingatD，willhavearrivedatOinlesstimethanthis，sayZK。NowthemagnitudeGOthatAhaspassedoverisgreaterthanthemagnitudeGE，andthetimeZKislessthanthewholetimeZH:sothatthequickerwillpassoveragreatermagnitudeinlesstime。Andfromthisitisalsoclearthatthequickerwillpassoveranequalmagnitudeinlesstimethantheslower。Forsinceitpassesoverthegreatermagnitudeinlesstimethantheslower，and(regardedbyitself)passesoverLMthegreaterinmoretimethanLXthelesser，thetimePRhinwhichitpassesoverLMwillbemorethanthetimePS，whichitpassesoverLX:sothat，thetimePRhbeinglessthanthetimePChinwhichtheslowerpassesoverLX，thetimePSwillalsobelessthanthetimePX:foritislessthanthetimePRh，andthatwhichislessthansomethingelsethatislessthanathingisalsoitselflessthanthatthing。 Henceitfollowsthatthequickerwilltraverseanequalmagnitudeinlesstimethantheslower。Again，sincethemotionofanythingmustalwaysoccupyeitheranequaltimeorlessormoretimeincomparisonwiththatofanotherthing，andsince，whereasathingisslowerifitsmotionoccupiesmoretimeandofequalvelocityifitsmotionoccupiesanequaltime，thequickerisneitherofequalvelocitynorslower，itfollowsthatthemotionofthequickercanoccupyneitheranequaltimenormoretime。Itcanonlybe，then，thatitoccupieslesstime，andthuswegetthenecessaryconsequencethatthequickerwillpassoveranequalmagnitude(aswellasagreater)inlesstimethantheslower。 Andsinceeverymotionisintimeandamotionmayoccupyanytime，andthemotionofeverythingthatisinmotionmaybeeitherquickerorslower，bothquickermotionandslowermotionmayoccupyanytime:andthisbeingso，itnecessarilyfollowsthattimealsoiscontinuous。BycontinuousImeanthatwhichisdivisibleintodivisiblesthatareinfinitelydivisible:andifwetakethisasthedefinitionofcontinuous，itfollowsnecessarilythattimeiscontinuous。Forsinceithasbeenshownthatthequickerwillpassoveranequalmagnitudeinlesstimethantheslower，supposethatA isquickerandBslower，andthattheslowerhastraversedthemagnitudeGDinthetimeZH。Nowitisclearthatthequickerwilltraversethesamemagnitudeinlesstimethanthis:letussayinthetimeZO。Again，sincethequickerhaspassedoverthewholeDinthetimeZO，theslowerwillinthesametimepassoverGK，say，whichislessthanGD。AndsinceB，theslower，haspassedoverGKinthetimeZO，thequickerwillpassoveritinlesstime:sothatthetimeZOwillagainbedivided。AndifthisisdividedthemagnitudeGK willalsobedividedjustasGDwas:andagain，ifthemagnitudeisdivided，thetimewillalsobedivided。Andwecancarryonthisprocessforever，takingtheslowerafterthequickerandthequickerafterthesloweralternately，andusingwhathasbeendemonstratedateachstageasanewpointofdeparture:forthequickerwilldividethetimeandtheslowerwilldividethelength。 If，then，thisalternationalwaysholdsgood，andateveryturninvolvesadivision，itisevidentthatalltimemustbecontinuous。 Andatthesametimeitisclearthatallmagnitudeisalsocontinuous；forthedivisionsofwhichtimeandmagnituderespectivelyaresusceptiblearethesameandequal。 Moreover，thecurrentpopularargumentsmakeitplainthat，iftimeiscontinuous，magnitudeiscontinuousalso，inasmuchasathingassesoverhalfagivenmagnitudeinhalfthetimetakentocoverthewhole:infactwithoutqualificationitpassesoveralessmagnitudeinlesstime；forthedivisionsoftimeandofmagnitudewillbethesame。Andifeitherisinfinite，soistheother，andtheoneissointhesamewayastheother；i。e。iftimeisinfiniteinrespectofitsextremities，lengthisalsoinfiniteinrespectofitsextremities:iftimeisinfiniteinrespectofdivisibility，lengthisalsoinfiniteinrespectofdivisibility:andiftimeisinfiniteinbothrespects，magnitudeisalsoinfiniteinbothrespects。 HenceZeno\'sargumentmakesafalseassumptioninassertingthatitisimpossibleforathingtopassoverorseverallytocomeincontactwithinfinitethingsinafinitetime。Fortherearetwosensesinwhichlengthandtimeandgenerallyanythingcontinuousarecalled\'infinite\':theyarecalledsoeitherinrespectofdivisibilityorinrespectoftheirextremities。Sowhileathinginafinitetimecannotcomeincontactwiththingsquantitativelyinfinite，itcancomeincontactwiththingsinfiniteinrespectofdivisibility:forinthissensethetimeitselfisalsoinfinite: andsowefindthatthetimeoccupiedbythepassageovertheinfiniteisnotafinitebutaninfinitetime，andthecontactwiththeinfinitesismadebymeansofmomentsnotfinitebutinfiniteinnumber。 Thepassageovertheinfinite，then，cannotoccupyafinitetime，andthepassageoverthefinitecannotoccupyaninfinitetime:ifthetimeisinfinitethemagnitudemustbeinfinitealso，andifthemagnitudeisinfinite，soalsoisthetime。Thismaybeshownasfollows。LetABbeafinitemagnitude，andletussupposethatitistraversedininfinitetimeG，andletafiniteperiodGDofthetimebetaken。Nowinthisperiodthethinginmotionwillpassoveracertainsegmentofthemagnitude:letBEbethesegmentthatithasthuspassedover。(ThiswillbeeitheranexactmeasureofABorlessorgreaterthananexactmeasure:itmakesnodifferencewhichitis。)Then，sinceamagnitudeequaltoBEwillalwaysbepassedoverinanequaltime，andBEmeasuresthewholemagnitude，thewholetimeoccupiedinpassingoverABwillbefinite:foritwillbedivisibleintoperiodsequalinnumbertothesegmentsintowhichthemagnitudeisdivisible。Moreover，ifitisthecasethatinfinitetimeisnotoccupiedinpassingovereverymagnitude，butitispossibletoassoversomemagnitude，sayBE，inafinitetime，andifthisBE measuresthewholeofwhichitisapart，andifanequalmagnitudeispassedoverinanequaltime，thenitfollowsthatthetimelikethemagnitudeisfinite。ThatinfinitetimewillnotbeoccupiedinpassingoverBEisevidentifthetimebetakenaslimitedinonedirection:forasthepartwillbepassedoverinlesstimethanthewhole，thetimeoccupiedintraversingthispartmustbefinite，thelimitinonedirectionbeinggiven。Thesamereasoningwillalsoshowthefalsityoftheassumptionthatinfinitelengthcanbetraversedinafinitetime。Itisevident，then，fromwhathasbeensaidthatneitheralinenorasurfacenorinfactanythingcontinuouscanbeindivisible。 Thisconclusionfollowsnotonlyfromthepresentargumentbutfromtheconsiderationthattheoppositeassumptionimpliesthedivisibilityoftheindivisible。Forsincethedistinctionofquickerandslowermayapplytomotionsoccupyinganyperiodoftimeandinanequaltimethequickerpassesoveragreaterlength，itmayhappenthatitwillpassoveralengthtwice，oroneandahalftimes，asgreatasthatpassedoverbytheslower:fortheirrespectivevelocitiesmaystandtooneanotherinthisproportion。 Suppose，then，thatthequickerhasinthesametimebeencarriedoveralengthoneandahalftimesasgreatasthattraversedbytheslower，andthattherespectivemagnitudesaredivided，thatofthequicker，themagnitudeABGD，intothreeindivisibles，andthatoftheslowerintothetwoindivisiblesEZ，ZH。Thenthetimemayalsobedividedintothreeindivisibles，foranequalmagnitudewillbepassedoverinanequaltime。SupposethenthatitisthusdividedintoKL，LM，MN。Again，sinceinthesametimetheslowerhasbeencarriedoverEZ，ZH，thetimemayalsobesimilarlydividedintotwo。Thustheindivisiblewillbedivisible，andthatwhichhasnopartswillbepassedovernotinanindivisiblebutinagreatertime。Itisevident，therefore，thatnothingcontinuousiswithoutparts。 3 Thepresentalsoisnecessarilyindivisible-thepresent，thatis，notinthesenseinwhichthewordisappliedtoonethinginvirtueofanother，butinitsproperandprimarysense；inwhichsenseitisinherentinalltime。Forthepresentissomethingthatisanextremityofthepast(nopartofthefuturebeingonthissideofit) andalsoofthefuture(nopartofthepastbeingontheothersideofit):itis，aswehavesaid，alimitofboth。Andifitisonceshownthatitisessentiallyofthischaracterandoneandthesame，itwillatoncebeevidentalsothatitisindivisible。 Nowthepresentthatistheextremityofbothtimesmustbeoneandthesame:forifeachextremityweredifferent，theonecouldnotbeinsuccessiontotheother，becausenothingcontinuouscanbecomposedofthingshavingnoparts:andiftheoneisapartfromtheother，therewillbetimeintermediatebetweenthem，becauseeverythingcontinuousissuchthatthereissomethingintermediatebetweenitslimitsanddescribedbythesamenameasitself。Butiftheintermediatethingistime，itwillbedivisible:foralltimehasbeenshowntobedivisible。Thusonthisassumptionthepresentisdivisible。Butifthepresentisdivisible，therewillbepartofthepastinthefutureandpartofthefutureinthepast:forpasttimewillbemarkedofffromfuturetimeattheactualpointofdivision。Alsothepresentwillbeapresentnotinthepropersensebutinvirtueofsomethingelse:forthedivisionwhichyieldsitwillnotbeadivisionproper。Furthermore，therewillbeapartofthepresentthatispastandapartthatisfuture，anditwillnotalwaysbethesamepartthatispastorfuture:infactoneandthesamepresentwillnotbesimultaneous:forthetimemaybedividedatmanypoints。If，therefore，thepresentcannotpossiblyhavethesecharacteristics，itfollowsthatitmustbethesamepresentthatbelongstoeachofthetwotimes。Butifthisissoitisevidentthatthepresentisalsoindivisible:forifitisdivisibleitwillbeinvolvedinthesameimplicationsasbefore。Itisclear，then，fromwhathasbeensaidthattimecontainssomethingindivisible，andthisiswhatwecallapresent。 Wewillnowshowthatnothingcanbeinmotioninapresent。Forifthisispossible，therecanbebothquickerandslowermotioninthepresent。SupposethenthatinthepresentNthequickerhastraversedthedistanceAB。Thatbeingso，theslowerwillinthesamepresenttraverseadistancelessthanAB，sayAG。ButsincetheslowerwillhaveoccupiedthewholepresentintraversingAG，thequickerwilloccupylessthanthisintraversingit。Thusweshallhaveadivisionofthepresent，whereaswefoundittobeindivisible。 Itisimpossible，therefore，foranythingtobeinmotioninapresent。 Norcananythingbeatrestinapresent:for，asweweresaying，onlycanbeatrestwhichisnaturallydesignedtobeinmotionbutisnotinmotionwhen，where，orasitwouldnaturallybeso:since，therefore，nothingisnaturallydesignedtobeinmotioninapresent，itisclearthatnothingcanbeatrestinapresenteither。 Moreover，inasmuchasitisthesamepresentthatbelongstoboththetimes，anditispossibleforathingtobeinmotionthroughoutonetimeandtobeatrestthroughouttheother，andthatwhichisinmotionoratrestforthewholeofatimewillbeinmotionoratrestasthecasemaybeinanypartofitinwhichitisnaturallydesignedtobeinmotionoratrest:thisbeingso，theassumptionthattherecanbemotionorrestinapresentwillcarrywithittheimplicationthatthesamethingcanatthesametimebeatrestandinmotion:forboththetimeshavethesameextremity，viz。thepresent。 Again，whenwesaythatathingisatrest，weimplythatitsconditioninwholeandinpartisatthetimeofspeakinguniformwithwhatitwaspreviously:butthepresentcontainsno\'previously\': consequently，therecanbenorestinit。 Itfollowsthenthatthemotionofthatwhichisinmotionandtherestofthatwhichisatrestmustoccupytime。 4 Further，everythingthatchangesmustbedivisible。Forsinceeverychangeisfromsomethingtosomething，andwhenathingisatthegoalofitschangeitisnolongerchanging，andwhenbothititselfandallitspartsareatthestarting-pointofitschangeitisnotchanging(forthatwhichisinwholeandinpartinanunvaryingconditionisnotinastateofchange)；itfollows，therefore，thatpartofthatwhichischangingmustbeatthestarting-pointandpartatthegoal:forasawholeitcannotbeinbothorinneither。 (Hereby\'goalofchange\'Imeanthatwhichcomesfirstintheprocessofchange:e。g。inaprocessofchangefromwhitethegoalinquestionwillbegrey，notblack:foritisnotnecessarythatthatthatwhichischangingshouldbeateitheroftheextremes。)Itisevident，therefore，thateverythingthatchangesmustbedivisible。 Nowmotionisdivisibleintwosenses。Inthefirstplaceitisdivisibleinvirtueofthetimethatitoccupies。Inthesecondplaceitisdivisibleaccordingtothemotionsoftheseveralpartsofthatwhichisinmotion:e。g。ifthewholeAGisinmotion，therewillbeamotionofABandamotionofBG。Thatbeingso，letDEbethemotionofthepartABandEZthemotionofthepartBG。ThenthewholeDZmustbethemotionofAG:forDZmustconstitutethemotionofAG inasmuchasDEandEZseverallyconstitutethemotionsofeachofitsparts。Butthemotionofathingcanneverbeconstitutedbythemotionofsomethingelse:consequentlythewholemotionisthemotionofthewholemagnitude。 Again，sinceeverymotionisamotionofsomething，andthewholemotionDZisnotthemotionofeitheroftheparts(foreachofthepartsDE，EZisthemotionofoneofthepartsAB，BG)orofanythingelse(for，thewholemotionbeingthemotionofawhole，thepartsofthemotionarethemotionsofthepartsofthatwhole: andthepartsofDZarethemotionsofAB，BGandofnothingelse: for，aswesaw，amotionthatisonecannotbethemotionofmorethingsthanone):sincethisisso，thewholemotionwillbethemotionofthemagnitudeABG。 Again，ifthereisamotionofthewholeotherthanDZ，saythetheofeachoftheartsmaybesubtractedfromit:andthesemotionswillbeequaltoDE，EZrespectively:forthemotionofthatwhichisonemustbeone。SoifthewholemotionOImaybedividedintothemotionsoftheparts，OIwillbeequaltoDZ:ifontheotherhandthereisanyremainder，sayKI，thiswillbeamotionofnothing: foritcanbethemotionneitherofthewholenoroftheparts(asthemotionofthatwhichisonemustbeone)norofanythingelse:foramotionthatiscontinuousmustbethemotionofthingsthatarecontinuous。AndthesameresultfollowsifthedivisionofOI revealsasurplusonthesideofthemotionsoftheparts。 Consequently，ifthisisimpossible，thewholemotionmustbethesameasandequaltoDZ。 Thistheniswhatismeantbythedivisionofmotionaccordingtothemotionsoftheparts:anditmustbeapplicabletoeverythingthatisdivisibleintoparts。 Motionisalsosusceptibleofanotherkindofdivision，thataccordingtotime。Forsinceallmotionisintimeandalltimeisdivisible，andinlesstimethemotionisless，itfollowsthateverymotionmustbedivisibleaccordingtotime。Andsinceeverythingthatisinmotionisinmotioninacertainsphereandforacertaintimeandhasamotionbelongingtoit，itfollowsthatthetime，themotion，thebeing-in-motion，thethingthatisinmotion，andthesphereofthemotionmustallbesusceptibleofthesamedivisions(thoughspheresofmotionarenotalldivisibleinalikemanner:thusquantityisessentially，qualityaccidentallydivisible)。ForsupposethatAisthetimeoccupiedbythemotionB。Thenifallthetimehasbeenoccupiedbythewholemotion，itwilltakelessofthemotiontooccupyhalfthetime，lessagaintooccupyafurthersubdivisionofthetime，andsoontoinfinity。Again，thetimewillbedivisiblesimilarlytothemotion:forifthewholemotionoccupiesallthetimehalfthemotionwilloccupyhalfthetime，andlessofthemotionagainwilloccupylessofthetime。 Inthesamewaythebeing-in-motionwillalsobedivisible。ForletGbethewholebeing-in-motion。Thenthebeing-in-motionthatcorrespondstohalfthemotionwillbelessthanthewholebeing-in-motion，thatwhichcorrespondstoaquarterofthemotionwillbelessagain，andsoontoinfinity。Moreoverbysettingoutsuccessivelythebeing-in-motioncorrespondingtoeachofthetwomotionsDG(say)andGE，wemayarguethatthewholebeing-in-motionwillcorrespondtothewholemotion(forifitweresomeotherbeing-in-motionthatcorrespondedtothewholemotion，therewouldbemorethanonebeing-inmotioncorrespondingtothesamemotion)，theargumentbeingthesameasthatwherebyweshowedthatthemotionofathingisdivisibleintothemotionsofthepartsofthething:forifwetakeseparatelythebeing-inmotioncorrespondingtoeachofthetwomotions，weshallseethatthewholebeing-inmotioniscontinuous。 Thesamereasoningwillshowthedivisibilityofthelength，andinfactofeverythingthatformsasphereofchange(thoughsomeoftheseareonlyaccidentallydivisiblebecausethatwhichchangesisso):forthedivisionofonetermwillinvolvethedivisionofall。 So，too，inthematteroftheirbeingfiniteorinfinite，theywillallalikebeeithertheoneortheother。Andwenowseethatinmostcasesthefactthatallthetermsaredivisibleorinfiniteisadirectconsequenceofthefactthatthethingthatchangesisdivisibleorinfinite:fortheattributes\'divisible\'and\'infinite\' belonginthefirstinstancetothethingthatchanges。Thatdivisibilitydoessowehavealreadyshown:thatinfinitydoessowillbemadeclearinwhatfollows?