第3章

2 WemaydistinguishgenerallybetweenpredicatingBofAbecauseit(A)isitself，andbecauseitissomethingelse；andparticularlybetweenplacewhichiscommonandinwhichallbodiesare，andthespecialplaceoccupiedprimarilybyeach。Imean，forinstance，thatyouarenowintheheavensbecauseyouareintheairanditisintheheavens；andyouareintheairbecauseyouareontheearth；andsimilarlyontheearthbecauseyouareinthisplacewhichcontainsnomorethanyou。 Nowifplaceiswhatprimarilycontainseachbody，itwouldbealimit，sothattheplacewouldbetheformorshapeofeachbodybywhichthemagnitudeorthematterofthemagnitudeisdefined:forthisisthelimitofeachbody。 If，then，welookatthequestioninthiswaytheplaceofathingisitsform。But，ifweregardtheplaceastheextensionofthemagnitude，itisthematter。Forthisisdifferentfromthemagnitude: itiswhatiscontainedanddefinedbytheform，asbyaboundingplane。Matterortheindeterminateisofthisnature；whentheboundaryandattributesofaspherearetakenaway，nothingbutthematterisleft。 ThisiswhyPlatointheTimaeussaysthatmatterandspacearethesame；forthe\'participant\'andspaceareidentical。(Itistrue，indeed，thattheaccounthegivesthereofthe\'participant\' isdifferentfromwhathesaysinhisso-called\'unwrittenteaching\'。Nevertheless，hedididentifyplaceandspace。)ImentionPlatobecause，whileallholdplacetobesomething，healonetriedtosaywhatitis。 Inviewofthesefactsweshouldnaturallyexpecttofinddifficultyindeterminingwhatplaceis，ifindeeditisoneofthesetwothings，matterorform。Theydemandaveryclosescrutiny，especiallyasitisnoteasytorecognizethemapart。 Butitisatanyratenotdifficulttoseethatplacecannotbeeitherofthem。Theformandthematterarenotseparatefromthething，whereastheplacecanbeseparated。Aswepointedout，whereairwas，waterinturncomestobe，theonereplacingtheother；andsimilarlywithotherbodies。Hencetheplaceofathingisneitherapartnorastateofit，butisseparablefromit。Forplaceissupposedtobesomethinglikeavessel-thevesselbeingatransportableplace。Butthevesselisnopartofthething。 Insofarthenasitisseparablefromthething，itisnottheform:quacontaining，itisdifferentfromthematter。 Alsoitisheldthatwhatisanywhereisbothitselfsomethingandthatthereisadifferentthingoutsideit。(Platoofcourse，ifwemaydigress，oughttotelluswhytheformandthenumbersarenotinplace，if\'whatparticipates\'isplace-whetherwhatparticipatesistheGreatandtheSmallorthematter，ashecalleditinwritingintheTimaeus。) Further，howcouldabodybecarriedtoitsownplace，ifplacewasthematterortheform?Itisimpossiblethatwhathasnoreferencetomotionorthedistinctionofupanddowncanbeplace。Soplacemustbelookedforamongthingswhichhavethesecharacteristics。 Iftheplaceisinthething(itmustbeifitiseithershapeormatter)placewillhaveaplace:forboththeformandtheindeterminateundergochangeandmotionalongwiththething，andarenotalwaysinthesameplace，butarewherethethingis。Hencetheplacewillhaveaplace。 Further，whenwaterisproducedfromair，theplacehasbeendestroyed，fortheresultingbodyisnotinthesameplace。Whatsortofdestructionthenisthat? Thisconcludesmystatementofthereasonswhyspacemustbesomething，andagainofthedifficultiesthatmayberaisedaboutitsessentialnature。 3 Thenextstepwemusttakeistoseeinhowmanysensesonethingissaidtobe\'in\'another。 (1)Asthefingeris\'in\'thehandandgenerallythepart\'in\'thewhole。 (2)Asthewholeis\'in\'theparts:forthereisnowholeoverandabovetheparts。 (3)Asmanis\'in\'animalandgenerallyspecies\'in\'genus。 (4)Asthegenusis\'in\'thespeciesandgenerallythepartofthespecificform\'in\'thedefinitionofthespecificform。 (5)Ashealthis\'in\'thehotandthecoldandgenerallytheform\'in\'thematter。 (6)AstheaffairsofGreececentre\'in\'theking，andgenerallyeventscentre\'in\'theirprimarymotiveagent。 (7)Astheexistenceofathingcentres\'initsgoodandgenerally\'in\'itsend，i。e。in\'thatforthesakeofwhich\'itexists。 (8)Inthestrictestsenseofall，asathingis\'in\'avessel，andgenerally\'in\'place。 Onemightraisethequestionwhetherathingcanbeinitself，orwhethernothingcanbeinitself-everythingbeingeithernowhereorinsomethingelse。 Thequestionisambiguous；wemaymeanthethingquaitselforquasomethingelse。 Whentherearepartsofawhole-theonethatinwhichathingis，theotherthethingwhichisinit-thewholewillbedescribedasbeinginitself。Forathingisdescribedintermsofitsparts，aswellasintermsofthethingasawhole，e。g。amanissaidtobewhitebecausethevisiblesurfaceofhimiswhite，ortobescientificbecausehisthinkingfacultyhasbeentrained。Thejarthenwillnotbeinitselfandthewinewillnotbeinitself。Butthejarofwinewill:forthecontentsandthecontainerarebothpartsofthesamewhole。 Inthissensethen，butnotprimarily，athingcanbeinitself，namely，as\'white\'isinbody(forthevisiblesurfaceisinbody)，andscienceisinthemind。 Itisfromthese，whichare\'parts\'(inthesenseatleastofbeing\'in\'theman)，thatthemaniscalledwhite，&c。Butthejarandthewineinseparationarenotpartsofawhole，thoughtogethertheyare。Sowhenthereareparts，athingwillbeinitself，as\'white\'isinmanbecauseitisinbody，andinbodybecauseitresidesinthevisiblesurface。Wecannotgofurtherandsaythatitisinsurfaceinvirtueofsomethingotherthanitself。(Yetitisnotinitself:thoughtheseareinawaythesamething，)theydifferinessence，eachhavingaspecialnatureandcapacity，\'surface\'and\'white\'。 Thusifwelookatthematterinductivelywedonotfindanythingtobe\'in\'itselfinanyofthesensesthathavebeendistinguished； anditcanbeseenbyargumentthatitisimpossible。Foreachoftwothingswillhavetobeboth，e。g。thejarwillhavetobebothvesselandwine，andthewinebothwineandjar，ifitispossibleforathingtobeinitself；sothat，howevertrueitmightbethattheywereineachother，thejarwillreceivethewineinvirtuenotofitsbeingwinebutofthewine\'sbeingwine，andthewinewillbeinthejarinvirtuenotofitsbeingajarbutofthejar\'sbeingajar。Nowthattheyaredifferentinrespectoftheiressenceisevident；for\'thatinwhichsomethingis\'and\'thatwhichisinit\'wouldbedifferentlydefined。 Norisitpossibleforathingtobeinitselfevenincidentally: fortwothingswouldatthesametimeinthesamething。Thejarwouldbeinitself-ifathingwhosenatureitistoreceivecanbeinitself；andthatwhichitreceives，namely(ifwine)wine，willbeinit。 Obviouslythenathingcannotbeinitselfprimarily。 Zeno\'sproblem-thatifPlaceissomethingitmustbeinsomething-isnotdifficulttosolve。Thereisnothingtopreventthefirstplacefrombeing\'in\'somethingelse-notindeedinthatas\'in\'place，butashealthis\'in\'thehotasapositivedeterminationofitorasthehotis\'in\'bodyasanaffection。Soweescapetheinfiniteregress。 Anotherthingisplain:sincethevesselisnopartofwhatisinit(whatcontainsinthestrictsenseisdifferentfromwhatiscontained)，placecouldnotbeeitherthematterortheformofthethingcontained，butmustdifferent-forthelatter，boththematterandtheshape，arepartsofwhatiscontained。 Thisthenmayserveasacriticalstatementofthedifficultiesinvolved。 4 Whatthenafterallisplace?Theanswertothisquestionmaybeelucidatedasfollows。 Letustakeforgrantedaboutitthevariouscharacteristicswhicharesupposedcorrectlytobelongtoitessentially。Weassumethen- (1)Placeiswhatcontainsthatofwhichitistheplace。 (2)Placeisnopartofthething。 (3)Theimmediateplaceofathingisneitherlessnorgreaterthanthething。 (4)Placecanbeleftbehindbythethingandisseparable。Inaddition: (5)Allplaceadmitsofthedistinctionofupanddown，andeachofthebodiesisnaturallycarriedtoitsappropriateplaceandreststhere，andthismakestheplaceeitherupordown。 Havinglaidthesefoundations，wemustcompletethetheory。Weoughttotrytomakeourinvestigationsuchaswillrenderanaccountofplace，andwillnotonlysolvethedifficultiesconnectedwithit，butwillalsoshowthattheattributessupposedtobelongtoitdoreallybelongtoit，andfurtherwillmakeclearthecauseofthetroubleandofthedifficultiesaboutit。Suchisthemostsatisfactorykindofexposition。 Firstthenwemustunderstandthatplacewouldnothavebeenthoughtof，iftherehadnotbeenaspecialkindofmotion，namelythatwithrespecttoplace。Itischieflyforthisreasonthatwesupposetheheavenalsotobeinplace，becauseitisinconstantmovement。Ofthiskindofchangetherearetwospecies-locomotionontheonehandand，ontheother，increaseanddiminution。Forthesetooinvolvevariationofplace:whatwastheninthisplacehasnowinturnchangedtowhatislargerorsmaller。 Again，whenwesayathingis\'moved\'，thepredicateeither(1) belongstoitactually，invirtueofitsownnature，or(2)invirtueofsomethingconjoinedwithit。Inthelattercaseitmaybeeither(a)somethingwhichbyitsownnatureiscapableofbeingmoved，e。g。thepartsofthebodyorthenailintheship，or(b) somethingwhichisnotinitselfcapableofbeingmoved，butisalwaysmovedthroughitsconjunctionwithsomethingelse，as\'whiteness\'or\'science\'。Thesehavechangedtheirplaceonlybecausethesubjectstowhichtheybelongdoso。 Wesaythatathingisintheworld，inthesenseofinplace，becauseitisintheair，andtheairisintheworld；andwhenwesayitisintheair，wedonotmeanitisineverypartoftheair，butthatitisintheairbecauseoftheoutersurfaceoftheairwhichsurroundsit；forifalltheairwereitsplace，theplaceofathingwouldnotbeequaltothething-whichitissupposedtobe，andwhichtheprimaryplaceinwhichathingisactuallyis。 Whenwhatsurrounds，then，isnotseparatefromthething，butisincontinuitywithit，thethingissaidtobeinwhatsurroundsit，notinthesenseofinplace，butasapartinawhole。Butwhenthethingisseparateandincontact，itisimmediately\'in\'theinnersurfaceofthesurroundingbody，andthissurfaceisneitherapartofwhatisinitnoryetgreaterthanitsextension，butequaltoit；fortheextremitiesofthingswhichtoucharecoincident。 Further，ifonebodyisincontinuitywithanother，itisnotmovedinthatbutwiththat。Ontheotherhanditismovedinthatifitisseparate。Itmakesnodifferencewhetherwhatcontainsismovedornot。 Again，whenitisnotseparateitisdescribedasapartinawhole，asthepupilintheeyeorthehandinthebody:whenitisseparate，asthewaterinthecaskorthewineinthejar。Forthehandismovedwiththebodyandthewaterinthecask。 Itwillnowbeplainfromtheseconsiderationswhatplaceis。 Therearejustfourthingsofwhichplacemustbeone-theshape，orthematter，orsomesortofextensionbetweentheboundingsurfacesofthecontainingbody，orthisboundaryitselfifitcontainsnoextensionoverandabovethebulkofthebodywhichcomestobeinit。 Threeoftheseitobviouslycannotbe: (1)Theshapeissupposedtobeplacebecauseitsurrounds，fortheextremitiesofwhatcontainsandofwhatiscontainedarecoincident。Boththeshapeandtheplace，itistrue，areboundaries。Butnotofthesamething:theformistheboundaryofthething，theplaceistheboundaryofthebodywhichcontainsit。 (2)Theextensionbetweentheextremitiesisthoughttobesomething，becausewhatiscontainedandseparatemayoftenbechangedwhilethecontainerremainsthesame(aswatermaybepouredfromavessel)-theassumptionbeingthattheextensionissomethingoverandabovethebodydisplaced。Butthereisnosuchextension。Oneofthebodieswhichchangeplacesandarenaturallycapableofbeingincontactwiththecontainerfallsinwhicheveritmaychancetobe。 Iftherewereanextensionwhichweresuchastoexistindependentlyandbepermanent，therewouldbeaninfinityofplacesinthesamething。Forwhenthewaterandtheairchangeplaces，alltheportionsofthetwotogetherwillplaythesamepartinthewholewhichwaspreviouslyplayedbyallthewaterinthevessel；atthesametimetheplacetoowillbeundergoingchange；sothattherewillbeanotherplacewhichistheplaceoftheplace，andmanyplaceswillbecoincident。Thereisnotadifferentplaceofthepart，inwhichitismoved，whenthewholevesselchangesitsplace:itisalwaysthesame:foritisinthe(proximate)placewheretheyarethattheairandthewater(orthepartsofthewater)succeedeachother，notinthatplaceinwhichtheycometobe，whichispartoftheplacewhichistheplaceofthewholeworld。 (3)Thematter，too，mightseemtobeplace，atleastifweconsideritinwhatisatrestandisthusseparatebutincontinuity。Forjustasinchangeofqualitythereissomethingwhichwasformerlyblackandisnowwhite，orformerlysoftandnowhard-thisisjustwhywesaythatthematterexists-soplace，becauseitpresentsasimilarphenomenon，isthoughttoexist-onlyintheonecasewesaysobecausewhatwasairisnowwater，intheotherbecausewhereairformerlywasthereaisnowwater。Butthematter，aswesaidbefore，isneitherseparablefromthethingnorcontainsit，whereasplacehasbothcharacteristics。 Well，then，ifplaceisnoneofthethree-neithertheformnorthematternoranextensionwhichisalwaysthere，differentfrom，andoverandabove，theextensionofthethingwhichisdisplaced-placenecessarilyistheoneofthefourwhichisleft，namely，theboundaryofthecontainingbodyatwhichitisincontactwiththecontainedbody。(Bythecontainedbodyismeantwhatcanbemovedbywayoflocomotion。) Placeisthoughttobesomethingimportantandhardtograsp，bothbecausethematterandtheshapepresentthemselvesalongwithit，andbecausethedisplacementofthebodythatismovedtakesplaceinastationarycontainer，foritseemspossiblethatthereshouldbeanintervalwhichisotherthanthebodieswhicharemoved。Theair，too，whichisthoughttobeincorporeal，contributessomethingtothebelief:itisnotonlytheboundariesofthevesselwhichseemtobeplace，butalsowhatisbetweenthem，regardedasempty。Just，infact，asthevesselistransportableplace，soplaceisanon-portablevessel。Sowhenwhatiswithinathingwhichismoved，ismovedandchangesitsplace，asaboatonariver，whatcontainsplaysthepartofavesselratherthanthatofplace。Placeontheotherhandisratherwhatismotionless:soitisratherthewholeriverthatisplace，becauseasawholeitismotionless。 Henceweconcludethattheinnermostmotionlessboundaryofwhatcontainsisplace。 Thisexplainswhythemiddleoftheheavenandthesurfacewhichfacesusoftherotatingsystemareheldtobe\'up\'and\'down\'inthestrictandfullestsenseforallmen:fortheoneisalwaysatrest，whiletheinnersideoftherotatingbodyremainsalwayscoincidentwithitself。Hencesincethelightiswhatisnaturallycarriedup，andtheheavywhatiscarrieddown，theboundarywhichcontainsinthedirectionofthemiddleoftheuniverse，andthemiddleitself，aredown，andthatwhichcontainsinthedirectionoftheoutermostpartoftheuniverse，andtheoutermostpartitself，areup。 Forthisreason，too，placeisthoughttobeakindofsurface，andasitwereavessel，i。e。acontainerofthething。 Further，placeiscoincidentwiththething，forboundariesarecoincidentwiththebounded。 5 Ifthenabodyhasanotherbodyoutsideitandcontainingit，itisinplace，andifnot，not。Thatiswhy，evenifthereweretobewaterwhichhadnotacontainer，thepartsofit，ontheonehand，willbemoved(foronepartiscontainedinanother)，while，ontheotherhand，thewholewillbemovedinonesense，butnotinanother。Forasawholeitdoesnotsimultaneouslychangeitsplace，thoughitwillbemovedinacircle:forthisplaceistheplaceofitsparts。(Somethingsaremoved，notupanddown，butinacircle； othersupanddown，suchthingsnamelyasadmitofcondensationandrarefaction。) Aswasexplained，somethingsarepotentiallyinplace，othersactually。So，whenyouhaveahomogeneoussubstancewhichiscontinuous，thepartsarepotentiallyinplace:whenthepartsareseparated，butincontact，likeaheap，theyareactuallyinplace。 Again，(1)somethingsareperseinplace，namelyeverybodywhichismovableeitherbywayoflocomotionorbywayofincreaseispersesomewhere，buttheheaven，ashasbeensaid，isnotanywhereasawhole，norinanyplace，ifatleast，aswemustsuppose，nobodycontainsit。Onthelineonwhichitismoved，itspartshaveplace: foreachiscontiguousthenext。 But(2)otherthingsareinplaceindirectly，throughsomethingconjoinedwiththem，asthesoulandtheheaven。Thelatteris，inaway，inplace，forallitspartsare:forontheorbonepartcontainsanother。Thatiswhytheupperpartismovedinacircle，whiletheAllisnotanywhere。Forwhatissomewhereisitselfsomething，andtheremustbealongsideitsomeotherthingwhereinitisandwhichcontainsit。ButalongsidetheAllortheWholethereisnothingoutsidetheAll，andforthisreasonallthingsareintheheaven；fortheheaven，wemaysay，istheAll。Yettheirplaceisnotthesameastheheaven。Itispartofit，theinnermostpartofit，whichisincontactwiththemovablebody；andforthisreasontheearthisinwater，andthisintheair，andtheairintheaether，andtheaetherinheaven，butwecannotgoonandsaythattheheavenisinanythingelse。 Itisclear，too，fromtheseconsiderationsthatalltheproblemswhichwereraisedaboutplacewillbesolvedwhenitisexplainedinthisway: (1)Thereisnonecessitythattheplaceshouldgrowwiththebodyinit，(2)Northatapointshouldhaveaplace，(3)Northattwobodiesshouldbeinthesameplace，(4)Northatplaceshouldbeacorporealinterval:forwhatisbetweentheboundariesoftheplaceisanybodywhichmaychancetobethere，notanintervalinbody。 Further，(5)placeisalsosomewhere，notinthesenseofbeinginaplace，butasthelimitisinthelimited；fornoteverythingthatisisinplace，butonlymovablebody。 Also(6)itisreasonablethateachkindofbodyshouldbecarriedtoitsownplace。Forabodywhichisnextintheseriesandincontact(notbycompulsion)isakin，andbodieswhichareuniteddonotaffecteachother，whilethosewhichareincontactinteractoneachother。 Nor(7)isitwithoutreasonthateachshouldremainnaturallyinitsproperplace。Forthisparthasthesamerelationtoitsplace，asaseparableparttoitswhole，aswhenonemovesapartofwaterorair:so，too，airisrelatedtowater，fortheoneislikematter，theotherform-wateristhematterofair，airasitweretheactualityofwater，forwaterispotentiallyair，whileairispotentiallywater，thoughinanotherway。 Thesedistinctionswillbedrawnmorecarefullylater。Onthepresentoccasionitwasnecessarytorefertothem:whathasnowbeenstatedobscurelywillthenbemademoreclear。Ifthematterandthefulfilmentarethesamething(forwaterisboth，theonepotentially，theothercompletely)，waterwillberelatedtoairinawayasparttowhole。Thatiswhythesehavecontact:itisorganicunionwhenbothbecomeactuallyone。 Thisconcludesmyaccountofplace-bothofitsexistenceandofitsnature。 6 Theinvestigationofsimilarquestionsaboutthevoid，also，mustbeheldtobelongtothephysicist-namelywhetheritexistsornot，andhowitexistsorwhatitis-justasaboutplace。Theviewstakenofitinvolveargumentsbothforandagainst，inmuchthesamesortofway。Forthosewhoholdthatthevoidexistsregarditasasortofplaceorvesselwhichissupposedtobe\'full\'whenitholdsthebulkwhichitiscapableofcontaining，\'void\'whenitisdeprivedofthat-asif\'void\'and\'full\'and\'place\'denotedthesamething，thoughtheessenceofthethreeisdifferent。 Wemustbegintheinquirybyputtingdowntheaccountgivenbythosewhosaythatitexists，thentheaccountofthosewhosaythatitdoesnotexist，andthirdthecurrentviewonthesequestions。 Thosewhotrytoshowthatthevoiddoesnotexistdonotdisprovewhatpeoplereallymeanbyit，butonlytheirerroneouswayofspeaking；thisistrueofAnaxagorasandofthosewhorefutetheexistenceofthevoidinthisway。Theymerelygiveaningeniousdemonstrationthatairissomething——bystrainingwine-skinsandshowingtheresistanceoftheair，andbycuttingitoffinclepsydras。Butpeoplereallymeanthatthereisanemptyintervalinwhichthereisnosensiblebody。Theyholdthateverythingwhichisinbodyisbodyandsaythatwhathasnothinginitatallisvoid(sowhatisfullofairisvoid)。Itisnotthentheexistenceofairthatneedstobeproved，butthenon-existenceofaninterval，differentfromthebodies，eitherseparableoractual-anintervalwhichdividesthewholebodysoastobreakitscontinuity，asDemocritusandLeucippushold，andmanyotherphysicists-orevenperhapsassomethingwhichisoutsidethewholebody，whichremainscontinuous。 Thesepeople，then，havenotreachedeventhethresholdoftheproblem，butratherthosewhosaythatthevoidexists。 (1)Theyargue，foronething，thatchangeinplace(i。e。locomotionandincrease)wouldnotbe。Foritismaintainedthatmotionwouldseemnottoexist，iftherewerenovoid，sincewhatisfullcannotcontainanythingmore。Ifitcould，andthereweretwobodiesinthesameplace，itwouldalsobetruethatanynumberofbodiescouldbetogether；foritisimpossibletodrawalineofdivisionbeyondwhichthestatementwouldbecomeuntrue。Ifthiswerepossible，itwouldfollowalsothatthesmallestbodywouldcontainthegreatest；for\'manyalittlemakesamickle\':thusifmanyequalbodiescanbetogether，soalsocanmanyunequalbodies。 Melissus，indeed，infersfromtheseconsiderationsthattheAllisimmovable；forifitweremovedtheremust，hesays，bevoid，butvoidisnotamongthethingsthatexist。 Thisargument，then，isonewayinwhichtheyshowthatthereisavoid。 (2)Theyreasonfromthefactthatsomethingsareobservedtocontractandbecompressed，aspeoplesaythatacaskwillholdthewinewhichformerlyfilledit，alongwiththeskinsintowhichthewinehasbeendecanted，whichimpliesthatthecompressedbodycontractsintothevoidspresentinit。 Again(3)increase，too，isthoughttotakealwaysbymeansofvoid，fornutrimentisbody，anditisimpossiblefortwobodiestobetogether。Aproofofthistheyfindalsoinwhathappenstoashes，whichabsorbasmuchwaterastheemptyvessel。 ThePythagoreans，too，(4)heldthatvoidexistsandthatitenterstheheavenitself，whichasitwereinhalesit，fromtheinfiniteair。Furtheritisthevoidwhichdistinguishesthenaturesofthings，asifitwerelikewhatseparatesanddistinguishesthetermsofaseries。Thisholdsprimarilyinthenumbers，forthevoiddistinguishestheirnature。 These，then，andsomany，arethemaingroundsonwhichpeoplehavearguedforandagainsttheexistenceofthevoid。 7 Asasteptowardssettlingwhichviewistrue，wemustdeterminethemeaningofthename。 Thevoidisthoughttobeplacewithnothinginit。Thereasonforthisisthatpeopletakewhatexiststobebody，andholdthatwhileeverybodyisinplace，voidisplaceinwhichthereisnobody，sothatwherethereisnobody，theremustbevoid。 Everybody，again，theysupposetobetangible；andofthisnatureiswhateverhasweightorlightness。 Hence，byasyllogism，whathasnothingheavyorlightinit，isvoid。 Thisresult，then，asIhavesaid，isreachedbysyllogism。Itwouldbeabsurdtosupposethatthepointisvoid；forthevoidmustbeplacewhichhasinitanintervalintangiblebody。 Butatalleventsweobservethenthatinonewaythevoidisdescribedaswhatisnotfullofbodyperceptibletotouch；andwhathasheavinessandlightnessisperceptibletotouch。Sowewouldraisethequestion:whatwouldtheysayofanintervalthathascolourorsound-isitvoidornot?Clearlytheywouldreplythatifitcouldreceivewhatistangibleitwasvoid，andifnot，not。 Inanotherwayvoidisthatinwhichthereisno\'this\'orcorporealsubstance。Sosomesaythatthevoidisthematterofthebody(theyidentifytheplace，too，withthis)，andinthistheyspeakincorrectly；forthematterisnotseparablefromthethings，buttheyareinquiringaboutthevoidasaboutsomethingseparable。 Sincewehavedeterminedthenatureofplace，andvoidmust，ifitexists，beplacedeprivedofbody，andwehavestatedbothinwhatsenseplaceexistsandinwhatsenseitdoesnot，itisplainthatonthisshowingvoiddoesnotexist，eitherunseparatedorseparated；thevoidismeanttobe，notbodybutratheranintervalinbody。Thisiswhythevoidisthoughttobesomething，viz。becauseplaceis，andforthesamereasons。Forthefactofmotioninrespectofplacecomestotheaidbothofthosewhomaintainthatplaceissomethingoverandabovethebodiesthatcometooccupyit，andofthosewhomaintainthatthevoidissomething。Theystatethatthevoidistheconditionofmovementinthesenseofthatinwhichmovementtakesplace；andthiswouldbethekindofthingthatsomesayplaceis。 Butthereisnonecessityfortherebeingavoidifthereismovement。Itisnotintheleastneededasaconditionofmovementingeneral，forareasonwhich，incidentally，escapedMelissus；viz。 thatthefullcansufferqualitativechange。 Butnotevenmovementinrespectofplaceinvolvesavoid；forbodiesmaysimultaneouslymakeroomforoneanother，thoughthereisnointervalseparateandapartfromthebodiesthatareinmovement。 Andthisisplainevenintherotationofcontinuousthings，asinthatofliquids。 Andthingscanalsobecompressednotintoavoidbutbecausetheysqueezeoutwhatiscontainedinthem(as，forinstance，whenwateriscompressedtheairwithinitissqueezedout)；andthingscanincreaseinsizenotonlybytheentranceofsomethingbutalsobyqualitativechange；e。g。ifwaterweretobetransformedintoair。 Ingeneral，boththeargumentaboutincreaseofsizeandthataboutwaterpouredontotheashesgetintheirownway。Foreithernotanyandeverypartofthebodyisincreased，orbodiesmaybeincreasedotherwisethanbytheadditionofbody，ortheremaybetwobodiesinthesameplace(inwhichcasetheyareclaimingtosolveaquitegeneraldifficulty，butarenotprovingtheexistenceofvoid)，orthewholebodymustbevoid，ifitisincreasedineverypartandisincreasedbymeansofvoid。Thesameargumentappliestotheashes。 Itisevident，then，thatitiseasytorefutetheargumentsbywhichtheyprovetheexistenceofthevoid。 8 Letusexplainagainthatthereisnovoidexistingseparately，assomemaintain。Ifeachofthesimplebodieshasanaturallocomotion，e。g。fireupwardandearthdownwardandtowardsthemiddleoftheuniverse，itisclearthatitcannotbethevoidthatistheconditionoflocomotion。What，then，willthevoidbetheconditionof?Itisthoughttobetheconditionofmovementinrespectofplace，anditisnottheconditionofthis。 Again，ifvoidisasortofplacedeprivedofbody，whenthereisavoidwherewillabodyplacedinitmoveto?Itcertainlycannotmoveintothewholeofthevoid。Thesameargumentappliesasagainstthosewhothinkthatplaceissomethingseparate，intowhichthingsarecarried；viz。howwillwhatisplacedinitmove，orrest?Muchthesameargumentwillapplytothevoidastothe\'up\'and\'down\'inplace，asisnaturalenoughsincethosewhomaintaintheexistenceofthevoidmakeitaplace。 Andinwhatwaywillthingsbepresenteitherinplace-orinthevoid?Fortheexpectedresultdoesnottakeplacewhenabodyisplacedasawholeinaplaceconceivedofasseparateandpermanent； forapartofit，unlessitbeplacedapart，willnotbeinaplacebutinthewhole。Further，ifseparateplacedoesnotexist，neitherwillvoid。 Ifpeoplesaythatthevoidmustexist，asbeingnecessaryifthereistobemovement，whatratherturnsouttobethecase，ifonethematter，istheopposite，thatnotasinglethingcanbemovedifthereisavoid；foraswiththosewhoforalikereasonsaytheearthisatrest，so，too，inthevoidthingsmustbeatrest； forthereisnoplacetowhichthingscanmovemoreorlessthantoanother；sincethevoidinsofarasitisvoidadmitsnodifference。 Thesecondreasonisthis:allmovementiseithercompulsoryoraccordingtonature，andifthereiscompulsorymovementtheremustalsobenatural(forcompulsorymovementiscontrarytonature，andmovementcontrarytonatureisposteriortothataccordingtonature，sothatifeachofthenaturalbodieshasnotanaturalmovement，noneoftheothermovementscanexist)；buthowcantherebenaturalmovementifthereisnodifferencethroughoutthevoidortheinfinite?Forinsofarasitisinfinite，therewillbenoupordownormiddle，andinsofarasitisavoid，updiffersnowhitfromdown；forasthereisnodifferenceinwhatisnothing，thereisnoneinthevoid(forthevoidseemstobeanon-existentandaprivationofbeing)，butnaturallocomotionseemstobedifferentiated，sothatthethingsthatexistbynaturemustbedifferentiated。Either，then，nothinghasanaturallocomotion，orelsethereisnovoid。 Further，inpointoffactthingsthatarethrownmovethoughthatwhichgavethemtheirimpulseisnottouchingthem，eitherbyreasonofmutualreplacement，assomemaintain，orbecausetheairthathasbeenpushedpushesthemwithamovementquickerthanthenaturallocomotionoftheprojectilewherewithitmovestoitsproperplace。 Butinavoidnoneofthesethingscantakeplace，norcananythingbemovedsaveasthatwhichiscarriedismoved。 Further，noonecouldsaywhyathingoncesetinmotionshouldstopanywhere；forwhyshoulditstophereratherthanhere?Sothatathingwilleitherbeatrestormustbemovedadinfinitum，unlesssomethingmorepowerfulgetinitsway。 Further，thingsarenowthoughttomoveintothevoidbecauseityields；butinavoidthisqualityispresentequallyeverywhere，sothatthingsshouldmoveinalldirections。 Further，thetruthofwhatweassertisplainfromthefollowingconsiderations。Weseethesameweightorbodymovingfasterthananotherfortworeasons，eitherbecausethereisadifferenceinwhatitmovesthrough，asbetweenwater，air，andearth，orbecause，otherthingsbeingequal，themovingbodydiffersfromtheotherowingtoexcessofweightoroflightness。 Nowthemediumcausesadifferencebecauseitimpedesthemovingthing，mostofallifitismovingintheoppositedirection，butinasecondarydegreeevenifitisatrest；andespeciallyamediumthatisnoteasilydivided，i。e。amediumthatissomewhatdense。A，then，willmovethroughBintimeG，andthroughD，whichisthinner，intimeE(ifthelengthofBisegualtoD)，inproportiontothedensityofthehinderingbody。ForletBbewaterandDair； thenbysomuchasairisthinnerandmoreincorporealthanwater，A willmovethroughDfasterthanthroughB。Letthespeedhavethesameratiotothespeed，then，thatairhastowater。Thenifairistwiceasthin，thebodywilltraverseBintwicethetimethatitdoesD，andthetimeGwillbetwicethetimeE。Andalways，bysomuchasthemediumismoreincorporealandlessresistantandmoreeasilydivided，thefasterwillbethemovement。 Nowthereisnoratioinwhichthevoidisexceededbybody，asthereisnoratioof0toanumber。Forif4exceeds3by1，and2 bymorethan1，and1bystillmorethanitexceeds2，stillthereisnoratiobywhichitexceeds0；forthatwhichexceedsmustbedivisibleintotheexcess+thatwhichisexceeded，sothatwillbewhatitexceeds0by+0。Forthisreason，too，alinedoesnotexceedapointunlessitiscomposedofpoints！Similarlythevoidcanbearnoratiotothefull，andthereforeneithercanmovementthroughtheonetomovementthroughtheother，butifathingmovesthroughthethickestmediumsuchandsuchadistanceinsuchandsuchatime，itmovesthroughthevoidwithaspeedbeyondanyratio。ForletZbevoid，equalinmagnitudetoBandtoD。ThenifAistotraverseandmovethroughitinacertaintime，H，atimelessthanE，however，thevoidwillbearthisratiotothefull。ButinatimeequaltoH，A willtraversethepartOofA。AnditwillsurelyalsotraverseinthattimeanysubstanceZwhichexceedsairinthicknessintheratiowhichthetimeEbearstothetimeH。ForifthebodyZbeasmuchthinnerthanDasEexceedsH，A，ifitmovesthroughZ，willtraverseitinatimeinversetothespeedofthemovement，i。e。inatimeequaltoH。If，then，thereisnobodyinZ，AwilltraverseZstillmorequickly。ButwesupposedthatitstraverseofZwhenZ wasvoidoccupiedthetimeH。SothatitwilltraverseZinanequaltimewhetherZbefullorvoid。Butthisisimpossible。Itisplain，then，thatifthereisatimeinwhichitwillmovethroughanypartofthevoid，thisimpossibleresultwillfollow:itwillbefoundtotraverseacertaindistance，whetherthisbefullorvoid，inanequaltime；fortherewillbesomebodywhichisinthesameratiototheotherbodyasthetimeistothetime。 Tosumthematterup，thecauseofthisresultisobvious，viz。thatbetweenanytwomovementsthereisaratio(fortheyoccupytime，andthereisaratiobetweenanytwotimes，solongasbotharefinite)，butthereisnoratioofvoidtofull。 Thesearetheconsequencesthatresultfromadifferenceinthemedia；thefollowingdependuponanexcessofonemovingbodyoveranother。Weseethatbodieswhichhaveagreaterimpulseeitherofweightoroflightness，iftheyarealikeinotherrespects，movefasteroveranequalspace，andintheratiowhichtheirmagnitudesbeartoeachother。Thereforetheywillalsomovethroughthevoidwiththisratioofspeed。Butthatisimpossible；forwhyshouldonemovefaster?(Inmovingthroughplenaitmustbeso；forthegreaterdividesthemfasterbyitsforce。Foramovingthingcleavesthemediumeitherbyitsshape，orbytheimpulsewhichthebodythatiscarriedalongorisprojectedpossesses。)Thereforeallwillpossessequalvelocity。Butthisisimpossible。 Itisevidentfromwhathasbeensaid，then，that，ifthereisavoid，aresultfollowswhichistheveryoppositeofthereasonforwhichthosewhobelieveinavoidsetitup。Theythinkthatifmovementinrespectofplaceistoexist，thevoidcannotexist，separatedallbyitself；butthisisthesameastosaythatplaceisaseparatecavity；andthishasalreadybeenstatedtobeimpossible。 Butevenifweconsideritonitsownmeritstheso-calledvacuumwillbefoundtobereallyvacuous。Foras，ifoneputsacubeinwater，anamountofwaterequaltothecubewillbedisplaced；sotooinair；buttheeffectisimperceptibletosense。Andindeedalwaysinthecaseofanybodythatcanbedisplaced，must，ifitisnotcompressed，bedisplacedinthedirectioninwhichitisitsnaturetobedisplaced-alwayseitherdown，ifitslocomotionisdownwardsasinthecaseofearth，orup，ifitisfire，orinbothdirections-whateverbethenatureoftheinsertedbody。Nowinthevoidthisisimpossible；foritisnotbody；thevoidmusthavepenetratedthecubetoadistanceequaltothatwhichthisportionofvoidformerlyoccupiedinthevoid，justasifthewaterorairhadnotbeendisplacedbythewoodencube，buthadpenetratedrightthroughit。 Butthecubealsohasamagnitudeequaltothatoccupiedbythevoid；amagnitudewhich，ifitisalsohotorcold，orheavyorlight，isnonethelessdifferentinessencefromallitsattributes，evenifitisnotseparablefromthem；Imeanthevolumeofthewoodencube。 Sothatevenifitwereseparatedfromeverythingelseandwereneitherheavynorlight，itwilloccupyanequalamountofvoid，andfillthesameplace，asthepartofplaceorofthevoidequaltoitself。Howthenwillthebodyofthecubedifferfromthevoidorplacethatisequaltoit?Andiftherecanbetwosuchthings，whycannottherebeanynumbercoinciding? This，then，isoneabsurdandimpossibleimplicationofthetheory。Itisalsoevidentthatthecubewillhavethissamevolumeevenifitisdisplaced，whichisanattributepossessedbyallotherbodiesalso。Thereforeifthisdiffersinnorespectfromitsplace，whyneedweassumeaplaceforbodiesoverandabovethevolumeofeach，iftheirvolumebeconceivedofasfreefromattributes?Itcontributesnothingtothesituationifthereisanequalintervalattachedtoitaswell。[Furtheritoughttobeclearbythestudyofmovingthingswhatsortofthingvoidis。Butinfactitisfoundnowhereintheworld。Forairissomething，thoughitdoesnotseemtobeso-nor，forthatmatter，wouldwater，iffishesweremadeofiron；forthediscriminationofthetangibleisbytouch。] Itisclear，then，fromtheseconsiderationsthatthereisnoseparatevoid。 9 Therearesomewhothinkthattheexistenceofrarityanddensityshowsthatthereisavoid。Ifrarityanddensitydonotexist，theysay，neithercanthingscontractandbecompressed。Butifthiswerenottotakeplace，eithertherewouldbenomovementatall，ortheuniversewouldbulge，asXuthussaid，orairandwatermustalwayschangeintoequalamounts(e。g。ifairhasbeenmadeoutofacupfulofwater，atthesametimeoutofanequalamountofairacupfulofwatermusthavebeenmade)，orvoidmustnecessarilyexist；forcompressionandexpansioncannottakeplaceotherwise。 Now，iftheymeanbytherarethatwhichhasmanyvoidsexistingseparately，itisplainthatifvoidcannotexistseparateanymorethanaplacecanexistwithanextensionalltoitself，neithercantherareexistinthissense。Butiftheymeanthatthereisvoid，notseparatelyexistent，butstillpresentintherare，thisislessimpossible，yet，first，thevoidturnsoutnottobeaconditionofallmovement，butonlyofmovementupwards(fortherareislight，whichisthereasonwhytheysayfireisrare)；second，thevoidturnsouttobeaconditionofmovementnotasthatinwhichittakesplace，butinthatthevoidcarriesthingsupasskinsbybeingcarriedupthemselvescarryupwhatiscontinuouswiththem。Yethowcanvoidhavealocalmovementoraplace?Forthusthatintowhichvoidmovesistillthenvoidofavoid。 Again，howwilltheyexplain，inthecaseofwhatisheavy，itsmovementdownwards?Anditisplainthatiftherarerandmorevoidathingisthequickeritwillmoveupwards，ifitwerecompletelyvoiditwouldmovewithamaximumspeed！Butperhapseventhisisimpossible，thatitshouldmoveatall；thesamereasonwhichshowedthatinthevoidallthingsareincapableofmovingshowsthatthevoidcannotmove，viz。thefactthatthespeedsareincomparable。 Sincewedenythatavoidexists，butfortheresttheproblemhasbeentrulystated，thateithertherewillbenomovement，ifthereisnottobecondensationandrarefaction，ortheuniversewillbulge，oratransformationofwaterintoairwillalwaysbebalancedbyanequaltransformationofairintowater(foritisclearthattheairproducedfromwaterisbulkierthanthewater):itisnecessarytherefore，ifcompressiondoesnotexist，eitherthatthenextportionwillbepushedoutwardsandmaketheoutermostpartbulge，orthatsomewhereelsetheremustbeanequalamountofwaterproducedoutofair，sothattheentirebulkofthewholemaybeequal，orthatnothingmoves。Forwhenanythingisdisplacedthiswillalwayshappen，unlessitcomesroundinacircle；butlocomotionisnotalwayscircular，butsometimesinastraightline。 Thesethenarethereasonsforwhichtheymightsaythatthereisavoid；ourstatementisbasedontheassumptionthatthereisasinglematterforcontraries，hotandcoldandtheothernaturalcontrarieties，andthatwhatexistsactuallyisproducedfromapotentialexistent，andthatmatterisnotseparablefromthecontrariesbutitsbeingisdifferent，andthatasinglemattermayserveforcolourandheatandcold。 Thesamematteralsoservesforbothalargeandasmallbody。 Thisisevident；forwhenairisproducedfromwater，thesamematterhasbecomesomethingdifferent，notbyacquiringanadditiontoit，buthasbecomeactuallywhatitwaspotentially，and，again，waterisproducedfromairinthesameway，thechangebeingsometimesfromsmallnesstogreatness，andsometimesfromgreatnesstosmallness。Similarly，therefore，ifairwhichislargeinextentcomestohaveasmallervolume，orbecomesgreaterfrombeingsmaller，itisthematterwhichispotentiallyboththatcomestobeeachofthetwo。 Forasthesamematterbecomeshotfrombeingcold，andcoldfrombeinghot，becauseitwaspotentiallyboth，sotoofromhotitcanbecomemorehot，thoughnothinginthematterhasbecomehotthatwasnothotwhenthethingwaslesshot；justas，ifthearcorcurveofagreatercirclebecomesthatofasmaller，whetheritremainsthesameorbecomesadifferentcurve，convexityhasnotcometoexistinanythingthatwasnotconvexbutstraight(fordifferencesofdegreedonotdependonanintermissionofthequality)；norcanwegetanyportionofaflame，inwhichbothheatandwhitenessarenotpresent。Sotoo，then，istheearlierheatrelatedtothelater。Sothatthegreatnessandsmallness，also，ofthesensiblevolumeareextended，notbythematter\'sacquiringanythingnew，butbecausethematterispotentiallymatterforbothstates；sothatthesamethingisdenseandrare，andthetwoqualitieshaveonematter。 Thedenseisheavy，andtherareislight。[Again，asthearcofacirclewhencontractedintoasmallerspacedoesnotacquireanewpartwhichisconvex，butwhatwastherehasbeencontracted；andasanypartoffirethatonetakeswillbehot；so，too，itisallaquestionofcontractionandexpansionofthesamematter。]Therearetwotypesineachcase，bothinthedenseandintherare；forboththeheavyandthehardarethoughttobedense，andcontrariwiseboththelightandthesoftarerare；andweightandhardnessfailtocoincideinthecaseofleadandiron。 Fromwhathasbeensaiditisevident，then，thatvoiddoesnotexisteitherseparate(eitherabsolutelyseparateorasaseparateelementintherare)orpotentially，unlessoneiswillingtocalltheconditionofmovementvoid，whateveritmaybe。Atthatratethematteroftheheavyandthelight，quamatterofthem，wouldbethevoid；forthedenseandtherareareproductiveoflocomotioninvirtueofthiscontrariety，andinvirtueoftheirhardnessandsoftnessproductiveofpassivityandimpassivity，i。e。notoflocomotionbutratherofqualitativechange。 Somuch，then，forthediscussionofthevoid，andofthesenseinwhichitexistsandthesenseinwhichitdoesnotexist。 10 NextfordiscussionafterthesubjectsmentionedisTime。Thebestplanwillbetobeginbyworkingoutthedifficultiesconnectedwithit，makinguseofthecurrentarguments。First，doesitbelongtotheclassofthingsthatexistortothatofthingsthatdonotexist? Thensecondly，whatisitsnature?Tostart，then:thefollowingconsiderationswouldmakeonesuspectthatiteitherdoesnotexistatallorbarely，andinanobscureway。Onepartofithasbeenandisnot，whiletheotherisgoingtobeandisnotyet。Yettime-bothinfinitetimeandanytimeyouliketotake-ismadeupofthese。Onewouldnaturallysupposethatwhatismadeupofthingswhichdonotexistcouldhavenoshareinreality。 Further，ifadivisiblethingistoexist，itisnecessarythat，whenitexists，allorsomeofitspartsmustexist。Butoftimesomepartshavebeen，whileothershavetobe，andnopartofitisthoughitisdivisible。Forwhatis\'now\'isnotapart:apartisameasureofthewhole，whichmustbemadeupofparts。Time，ontheotherhand，isnotheldtobemadeupof\'nows\'。 Again，the\'now\'whichseemstoboundthepastandthefuture-doesitalwaysremainoneandthesameorisitalwaysotherandother? Itishardtosay。 (1)Ifitisalwaysdifferentanddifferent，andifnoneofthepartsintimewhichareotherandotheraresimultaneous(unlesstheonecontainsandtheotheriscontained，astheshortertimeisbythelonger)，andifthe\'now\'whichisnot，butformerlywas，musthaveceased-to-beatsometime，the\'nows\'toocannotbesimultaneouswithoneanother，buttheprior\'now\'mustalwayshaveceased-to-be。 Buttheprior\'now\'cannothaveceased-to-beinitself(sinceitthenexisted)；yetitcannothaveceased-to-beinanother\'now\'。Forwemaylayitdownthatone\'now\'cannotbenexttoanother，anymorethanpointtopoint。Ifthenitdidnotcease-to-beinthenext\'now\'butinanother，itwouldexistsimultaneouslywiththeinnumerable\'nows\'betweenthetwo-whichisimpossible。 Yes，but(2)neitherisitpossibleforthe\'now\'toremainalwaysthesame。Nodeterminatedivisiblethinghasasingletermination，whetheritiscontinuouslyextendedinoneorinmorethanonedimension:butthe\'now\'isatermination，anditispossibletocutoffadeterminatetime。Further，ifcoincidenceintime(i。e。beingneitherpriornorposterior)meanstobe\'inoneandthesame“now“\'，then，ifbothwhatisbeforeandwhatisafterareinthissame\'now\'，thingswhichhappenedtenthousandyearsagowouldbesimultaneouswithwhathashappenedto-day，andnothingwouldbebeforeorafteranythingelse。 Thismayserveasastatementofthedifficultiesabouttheattributesoftime。 Astowhattimeisorwhatisitsnature，thetraditionalaccountsgiveusaslittlelightasthepreliminaryproblemswhichwehaveworkedthrough。 Someassertthatitis(1)themovementofthewhole，othersthatitis(2)thesphereitself。 (1)Yetpart，too，oftherevolutionisatime，butitcertainlyisnotarevolution:forwhatistakenispartofarevolution，notarevolution。Besides，ifthereweremoreheavensthanone，themovementofanyofthemequallywouldbetime，sothattherewouldbemanytimesatthesametime。 (2)Thosewhosaidthattimeisthesphereofthewholethoughtso，nodoubt，onthegroundthatallthingsareintimeandallthingsareinthesphereofthewhole。Theviewistoonaiveforittobeworthwhiletoconsidertheimpossibilitiesimpliedinit。 Butastimeismostusuallysupposedtobe(3)motionandakindofchange，wemustconsiderthisview。 Now(a)thechangeormovementofeachthingisonlyinthethingwhichchangesorwherethethingitselfwhichmovesorchangesmaychancetobe。Buttimeispresentequallyeverywhereandwithallthings。 Again，(b)changeisalwaysfasterorslower，whereastimeisnot: for\'fast\'and\'slow\'aredefinedbytime-\'fast\'iswhatmovesmuchinashorttime，\'slow\'whatmoveslittleinalongtime；buttimeisnotdefinedbytime，bybeingeitheracertainamountoracertainkindofit。 Clearlythenitisnotmovement。(Weneednotdistinguishatpresentbetween\'movement\'and\'change\'。) 11 Butneitherdoestimeexistwithoutchange；forwhenthestateofourownmindsdoesnotchangeatall，orwehavenotnoticeditschanging，wedonotrealizethattimehaselapsed，anymorethanthosewhoarefabledtosleepamongtheheroesinSardiniadowhentheyareawakened；fortheyconnecttheearlier\'now\'withthelaterandmakethemone，cuttingouttheintervalbecauseoftheirfailuretonoticeit。So，justas，ifthe\'now\'werenotdifferentbutoneandthesame，therewouldnothavebeentime，sotoowhenitsdifferenceescapesournoticetheintervaldoesnotseemtobetime。If，then，thenon-realizationoftheexistenceoftimehappenstouswhenwedonotdistinguishanychange，butthesoulseemstostayinoneindivisiblestate，andwhenweperceiveanddistinguishwesaytimehaselapsed，evidentlytimeisnotindependentofmovementandchange。 Itisevident，then，thattimeisneithermovementnorindependentofmovement。 Wemusttakethisasourstarting-pointandtrytodiscover-sincewewishtoknowwhattimeis-whatexactlyithastodowithmovement。 Nowweperceivemovementandtimetogether:forevenwhenitisdarkandwearenotbeingaffectedthroughthebody，ifanymovementtakesplaceinthemindweatoncesupposethatsometimealsohaselapsed；andnotonlythatbutalso，whensometimeisthoughttohavepassed，somemovementalsoalongwithitseemstohavetakenplace。 Hencetimeiseithermovementorsomethingthatbelongstomovement。 Sincethenitisnotmovement，itmustbetheother。 Butwhatismovedismovedfromsomethingtosomething，andallmagnitudeiscontinuous。Thereforethemovementgoeswiththemagnitude。Becausethemagnitudeiscontinuous，themovementtoomustbecontinuous，andifthemovement，thenthetime；forthetimethathaspassedisalwaysthoughttobeinproportiontothemovement。 Thedistinctionof\'before\'and\'after\'holdsprimarily，then，inplace；andthereinvirtueofrelativeposition。Sincethen\'before\' and\'after\'holdinmagnitude，theymustholdalsoinmovement，thesecorrespondingtothose。Butalsointimethedistinctionof\'before\'and\'after\'musthold，fortimeandmovementalwayscorrespondwitheachother。The\'before\'and\'after\'inmotionisidenticalinsubstratumwithmotionyetdiffersfromitindefinition，andisnotidenticalwithmotion。 Butweapprehendtimeonlywhenwehavemarkedmotion，markingitby\'before\'and\'after\'；anditisonlywhenwehaveperceived\'before\' and\'after\'inmotionthatwesaythattimehaselapsed。NowwemarkthembyjudgingthatAandBaredifferent，andthatsomethirdthingisintermediatetothem。Whenwethinkoftheextremesasdifferentfromthemiddleandthemindpronouncesthatthe\'nows\' aretwo，onebeforeandoneafter，itisthenthatwesaythatthereistime，andthisthatwesayistime。Forwhatisboundedbythe\'now\'isthoughttobetime-wemayassumethis。 When，therefore，weperceivethe\'now\'one，andneitherasbeforeandafterinamotionnorasanidentitybutinrelationtoa\'before\' andan\'after\'，notimeisthoughttohaveelapsed，becausetherehasbeennomotioneither。Ontheotherhand，whenwedoperceivea\'before\'andan\'after\'，thenwesaythatthereistime。Fortimeisjustthis-numberofmotioninrespectof\'before\'and\'after\'。 Hencetimeisnotmovement，butonlymovementinsofarasitadmitsofenumeration。Aproofofthis:wediscriminatethemoreorthelessbynumber，butmoreorlessmovementbytime。Timethenisakindofnumber。(Number，wemustnote，isusedintwosenses-bothofwhatiscountedorthecountableandalsoofthatwithwhichwecount。Timeobviouslyiswhatiscounted，notthatwithwhichwecount:therearedifferentkindsofthing。)Justasmotionisaperpetualsuccession，soalsoistime。Buteverysimultaneoustimeisself-identical；forthe\'now\'asasubjectisanidentity，butitacceptsdifferentattributes。The\'now\'measurestime，insofarastimeinvolvesthe\'beforeandafter\'。 The\'now\'inonesenseisthesame，inanotheritisnotthesame。 Insofarasitisinsuccession，itisdifferent(whichisjustwhatitsbeingwassupposedtomean)，butitssubstratumisanidentity:formotion，aswassaid，goeswithmagnitude，andtime，aswemaintain，withmotion。Similarly，then，therecorrespondstothepointthebodywhichiscarriedalong，andbywhichweareawareofthemotionandofthe\'beforeandafter\'involvedinit。Thisisanidenticalsubstratum(whetherapointorastoneorsomethingelseofthekind)，butithasdifferentattributesasthesophistsassumethatCoriscus\'beingintheLyceumisadifferentthingfromCoriscus\' beinginthemarket-place。Andthebodywhichiscarriedalongisdifferent，insofarasitisatonetimehereandatanotherthere。 Butthe\'now\'correspondstothebodythatiscarriedalong，astimecorrespondstothemotion。Foritisbymeansofthebodythatiscarriedalongthatwebecomeawareofthe\'beforeandafter\'themotion，andifweregardtheseascountablewegetthe\'now\'。Henceinthesealsothe\'now\'assubstratumremainsthesame(foritiswhatisbeforeandafterinmovement)，butwhatispredicatedofitisdifferent；foritisinsofarasthe\'beforeandafter\'isnumerablethatwegetthe\'now\'。Thisiswhatismostknowable:for，similarly，motionisknownbecauseofthatwhichismoved，locomotionbecauseofthatwhichiscarried。whatiscarriedisarealthing，themovementisnot。Thuswhatiscalled\'now\'inonesenseisalwaysthesame；inanotheritisnotthesame:forthisistruealsoofwhatiscarried。 Clearly，too，iftherewerenotime，therewouldbeno\'now\'，andviceversa。justasthemovingbodyanditslocomotioninvolveeachothermutually，sotoodothenumberofthemovingbodyandthenumberofitslocomotion。Forthenumberofthelocomotionistime，whilethe\'now\'correspondstothemovingbody，andisliketheunitofnumber。 Time，then，alsoisbothmadecontinuousbythe\'now\'anddividedatit。Forheretoothereisacorrespondencewiththelocomotionandthemovingbody。Forthemotionorlocomotionismadeonebythethingwhichismoved，becauseitisone-notbecauseitisoneinitsownnature(fortheremightbepausesinthemovementofsuchathing)-butbecauseitisoneindefinition:forthisdeterminesthemovementas\'before\'and\'after\'。Here，toothereisacorrespondencewiththepoint；forthepointalsobothconnectsandterminatesthelength-itisthebeginningofoneandtheendofanother。Butwhenyoutakeitinthisway，usingtheonepointastwo，apauseisnecessary，ifthesamepointistobethebeginningandtheend。The\'now\'ontheotherhand，sincethebodycarriedismoving，isalwaysdifferent。 Hencetimeisnotnumberinthesenseinwhichthereis\'number\' ofthesamepointbecauseitisbeginningandend，butratherastheextremitiesofalineformanumber，andnotasthepartsofthelinedoso，bothforthereasongiven(forwecanusethemiddlepointastwo，sothatonthatanalogytimemightstandstill)，andfurtherbecauseobviouslythe\'now\'isnopartoftimenorthesectionanypartofthemovement，anymorethanthepointsarepartsoftheline-foritistwolinesthatarepartsofoneline。 Insofarthenasthe\'now\'isaboundary，itisnottime，butanattributeofit；insofarasitnumbers，itisnumber；forboundariesbelongonlytothatwhichtheybound，butnumber(e。g。ten)isthenumberofthesehorses，andbelongsalsoelsewhere。 Itisclear，then，thattimeis\'numberofmovementinrespectofthebeforeandafter\'，andiscontinuoussinceitisanattributeofwhatiscontinuous。 12 Thesmallestnumber，inthestrictsenseoftheword\'number\'，istwo。Butofnumberasconcrete，sometimesthereisaminimum，sometimesnot:e。g。ofa\'line\'，thesmallestinrespectofmultiplicityistwo(or，ifyoulike，one)，butinrespectofsizethereisnominimum；foreverylineisdividedadinfinitum。Henceitissowithtime。Inrespectofnumbertheminimumisone(ortwo)；inpointofextentthereisnominimum。 Itisclear，too，thattimeisnotdescribedasfastorslow，butasmanyorfewandaslongorshort。Forascontinuousitislongorshortandasanumbermanyorfew，butitisnotfastorslow-anymorethananynumberwithwhichwenumberisfastorslow。 Further，thereisthesametimeeverywhereatonce，butnotthesametimebeforeandafter，forwhilethepresentchangeisone，thechangewhichhashappenedandthatwhichwillhappenaredifferent。Timeisnotnumberwithwhichwecount，butthenumberofthingswhicharecounted，andthisaccordingasitoccursbeforeorafterisalwaysdifferent，forthe\'nows\'aredifferent。Andthenumberofahundredhorsesandahundredmenisthesame，butthethingsnumberedaredifferent-thehorsesfromthemen。Further，asamovementcanbeoneandthesameagainandagain，sotoocantime，e。g。ayearoraspringoranautumn。 Notonlydowemeasurethemovementbythetime，butalsothetimebythemovement，becausetheydefineeachother。Thetimemarksthemovement，sinceitisitsnumber，andthemovementthetime。Wedescribethetimeasmuchorlittle，measuringitbythemovement，justasweknowthenumberbywhatisnumbered，e。g。thenumberofthehorsesbyonehorseastheunit。Forweknowhowmanyhorsestherearebytheuseofthenumber；andagainbyusingtheonehorseasunitweknowthenumberofthehorsesitself。Soitiswiththetimeandthemovement；forwemeasurethemovementbythetimeandviceversa。Itisnaturalthatthisshouldhappen；forthemovementgoeswiththedistanceandthetimewiththemovement，becausetheyarequantaandcontinuousanddivisible。Themovementhastheseattributesbecausethedistanceisofthisnature，andthetimehasthembecauseofthemovement。Andwemeasureboththedistancebythemovementandthemovementbythedistance；forwesaythattheroadislong，ifthejourneyislong，andthatthisislong，iftheroadislong-thetime，too，ifthemovement，andthemovement，ifthetime。 Timeisameasureofmotionandofbeingmoved，anditmeasuresthemotionbydeterminingamotionwhichwillmeasureexactlythewholemotion，asthecubitdoesthelengthbydetermininganamountwhichwillmeasureoutthewhole。Further\'tobeintime\'meansformovement，thatbothitanditsessencearemeasuredbytime(forsimultaneouslyitmeasuresboththemovementanditsessence，andthisiswhatbeingintimemeansforit，thatitsessenceshouldbemeasured)。 Clearlythen\'tobeintime\'hasthesamemeaningforotherthingsalso，namely，thattheirbeingshouldbemeasuredbytime。\'Tobeintime\'isoneoftwothings:(1)toexistwhentimeexists，(2)aswesayofsomethingsthattheyare\'innumber\'。Thelattermeanseitherwhatisapartormodeofnumber-ingeneral，somethingwhichbelongstonumber-orthatthingshaveanumber。 Now，sincetimeisnumber，the\'now\'andthe\'before\'andthelikeareintime，justas\'unit\'and\'odd\'and\'even\'areinnumber，i。e。 inthesensethattheonesetbelongstonumber，theothertotime。 Butthingsareintimeastheyareinnumber。Ifthisisso，theyarecontainedbytimeasthingsinplacearecontainedbyplace。 Plainly，too，tobeintimedoesnotmeantoco-existwithtime，anymorethantobeinmotionorinplacemeanstoco-existwithmotionorplace。Forif\'tobeinsomething\'istomeanthis，thenallthingswillbeinanything，andtheheavenwillbeinagrain；forwhenthegrainis，thenalsoistheheaven。Butthisisamerelyincidentalconjunction，whereastheotherisnecessarilyinvolved:thatwhichisintimenecessarilyinvolvesthatthereistimewhenitis，andthatwhichisinmotionthatthereismotionwhenitis。 Sincewhatis\'intime\'issointhesamesenseaswhatisinnumberisso，atimegreaterthaneverythingintimecanbefound。Soitisnecessarythatallthethingsintimeshouldbecontainedbytime，justlikeotherthingsalsowhichare\'inanything\'，e。g。thethings\'inplace\'byplace。 Athing，then，willbeaffectedbytime，justasweareaccustomedtosaythattimewastesthingsaway，andthatallthingsgrowoldthroughtime，andthatthereisoblivionowingtothelapseoftime，butwedonotsaythesameofgettingtoknoworofbecomingyoungorfair。Fortimeisbyitsnaturethecauseratherofdecay，sinceitisthenumberofchange，andchangeremoveswhatis。 Hence，plainly，thingswhicharealwaysarenot，assuch，intime，fortheyarenotcontainedtime，noristheirbeingmeasuredbytime。Aproofofthisisthatnoneofthemisaffectedbytime，whichindicatesthattheyarenotintime。 Sincetimeisthemeasureofmotion，itwillbethemeasureofresttoo-indirectly。Forallrestisintime。Foritdoesnotfollowthatwhatisintimeismoved，thoughwhatisinmotionisnecessarilymoved。Fortimeisnotmotion，but\'numberofmotion\':andwhatisatrest，also，canbeinthenumberofmotion。Noteverythingthatisnotinmotioncanbesaidtobe\'atrest\'-butonlythatwhichcanbemoved，thoughitactuallyisnotmoved，aswassaidabove。 \'Tobeinnumber\'meansthatthereisanumberofthething，andthatitsbeingismeasuredbythenumberinwhichitis。Henceifathingis\'intime\'itwillbemeasuredbytime。Buttimewillmeasurewhatismovedandwhatisatrest，theonequamoved，theotherquaatrest；foritwillmeasuretheirmotionandrestrespectively。 Hencewhatismovedwillnotbemeasurablebythetimesimplyinsofarasithasquantity，butinsofarasitsmotionhasquantity。 Thusnoneofthethingswhichareneithermovednoratrestareintime:for\'tobeintime\'is\'tobemeasuredbytime\'，whiletimeisthemeasureofmotionandrest。 Plainly，then，neitherwilleverythingthatdoesnotexistbeintime，i。e。thosenon-existentthingsthatcannotexist，asthediagonalcannotbecommensuratewiththeside。 Generally，iftimeisdirectlythemeasureofmotionandindirectlyofotherthings，itisclearthatathingwhoseexistenceismeasuredbyitwillhaveitsexistenceinrestormotion。Thosethingsthereforewhicharesubjecttoperishingandbecoming-generally，thosewhichatonetimeexist，atanotherdonot-arenecessarilyintime:forthereisagreatertimewhichwillextendbothbeyondtheirexistenceandbeyondthetimewhichmeasurestheirexistence。Ofthingswhichdonotexistbutarecontainedbytimesomewere，e。g。Homeroncewas，somewillbe，e。g。afutureevent；thisdependsonthedirectioninwhichtimecontainsthem；ifonboth，theyhavebothmodesofexistence。Astosuchthingsasitdoesnotcontaininanyway，theyneitherwerenorarenorwillbe。Thesearethosenonexistentswhoseoppositesalwaysare，astheincommensurabilityofthediagonalalwaysis-andthiswillnotbeintime。Norwillthecommensurability，therefore；hencethiseternallyisnot，becauseitiscontrarytowhateternallyis。Athingwhosecontraryisnoteternalcanbeandnotbe，anditisofsuchthingsthatthereiscomingtobeandpassingaway。 13 The\'now\'isthelinkoftime，ashasbeensaid(foritconnectspastandfuturetime)，anditisalimitoftime(foritisthebeginningoftheoneandtheendoftheother)。Butthisisnotobviousasitiswiththepoint，whichisfixed。Itdividespotentially，andinsofarasitisdividingthe\'now\'isalwaysdifferent，butinsofarasitconnectsitisalwaysthesame，asitiswithmathematicallines。Fortheintellectitisnotalwaysoneandthesamepoint，sinceitisotherandotherwhenonedividestheline； butinsofarasitisone，itisthesameineveryrespect。 Sothe\'now\'alsoisinonewayapotentialdividingoftime，inanothertheterminationofbothparts，andtheirunity。Andthedividingandtheunitingarethesamethingandinthesamereference，butinessencetheyarenotthesame。 Soonekindof\'now\'isdescribedinthisway:anotheriswhenthetimeisnearthiskindof\'now\'。\'Hewillcomenow\'becausehewillcometo-day；\'hehascomenow\'becausehecameto-day。ButthethingsintheIliadhavenothappened\'now\'，noristheflood\'now\'-notthatthetimefromnowtothemisnotcontinuous，butbecausetheyarenotnear。 \'Atsometime\'meansatimedeterminedinrelationtothefirstofthetwotypesof\'now\'，e。g。\'atsometime\'Troywastaken，and\'atsometime\'therewillbeaflood；foritmustbedeterminedwithreferencetothe\'now\'。Therewillthusbeadeterminatetimefromthis\'now\'tothat，andtherewassuchinreferencetothepastevent。 Butiftherebenotimewhichisnot\'sometime\'，everytimewillbedetermined。 Willtimethenfail?Surelynot，ifmotionalwaysexists。Istimethenalwaysdifferentordoesthesametimerecur?Clearlytimeis，inthesamewayasmotionis。Forifoneandthesamemotionsometimesrecurs，itwillbeoneandthesametime，andifnot，not。 Sincethe\'now\'isanendandabeginningoftime，notofthesametimehowever，buttheendofthatwhichispastandthebeginningofthatwhichistocome，itfollowsthat，asthecirclehasitsconvexityanditsconcavity，inasense，inthesamething，sotimeisalwaysatabeginningandatanend。Andforthisreasonitseemstobealwaysdifferent；forthe\'now\'isnotthebeginningandtheendofthesamething；ifitwere，itwouldbeatthesametimeandinthesamerespecttwoopposites。Andtimewillnotfail；foritisalwaysatabeginning。 \'Presently\'or\'just\'referstothepartoffuturetimewhichisneartheindivisiblepresent\'now\'(\'Whendoyouwalk?\'Presently\'，becausethetimeinwhichheisgoingtodosoisnear)，andtothepartofpasttimewhichisnotfarfromthe\'now\'(\'Whendoyouwalk?\' \'Ihavejustbeenwalking\')。ButtosaythatTroyhasjustbeentaken-wedonotsaythat，becauseitistoofarfromthe\'now\'。 \'Lately\'，too，referstothepartofpasttimewhichisnearthepresent\'now\'。\'Whendidyougo?\'\'Lately\'，ifthetimeisneartheexistingnow。\'Longago\'referstothedistantpast。 \'Suddenly\'referstowhathasdepartedfromitsformerconditioninatimeimperceptiblebecauseofitssmallness；butitisthenatureofallchangetoalterthingsfromtheirformercondition。Intimeallthingscomeintobeingandpassaway；forwhichreasonsomecalleditthewisestofallthings，butthePythagoreanParoncalleditthemoststupid，becauseinitwealsoforget；andhiswasthetruerview。 Itisclearthenthatitmustbeinitself，aswesaidbefore，theconditionofdestructionratherthanofcomingintobeing(forchange，initself，makesthingsdepartfromtheirformercondition)，andonlyincidentallyofcomingintobeing，andofbeing。Asufficientevidenceofthisisthatnothingcomesintobeingwithoutitselfmovingsomehowandacting，butathingcanbedestroyedevenifitdoesnotmoveatall。Andthisiswhat，asarule，wechieflymeanbyathing\'sbeingdestroyedbytime。Still，timedoesnotworkeventhischange；eventhissortofchangetakesplaceincidentallyintime。 Wehavestated，then，thattimeexistsandwhatitis，andinhowmanysenseswespeakofthe\'now\'，andwhat\'atsometime\'，\'lately\'，\'presently\'or\'just\'，\'longago\'，and\'suddenly\'mean。