ChapterXIV
IdeaofDurationanditsSimpleModes1。Durationisfleetingextension。Thereisanothersortofdistance，orlength，theideawhereofwegetnotfromthepermanentpartsofspace，butfromthefleetingandperpetuallyperishingpartsofsuccession。Thiswecallduration；thesimplemodeswhereofareanydifferentlengthsofitwhereofwehavedistinctideas，ashours，days，years，&c。，timeandeternity。
2。Itsideafromreflectiononthetrainofourideas。Theanswerofagreatman，toonewhoaskedwhattimewas:Sinonrogasintelligo，(whichamountstothis；ThemoreIsetmyselftothinkofit，thelessIunderstandit，)mightperhapspersuadeonethattime，whichrevealsallotherthings，isitselfnottobediscovered。Duration，time，andeternity，are，notwithoutreason，thoughttohavesomethingveryabstruseintheirnature。Buthoweverremotethesemayseemfromourcomprehension，yetifwetracethemrighttotheiroriginals，Idoubtnotbutoneofthosesourcesofallourknowledge，viz。
sensationandreflection，willbeabletofurnishuswiththeseideas，asclearanddistinctasmanyotherswhicharethoughtmuchlessobscure；andweshallfindthattheideaofeternityitselfisderivedfromthesamecommonoriginalwiththerestofourideas。
3。Natureandoriginoftheideaofduration。Tounderstandtimeandeternityaright，weoughtwithattentiontoconsiderwhatideaitiswehaveofduration，andhowwecamebyit。Itisevidenttoanyonewhowillbutobservewhatpassesinhisownmind，thatthereisatrainofideaswhichconstantlysucceedoneanotherinhisunderstanding，aslongasheisawake。Reflectionontheseappearancesofseveralideasoneafteranotherinourminds，isthatwhichfurnishesuswiththeideaofsuccession:andthedistancebetweenanypartsofthatsuccession，orbetweentheappearanceofanytwoideasinourminds，isthatwecallduration。Forwhilstwearethinking，orwhilstwereceivesuccessivelyseveralideasinourminds，weknowthatwedoexist；andsowecalltheexistence，orthecontinuationoftheexistenceofourselves，oranythingelse，commensuratetothesuccessionofanyideasinourminds，thedurationofourselves，oranysuchotherthingco-existentwithourthinking。
4。Proofthatitsideaisgotfromreflectiononthetrainofourideas。Thatwehaveournotionofsuccessionanddurationfromthisoriginal，viz。fromreflectiononthetrainofideas，whichwefindtoappearoneafteranotherinourownminds，seemsplaintome，inthatwehavenoperceptionofdurationbutbyconsideringthetrainofideasthattaketheirturnsinourunderstandings。Whenthatsuccessionofideasceases，ourperceptionofdurationceaseswithit；
whicheveryoneclearlyexperimentsinhimself，whilsthesleepssoundly，whetheranhouroraday，amonthorayear；ofwhichdurationofthings，whilehesleepsorthinksnot，hehasnoperceptionatall，butitisquitelosttohim；andthemomentwhereinheleavesofftothink，tillthemomenthebeginstothinkagain，seemstohimtohavenodistance。AndsoIdoubtnotitwouldbetoawakingman，ifitwerepossibleforhimtokeeponlyoneideainhismind，withoutvariationandthesuccessionofothers。Andwesee，thatonewhofixeshisthoughtsveryintentlyononething，soastotakebutlittlenoticeofthesuccessionofideasthatpassinhismind，whilstheistakenupwiththatearnestcontemplation，letsslipoutofhisaccountagoodpartofthatduration，andthinksthattimeshorterthanitis。Butifsleepcommonlyunitesthedistantpartsofduration，itisbecauseduringthattimewehavenosuccessionofideasinourminds。Forifaman，duringhissleep，dreams，andvarietyofideasmakethemselvesperceptibleinhismindoneafteranother，hehaththen，duringsuchdreaming，asenseofduration，andofthelengthofit。Bywhichitistomeveryclear，thatmenderivetheirideasofdurationfromtheirreflectionsonthetrainoftheideastheyobservetosucceedoneanotherintheirownunderstandings；withoutwhichobservationtheycanhavenonotionofduration，whatevermayhappenintheworld。
5。Theideaofdurationapplicabletothingswhilstwesleep。Indeedamanhaving，fromreflectingonthesuccessionandnumberofhisownthoughts，gotthenotionorideaofduration，hecanapplythatnotiontothingswhichexistwhilehedoesnotthink；ashethathasgottheideaofextensionfrombodiesbyhissightortouch，canapplyittodistances，wherenobodyisseenorfelt。Andtherefore，thoughamanhasnoperceptionofthelengthofdurationwhichpassedwhilsthesleptorthoughtnot；yet，havingobservedtherevolutionofdaysandnights，andfoundthelengthoftheirdurationtobeinappearanceregularandconstant，hecan，uponthesuppositionthatthatrevolutionhasproceededafterthesamemannerwhilsthewasasleeporthoughtnot，asitusedtodoatothertimes，hecan，Isay，imagineandmakeallowanceforthelengthofdurationwhilstheslept。ButifAdamandEve，(whentheywerealoneintheworld)，insteadoftheirordinarynight’ssleep，hadpassedthewholetwenty-fourhoursinonecontinuedsleep，thedurationofthattwenty-fourhourshadbeenirrecoverablylosttothem，andbeenforeverleftoutoftheiraccountoftime。
6。Theideaofsuccessionnotfrommotion。Thusbyreflectingontheappearingofvariousideasoneafteranotherinourunderstandings，wegetthenotionofsuccession；which，ifanyoneshouldthinkwedidrathergetfromourobservationofmotionbyoursenses，hewillperhapsbeofmymindwhenheconsiders，thatevenmotionproducesinhismindanideaofsuccessionnootherwisethanasitproducesthereacontinuedtrainofdistinguishableideas。Foramanlookinguponabodyreallymoving，perceivesyetnomotionatallunlessthatmotionproducesaconstanttrainofsuccessiveideas:v。g。amanbecalmedatsea，outofsightofland，inafairday，maylookonthesun，orsea，orship，awholehourtogether，andperceivenomotionatallineither；thoughitbecertainthattwo，andperhapsallofthem，havemovedduringthattimeagreatway。Butassoonasheperceiveseitherofthemtohavechangeddistancewithsomeotherbody，assoonasthismotionproducesanynewideainhim，thenheperceivesthattherehasbeenmotion。Butwhereveramanis，withallthingsatrestabouthim，withoutperceivinganymotionatall，-
ifduringthishourofquiethehasbeenthinking，hewillperceivethevariousideasofhisownthoughtsinhisownmind，appearingoneafteranother，andtherebyobserveandfindsuccessionwherehecouldobservenomotion。
7。Veryslowmotionsunperceived。Andthis，Ithink，isthereasonwhymotionsveryslow，thoughtheyareconstant，arenotperceivedbyus；becauseintheirremovefromonesensibleparttowardsanother，theirchangeofdistanceissoslow，thatitcausesnonewideasinus，butagoodwhileoneafteranother。Andsonotcausingaconstanttrainofnewideastofollowoneanotherimmediatelyinourminds，wehavenoperceptionofmotion；whichconsistinginaconstantsuccession，wecannotperceivethatsuccessionwithoutaconstantsuccessionofvaryingideasarisingfromit。
8。Veryswiftmotionsunperceived。Onthecontrary，thingsthatmovesoswiftasnottoaffectthesensesdistinctlywithseveraldistinguishabledistancesoftheirmotion，andsocausenotanytrainofideasinthemind，arenotalsoperceived。Foranythingthatmovesroundaboutinacircle，inlesstimesthanourideasarewonttosucceedoneanotherinourminds，isnotperceivedtomove；
butseemstobeaperfectentirecircleofthatmatterorcolour，andnotapartofacircleinmotion。
9。Thetrainofideashasacertaindegreeofquickness。HenceI
leaveittootherstojudge，whetheritbenotprobablethatourideasdo，whilstweareawake，succeedoneanotherinourmindsatcertaindistances；notmuchunliketheimagesintheinsideofalantern，turnedroundbytheheatofacandle。Thisappearanceoftheirsintrain，thoughperhapsitmaybesometimesfasterandsometimesslower，yet，Iguess，variesnotverymuchinawakingman:thereseemtobecertainboundstothequicknessandslownessofthesuccessionofthoseideasonetoanotherinourminds，beyondwhichtheycanneitherdelaynorhasten。
10。Realsuccessioninswiftmotionswithoutsenseofsuccession。
ThereasonIhaveforthisoddconjectureis，fromobservingthat，intheimpressionsmadeuponanyofoursenses，wecanbuttoacertaindegreeperceiveanysuccession；which，ifexceedingquick，thesenseofsuccessionislost，evenincaseswhereitisevidentthatthereisarealsuccession。Letacannon-bulletpassthrougharoom，andinitswaytakewithitanylimb，orfleshypartsofaman，itisasclearasanydemonstrationcanbe，thatitmuststrikesuccessivelythetwosidesoftheroom:itisalsoevidentthatitmusttouchonepartofthefleshfirst，andanotherafter，andsoinsuccession:andyet，Ibelieve，nobodywhoeverfeltthepainofsuchashot，orheardtheblowagainstthetwodistantwalls，couldperceiveanysuccessioneitherinthepainorsoundofsoswiftastroke。Suchapartofdurationasthis，whereinweperceivenosuccession，isthatwhichwecallaninstant，andisthatwhichtakesupthetimeofonlyoneideainourminds，withoutthesuccessionofanother；wherein，therefore，weperceivenosuccessionatall。
11。Inslowmotions。Thisalsohappenswherethemotionissoslowasnottosupplyaconstanttrainoffreshideastothesenses，asfastasthemindiscapableofreceivingnewonesintoit；andsootherideasofourownthoughts，havingroomtocomeintoourmindsbetweenthoseofferedtooursensesbythemovingbody，therethesenseofmotionislost；andthebody，thoughitreallymoves，yet，notchangingperceivabledistancewithsomeotherbodiesasfastastheideasofourownmindsdonaturallyfollowoneanotherintrain，thethingseemstostandstill；asisevidentinthehandsofclocks，andshadowsofsun-dials，andotherconstantbutslowmotions，where，though，aftercertainintervals，weperceive，bythechangeofdistance，thatithathmoved，yetthemotionitselfweperceivenot。
12。Thistrain，themeasureofothersuccessions。Sothattomeitseems，thattheconstantandregularsuccessionofideasinawakingman，is，asitwere，themeasureandstandardofallothersuccessions。Whereof，ifanyoneeitherexceedsthepaceofourideas，aswheretwosoundsorpains，&c。，takeupintheirsuccessionthedurationofbutoneidea；orelsewhereanymotionorsuccessionissoslow，asthatitkeepsnotpacewiththeideasinourminds，orthequicknessinwhichtheytaketheirturns，aswhenanyoneormoreideasintheirordinarycoursecomeintoourmind，betweenthosewhichareofferedtothesightbythedifferentperceptibledistancesofabodyinmotion，orbetweensoundsorsmellsfollowingoneanother，-
therealsothesenseofaconstantcontinuedsuccessionislost，andweperceiveitnot，butwithcertaingapsofrestbetween。
13。Themindcannotfixlongononeinvariableidea。Ifitbeso，thattheideasofourminds，whilstwehaveanythere，doconstantlychangeandshiftinacontinualsuccession，itwouldbeimpossible，mayanyonesay，foramantothinklongofanyonething。Bywhich，ifitbemeantthatamanmayhaveoneself-samesingleideaalongtimealoneinhismind，withoutanyvariationatall，Ithink，inmatteroffact，itisnotpossible。Forwhich(notknowinghowtheideasofourmindsareframed，ofwhatmaterialstheyaremade，whencetheyhavetheirlight，andhowtheycometomaketheirappearances)
Icangivenootherreasonbutexperience:andIwouldhaveanyonetry，whetherhecankeeponeunvariedsingleideainhismind，withoutanyother，foranyconsiderabletimetogether。
14。Proof。Fortrial，lethimtakeanyfigure，anydegreeoflightorwhiteness，orwhatotherhepleases，andhewill，Isuppose，finditdifficulttokeepallotherideasoutofhismind；butthatsome，eitherofanotherkind，orvariousconsiderationsofthatidea，(eachofwhichconsiderationsisanewidea)，willconstantlysucceedoneanotherinhisthoughts，lethimbeaswaryashecan。
15。Theextentofourpoweroverthesuccessionofourideas。Allthatisinaman’spowerinthiscase，Ithink，isonlytomindandobservewhattheideasarethattaketheirturnsinhisunderstanding；
orelsetodirectthesort，andcallinsuchashehathadesireoruseof:buthindertheconstantsuccessionoffreshones，Ithinkhecannot，thoughhemaycommonlychoosewhetherhewillheedfullyobserveandconsiderthem。
16。Ideas，howevermade，includenosenseofmotion。Whethertheseseveralideasinaman’smindbemadebycertainmotions，Iwillnotheredispute；butthisIamsure，thattheyincludenoideaofmotionintheirappearance；andifamanhadnottheideaofmotionotherwise，Ithinkhewouldhavenoneatall，whichisenoughtomypresentpurpose；andsufficientlyshowsthatthenoticewetakeoftheideasofourownminds，appearingthereoneafteranother，isthatwhichgivesustheideaofsuccessionandduration，withoutwhichweshouldhavenosuchideasatall。Itisnotthenmotion，buttheconstanttrainofideasinourmindswhilstwearewaking，thatfurnishesuswiththeideaofduration；whereofmotionnootherwisegivesusanyperceptionthanasitcausesinourmindsaconstantsuccessionofideas，asIhavebeforeshowed:andwehaveasclearanideaofsuccessionandduration，bythetrainofotherideassucceedingoneanotherinourminds，withouttheideaofanymotion，asbythetrainofideascausedbytheuninterruptedsensiblechangeofdistancebetweentwobodies，whichwehavefrommotion；andthereforeweshouldaswellhavetheideaofdurationweretherenosenseofmotionatall。
17。Timeisdurationsetoutbymeasures。Havingthusgottheideaofduration，thenextthingnaturalforthemindtodo，istogetsomemeasureofthiscommonduration，wherebyitmightjudgeofitsdifferentlengths，andconsiderthedistinctorderwhereinseveralthingsexist；withoutwhichagreatpartofourknowledgewouldbeconfused，andagreatpartofhistoryberenderedveryuseless。Thisconsiderationofduration，assetoutbycertainperiods，andmarkedbycertainmeasuresorepochs，isthat，Ithink，whichmostproperlywecalltime。
18。Agoodmeasureoftimemustdivideitswholedurationintoequalperiods。Inthemeasuringofextension，thereisnothingmorerequiredbuttheapplicationofthestandardormeasurewemakeuseoftothethingofwhoseextensionwewouldbeinformed。Butinthemeasuringofdurationthiscannotbedone，becausenotwodifferentpartsofsuccessioncanbeputtogethertomeasureoneanother。Andnothingbeingameasureofdurationbutduration，asnothingisofextensionbutextension，wecannotkeepbyusanystanding，unvaryingmeasureofduration，whichconsistsinaconstantfleetingsuccession，aswecanofcertainlengthsofextension，asinches，feet，yards，&c。，markedoutinpermanentparcelsofmatter。Nothingthencouldservewellforaconvenientmeasureoftime，butwhathasdividedthewholelengthofitsdurationintoapparentlyequalportions，byconstantlyrepeatedperiods。Whatportionsofdurationarenotdistinguished，orconsideredasdistinguishedandmeasured，bysuchperiods，comenotsoproperlyunderthenotionoftime；asappearsbysuchphrasesasthese，viz。\"Beforealltime，\"and\"Whentimeshallbenomore。\"
19。Therevolutionsofthesunandmoon，theproperestmeasuresoftimeformankind。Thediurnalandannualrevolutionsofthesun，ashavingbeen，fromthebeginningofnature，constant，regular，anduniversallyobservablebyallmankind，andsupposedequaltooneanother，havebeenwithreasonmadeuseofforthemeasureofduration。Butthedistinctionofdaysandyearshavingdependedonthemotionofthesun，ithasbroughtthismistakewithit，thatithasbeenthoughtthatmotionanddurationwerethemeasureoneofanother。
Formen，inthemeasuringofthelengthoftime，havingbeenaccustomedtotheideasofminutes，hours，days，months，years，&c。，whichtheyfoundthemselvesuponanymentionoftimeordurationpresentlytothinkon，allwhichportionsoftimeweremeasuredoutbythemotionofthoseheavenlybodies，theywereapttoconfoundtimeandmotion；oratleasttothinkthattheyhadanecessaryconnexiononewithanother。Whereasanyconstantperiodicalappearance，oralterationofideas，inseeminglyequidistantspacesofduration，ifconstantanduniversallyobservable，wouldhaveaswelldistinguishedtheintervalsoftime，asthosethathavebeenmadeuseof。For，supposingthesun，whichsomehavetakentobeafire，hadbeenlightedupatthesamedistanceoftimethatitnoweverydaycomesabouttothesamemeridian，andthengoneoutagainabouttwelvehoursafter，andthatinthespaceofanannualrevolutionithadsensiblyincreasedinbrightnessandheat，andsodecreasedagain，-
wouldnotsuchregularappearancesservetomeasureoutthedistancesofdurationtoallthatcouldobserveit，aswellwithoutaswithmotion？Foriftheappearanceswereconstant，universallyobservable，inequidistantperiods，theywouldservemankindformeasureoftimeaswellwerethemotionaway。
20。Butnotbytheirmotion，butperiodicalappearances。Forthefreezingofwater，ortheblowingofaplant，returningatequidistantperiodsinallpartsoftheearth，wouldaswellservementoreckontheiryearsbyasthemotionsofthesun:andineffectwesee，thatsomepeopleinAmericacountedtheiryearsbythecomingofcertainbirdsamongstthemattheircertainseasons，andleavingthematothers。Forafitofanague；thesenseofhungerorthirst；asmellorataste；oranyotherideareturningconstantlyatequidistantperiods，andmakingitselfuniversallybetakennoticeof，wouldnotfailtomeasureoutthecourseofsuccession，anddistinguishthedistancesoftime。Thusweseethatmenbornblindcounttimewellenoughbyyears，whoserevolutionsyettheycannotdistinguishbymotionsthattheyperceivenot。AndIaskwhetherablindman，whodistinguishedhisyearseitherbytheheatofsummer，orcoldofwinter；bythesmellofanyflowerofthespring，ortasteofanyfruitoftheautumn，wouldnothaveabettermeasureoftimethantheRomanshadbeforethereformationoftheircalendarbyJuliusCaesar，ormanyotherpeoplewhoseyears，notwithstandingthemotionofthesun，whichtheypretendedtomakeuseof，areveryirregular？
Anditaddsnosmalldifficultytochronology，thattheexactlengthsoftheyearsthatseveralnationscountedby，arehardtobeknown，theydifferingverymuchonefromanother，andIthinkImaysayallofthemfromtheprecisemotionofthesun。Andifthesunmovedfromthecreationtothefloodconstantlyintheequator，andsoequallydisperseditslightandheattoallthehabitablepartsoftheearth，indaysallofthesamelength，withoutitsannualvariationstothetropics，asalateingeniousauthorsupposes，Idonotthinkitveryeasytoimagine，that(notwithstandingthemotionofthesun)menshouldintheantediluvianworld，fromthebeginning，countbyyears，ormeasuretheirtimebyperiodsthathadnosensiblemarksveryobvioustodistinguishthemby。
21。Notwopartsofdurationcanbecertainlyknowntobeequal。Butperhapsitwillbesaid，-withoutaregularmotion，suchasofthesun，orsomeother，howcoulditeverbeknownthatsuchperiodswereequal？TowhichIanswer，-theequalityofanyotherreturningappearancesmightbeknownbythesamewaythatthatofdayswasknown，orpresumedtobesoatfirst；whichwasonlybyjudgingofthembythetrainofideaswhichhadpassedinmen’smindsintheintervals；bywhichtrainofideasdiscoveringinequalityinthenaturaldays，butnoneintheartificialdays，theartificialdays，ornuchtheerha，wereguessedtobeequal，whichwassufficienttomakethemserveforameasure；thoughexactersearchhassincediscoveredinequalityinthediurnalrevolutionsofthesun，andweknownotwhethertheannualalsobenotunequal。Theseyet，bytheirpresumedandapparentequality，serveaswelltoreckontimeby(thoughnottomeasurethepartsofdurationexactly)asiftheycouldbeprovedtobeexactlyequal。Wemust，therefore，carefullydistinguishbetwixtdurationitself，andthemeasureswemakeuseoftojudgeofitslength。Duration，initself，istobeconsideredasgoingoninoneconstant，equal，uniformcourse:butnoneofthemeasuresofitwhichwemakeuseofcanbeknowntodoso，norcanwebeassuredthattheirassignedpartsorperiodsareequalindurationonetoanother；fortwosuccessivelengthsofduration，howevermeasured，canneverbedemonstratedtobeequal。Themotionofthesun，whichtheworldusedsolongandsoconfidentlyforanexactmeasureofduration，has，asIsaid，beenfoundinitsseveralpartsunequal。Andthoughmenhave，oflate，madeuseofapendulum，asamoresteadyandregularmotionthanthatofthesun，or，(tospeakmoretruly)，oftheearth；-yetifanyoneshouldbeaskedhowhecertainlyknowsthatthetwosuccessiveswingsofapendulumareequal，itwouldbeveryhardtosatisfyhimthattheyareinfalliblyso；sincewecannotbesurethatthecauseofthatmotion，whichisunknowntous，shallalwaysoperateequally；andwearesurethatthemediuminwhichthependulummovesisnotconstantlythesame:eitherofwhichvarying，mayaltertheequalityofsuchperiods，andtherebydestroythecertaintyandexactnessofthemeasurebymotion，aswellasanyotherperiodsofotherappearances；thenotionofdurationstillremainingclear，thoughourmeasuresofitcannot(anyofthem)bedemonstratedtobeexact。Sincethennotwoportionsofsuccessioncanbebroughttogether，itisimpossibleevercertainlytoknowtheirequality。
Allthatwecandoforameasureoftimeis，totakesuchashavecontinualsuccessiveappearancesatseeminglyequidistantperiods；
ofwhichseemingequalitywehavenoothermeasure，butsuchasthetrainofourownideashavelodgedinourmemories，withtheconcurrenceofotherprobablereasons，topersuadeusoftheirequality。
22。Timenotthemeasureofmotion。Onethingseemsstrangetome，-thatwhilstallmenmanifestlymeasuredtimebythemotionofthegreatandvisiblebodiesoftheworld，timeyetshouldbedefinedtobethe\"measureofmotion\":whereasitisobvioustoeveryonewhoreflectseversolittleonit，thattomeasuremotion，spaceisasnecessarytobeconsideredastime；andthosewholookalittlefartherwillfindalsothebulkofthethingmovednecessarytobetakenintothecomputation，byanyonewhowillestimateormeasuremotionsoastojudgerightofit。Norindeeddoesmotionanyotherwiseconducetothemeasuringofduration，thanasitconstantlybringsaboutthereturnofcertainsensibleideas，inseemingequidistantperiods。Forifthemotionofthesunwereasunequalasofashipdrivenbyunsteadywinds，sometimesveryslow，andatothersirregularlyveryswift；orif，beingconstantlyequallyswift，ityetwasnotcircular，andproducednotthesameappearances，-itwouldnotatallhelpustomeasuretime，anymorethantheseemingunequalmotionofacometdoes。
23。Minutes，hours，days，andyearsnotnecessarymeasuresofduration。Minutes，hours，days，andyearsare，then，nomorenecessarytotimeorduration，thaninches，feet，yards，andmiles，markedoutinanymatter，aretoextension。For，thoughweinthispartoftheuniverse，bytheconstantuseofthem，asofperiodssetoutbytherevolutionsofthesun，orasknownpartsofsuchperiods，havefixedtheideasofsuchlengthsofdurationinourminds，whichweapplytoallpartsoftimewhoselengthswewouldconsider；yettheremaybeotherpartsoftheuniverse，wheretheynomoreusetheremeasuresofours，thaninJapantheydoourinches，feet，ormiles；
butyetsomethinganalogoustothemtheremustbe。Forwithoutsomeregularperiodicalreturns，wecouldnotmeasureourselves，orsignifytoothers，thelengthofanyduration；thoughatthesametimetheworldwereasfullofmotionasitisnow，butnopartofitdisposedintoregularandapparentlyequidistantrevolutions。Butthedifferentmeasuresthatmaybemadeuseoffortheaccountoftime，donotatallalterthenotionofduration，whichisthethingtobemeasured；nomorethanthedifferentstandardsofafootandacubitalterthenotionofextensiontothosewhomakeuseofthosedifferentmeasures。
24。Ourmeasureoftimeapplicabletodurationbeforetime。Themindhavingoncegotsuchameasureoftimeastheannualrevolutionofthesun，canapplythatmeasuretodurationwhereinthatmeasureitselfdidnotexist，andwithwhich，intherealityofitsbeing，ithadnothingtodo。Forshouldonesay，thatAbrahamwasborninthetwothousandsevenhundredandtwelfthyearoftheJulianperiod，itisaltogetherasintelligibleasreckoningfromthebeginningoftheworld，thoughthereweresofarbacknomotionofthesun，noranymotionatall。For，thoughtheJulianperiodbesupposedtobeginseveralhundredyearsbeforetherewerereallyeitherdays，nights，oryears，markedoutbyanyrevolutionsofthesun，-yetwereckonasright，andtherebymeasuredurationsaswell，asifreallyatthattimethesunhadexisted，andkeptthesameordinarymotionitdothnow。Theideaofdurationequaltoanannualrevolutionofthesun，isaseasilyapplicableinourthoughtstoduration，wherenosunormotionwas，astheideaofafootoryard，takenfrombodieshere，canbeappliedinourthoughtstoduration，wherenosunormotionwas，astheideaofafootoryard，takenfrombodieshere，canbeappliedinourthoughtstodistancesbeyondtheconfinesoftheworld，wherearenobodiesatall。
25。Aswecanmeasurespaceinourthoughtswherethereisnobody。Forsupposingitwere5639miles，ormillionsofmiles，fromthisplacetotheremotestbodyoftheuniverse，(forbeingfinite，itmustbeatacertaindistance)，aswesupposeittobe5639yearsfromthistimetothefirstexistenceofanybodyinthebeginningoftheworld；-wecan，inourthoughts，applythismeasureofayeartodurationbeforethecreation，orbeyondthedurationofbodiesormotion，aswecanthismeasureofamiletospacebeyondtheutmostbodies；andbytheonemeasureduration，wheretherewasnomotion，aswellasbytheothermeasurespaceinourthoughts，wherethereisnobody。
26。Theassumptionthattheworldisneitherboundlessnoreternal。Ifitbeobjectedtomehere，that，inthiswayofexplainingoftime，IhavebeggedwhatIshouldnot，viz。thattheworldisneithereternalnorinfinite；Ianswer，Thattomypresentpurposeitisnotneedful，inthisplace，tomakeuseofargumentstoevincetheworldtobefinitebothindurationandextension。Butitbeingatleastasconceivableasthecontrary，Ihavecertainlythelibertytosupposeit，aswellasanyonehathtosupposethecontrary；andIdoubtnot，butthateveryonethatwillgoaboutit，mayeasilyconceiveinhismindthebeginningofmotion，thoughnotofallduration，andsomaycometoastepandnonultrainhisconsiderationofmotion。Soalso，inhisthoughts，hemaysetlimitstobody，andtheextensionbelongingtoit；butnottospace，wherenobodyis，theutmostboundsofspaceanddurationbeingbeyondthereachofthought，aswellastheutmostboundsofnumberarebeyondthelargestcomprehensionofthemind；andallforthesamereason，asweshallseeinanotherplace。
27。Eternity。Bythesamemeans，therefore，andfromthesameoriginalthatwecometohavetheideaoftime，wehavealsothatideawhichwecallEternity；viz。havinggottheideaofsuccessionandduration，byreflectingonthetrainofourownideas，causedinuseitherbythenaturalappearancesofthoseideascomingconstantlyofthemselvesintoourwakingthoughts，orelsecausedbyexternalobjectssuccessivelyaffectingoursenses；andhavingfromtherevolutionsofthesungottheideasofcertainlengthsofduration，-wecaninourthoughtsaddsuchlengthsofdurationtooneanother，asoftenasweplease，andapplythem，soadded，todurationspastortocome。Andthiswecancontinuetodoon，withoutboundsorlimits，andproceedininfinitum，andapplythusthelengthoftheannualmotionofthesuntoduration，supposedbeforethesun’soranyothermotionhaditsbeing；whichisnomoredifficultorabsurd，thantoapplythenotionIhaveofthemovingofashadowonehourto-dayuponthesun-dialtothedurationofsomethinglastnight，v。g。theburningofacandle，whichisnowabsolutelyseparatefromallactualmotion；anditisasimpossibleforthedurationofthatflameforanhourlastnighttoco-existwithanymotionthatnowis，orforevershallbe，asforanypartofduration，thatwasbeforethebeginningoftheworld，toco-existwiththemotionofthesunnow。Butyetthishindersnotbutthat，havingtheideaofthelengthofthemotionoftheshadowonadialbetweenthemarksoftwohours，Icanasdistinctlymeasureinmythoughtsthedurationofthatcandle-lightlastnight，asIcanthedurationofanythingthatdoesnowexist:anditisnomorethantothink，that，hadthesunshonethenonthedial，andmovedafterthesamerateitdothnow，theshadowonthedialwouldhavepassedfromonehour-linetoanotherwhilstthatflameofthecandlelasted。
28。Ourmeasuresofdurationdependentonourideas。Thenotionofanhour，day，oryear，beingonlytheideaIhaveofthelengthofcertainperiodicalregularmotions，neitherofwhichmotionsdoeverallatonceexist，butonlyintheideasIhaveoftheminmymemoryderivedfrommysensesorreflection；Icanwiththesameease，andforthesamereason，applyitinmythoughtstodurationantecedenttoallmannerofmotion，aswellastoanythingthatisbutaminuteoradayantecedenttothemotionthatatthisverymomentthesunisin。
Allthingspastareequallyandperfectlyatrest；andtothiswayofconsiderationofthemareallone，whethertheywerebeforethebeginningoftheworld，orbutyesterday:themeasuringofanydurationbysomemotiondependingnotatallontherealco-existenceofthatthingtothatmotion，oranyotherperiodsofrevolution，butthehavingaclearideaofthelengthofsomeperiodicalknownmotion，orotherintervalofduration，inmymind，andapplyingthattothedurationofthethingIwouldmeasure。
29。Thedurationofanythingneednotbeco-existentwiththemotionwemeasureitby。Henceweseethatsomemenimaginethedurationoftheworld，fromitsfirstexistencetothispresentyear1689，tohavebeen5639years，orequalto5639annualrevolutionsofthesun，andothersagreatdealmore；astheEgyptiansofold，whointhetimeofAlexandercounted23，000yearsfromthereignofthesun；andtheChinesenow，whoaccounttheworld3，269，000yearsold，ormore；whichlongerdurationoftheworld，accordingtotheircomputation，thoughI
shouldnotbelievetobetrue，yetIcanequallyimagineitwiththem，andastrulyunderstand，andsayoneislongerthantheother，asI
understand，thatMethusalem’slifewaslongerthanEnoch’s。AndifthecommonreckoningOf5639shouldbetrue，(asitmaybeaswellasanyotherassigned，)ithindersnotatallmyimaginingwhatothersmean，whentheymaketheworldonethousandyearsolder，sinceeveryonemaywiththesamefacilityimagine(Idonotsaybelieve)theworldtobe50，000yearsold，as5639；andmayaswellconceivethedurationof50，000yearsas5639。Wherebyitappearsthat，tothemeasuringthedurationofanythingbytime，itisnotrequisitethatthatthingshouldbeco-existenttothemotionwemeasureby，oranyotherperiodicalrevolution；butitsufficestothispurpose，thatwehavetheideaofthelengthofanyregularperiodicalappearances，whichwecaninourmindsapplytoduration，withwhichthemotionorappearanceneverco-existed。
30。Infinityinduration。For，asinthehistoryofthecreationdeliveredbyMoses，Icanimaginethatlightexistedthreedaysbeforethesunwas，orhadanymotion，barelybythinkingthatthedurationoflightbeforethesunwascreatedwassolongas(ifthesunhadmovedthenasitdothnow)wouldhavebeenequaltothreeofhisdiurnalrevolutions；sobythesamewayIcanhaveanideaofthechaos，orangels，beingcreatedbeforetherewaseitherlightoranycontinuedmotion，aminute，anhour，aday，ayear，oronethousandyears。For，ifIcanbutconsiderdurationequaltooneminute，beforeeitherthebeingormotionofanybody，IcanaddoneminutemoretillIcometosixty；andbythesamewayofaddingminutes，hours，oryears(i。e。suchorsuchpartsofthesun’srevolutions，oranyotherperiodwhereofIhavetheidea)proceedininfinitum，andsupposeadurationexceedingasmanysuchperiodsasIcanreckon，letmeaddwhilstIwill，whichIthinkisthenotionwehaveofeternity；
ofwhoseinfinitywehavenoothernotionthanwehaveoftheinfinityofnumber，towhichwecanaddforeverwithoutend。
31。Originofourideasofduration，andofthemeasuresofit。
AndthusIthinkitisplain，thatfromthosetwofountainsofallknowledgebeforementioned，viz。reflectionandsensation，wegottheideasofduration，andthemeasuresofit。
For，First，byobservingwhatpassesinourminds，howourideasthereintrainconstantlysomevanishandothersbegintoappear，wecomebytheideaofsuccession。
Secondly，byobservingadistanceinthepartsofthissuccession，wegettheideaofduration。
Thirdly，bysensationobservingcertainappearances，atcertainregularandseemingequidistantperiods，wegettheideasofcertainlengthsormeasuresofduration，asminutes，hours，days，years，&c。
Fourthly，bybeingabletorepeatthosemeasuresoftime，orideasofstatedlengthofduration，inourminds，asoftenaswewill，wecancometoimagineduration，wherenothingdoesreallyendureorexist；andthusweimagineto-morrow，nextyear，orsevenyearshence。
Fifthly，bybeingabletorepeatideasofanylengthoftime，asofaminute，ayear，oranage，asoftenaswewillinourownthoughts，andaddingthemonetoanother，withoutevercomingtotheendofsuchaddition，anynearerthanwecantotheendofnumber，towhichwecanalwaysadd；wecomebytheideaofeternity，asthefutureeternaldurationofoursouls，aswellastheeternityofthatinfiniteBeingwhichmustnecessarilyhavealwaysexisted。
Sixthly，byconsideringanypartofinfiniteduration，assetoutbyperiodicalmeasures，wecomebytheideaofwhatwecalltimeingeneral。
ChapterXV
IdeasofDurationandExpansion，consideredtogether1。Bothcapableofgreaterandless。Thoughwehaveintheprecedentchaptersdweltprettylongontheconsiderationsofspaceandduration，yet，theybeingideasofgeneralconcernment，thathavesomethingveryabstruseandpeculiarintheirnature，thecomparingthemonewithanothermayperhapsbeofusefortheirillustration；
andwemayhavethemoreclearanddistinctconceptionofthembytakingaviewofthemtogether。Distanceorspace，initssimpleabstractconception，toavoidconfusion，Icallexpansion，todistinguishitfromextension，whichbysomeisusedtoexpressthisdistanceonlyasitisinthesolidpartsofmatter，andsoincludes，oratleastintimates，theideaofbody:whereastheideaofpuredistanceincludesnosuchthing。Ipreferalsothewordexpansiontospace，becausespaceisoftenappliedtodistanceoffleetingsuccessiveparts，whichneverexisttogether，aswellastothosewhicharepermanent。Inboththese(viz。expansionandduration)themindhasthiscommonideaofcontinuedlengths，capableofgreaterorlessquantities。Foramanhasasclearanideaofthedifferenceofthelengthofanhourandaday，asofaninchandafoot。
2。Expansionnotboundedbymatter。Themind，havinggottheideaofthelengthofanypartofexpansion，letitbeaspan，orapace，orwhatlengthyouwill，can，ashasbeensaid，repeatthatidea，andso，addingittotheformer，enlargeitsideaoflength，andmakeitequaltotwospans，ortwopaces；andso，asoftenasitwill，tillitequalsthedistanceofanypartsoftheearthonefromanother，andincreasethustillitamountstothedistanceofthesunorremoteststar。Bysuchaprogressionasthis，settingoutfromtheplacewhereitis，oranyotherplace，itcanproceedandpassbeyondallthoselengths，andfindnothingtostopitsgoingon，eitherinorwithoutbody。Itistrue，wecaneasilyinourthoughtscometotheendofsolidextension；theextremityandboundsofallbodywehavenodifficultytoarriveat:butwhenthemindisthere，itfindsnothingtohinderitsprogressintothisendlessexpansion；ofthatitcanneitherfindnorconceiveanyend。Norletanyonesay，thatbeyondtheboundsofbody，thereisnothingatall；unlesshewillconfineGodwithinthelimitsofmatter。Solomon，whoseunderstandingwasfilledandenlargedwithwisdom，seemstohaveotherthoughtswhenhesays，\"Heaven，andtheheavenofheavens，cannotcontainthee。\"Andhe，Ithink，verymuchmagnifiestohimselfthecapacityofhisownunderstanding，whopersuadeshimselfthathecanextendhisthoughtsfurtherthanGodexists，orimagineanyexpansionwhereHeisnot。
3。Nordurationbymotion。Justsoisitinduration。Themindhavinggottheideaofanylengthofduration，candouble，multiply，andenlargeit，notonlybeyonditsown，butbeyondtheexistenceofallcorporealbeings，andallthemeasuresoftime，takenfromthegreatbodiesofalltheworldandtheirmotions。Butyeteveryoneeasilyadmits，that，thoughwemakedurationboundless，ascertainlyitis，wecannotyetextenditbeyondallbeing。God，everyoneeasilyallows，fillseternity；anditishardtofindareasonwhyanyoneshoulddoubtthatHelikewisefillsimmensity。Hisinfinitebeingiscertainlyasboundlessonewayasanother；andmethinksitascribesalittletoomuchtomattertosay，wherethereisnobody，thereisnothing。
4。Whymenmoreeasilyadmitinfinitedurationthaninfiniteexpansion。HenceIthinkwemaylearnthereasonwhyeveryonefamiliarlyandwithouttheleasthesitationspeaksofandsupposesEternity，andsticksnottoascribeinfinitytoduration；butitiswithmoredoubtingandreservethatmanyadmitorsupposetheinfinityofspace。Thereasonwhereofseemstometobethis，-Thatdurationandextensionbeingusedasnamesofaffectionsbelongingtootherbeings，weeasilyconceiveinGodinfiniteduration，andwecannotavoiddoingso:but，notattributingtoHimextension，butonlytomatter，whichisfinite，weareaptertodoubtoftheexistenceofexpansionwithoutmatter；ofwhichalonewecommonlysupposeitanattribute。And，therefore，whenmenpursuetheirthoughtsofspace，theyareapttostopattheconfinesofbody:asifspacewerethereatanendtoo，andreachednofurther。Oriftheirideas，uponconsideration，carrythemfurther，yettheytermwhatisbeyondthelimitsoftheuniverse，imaginaryspace:asifitwerenothing，becausethereisnobodyexistinginit。Whereasduration，antecedenttoallbody，andtothemotionswhichitismeasuredby，theynevertermimaginary:becauseitisneversupposedvoidofsomeotherrealexistence。Andifthenamesofthingsmayatalldirectourthoughtstowardstheoriginalofmen’sideas，(asIamapttothinktheymayverymuch，)onemayhaveoccasiontothinkbythenameduration，thatthecontinuationofexistence，withakindofresistancetoanydestructiveforce，andthecontinuationofsolidity(whichisapttobeconfoundedwith，andifwewilllookintotheminuteanatomicalpartsofmatter，islittledifferentfrom，hardness)werethoughttohavesomeanalogy，andgaveoccasiontowordssonearofkinasdurareanddurumesse。Andthatdurareisappliedtotheideaofhardness，aswellasthatofexistence，weseeinHorace，Epod。xvi。ferroduravitsecula。But，bethatasitwill，thisiscertain，thatwhoeverpursueshisownthoughts，willfindthemsometimeslaunchoutbeyondtheextentofbody，intotheinfinityofspaceorexpansion；theideawhereofisdistinctandseparatefrombodyandallotherthings:whichmay，(tothosewhoplease)，beasubjectoffurthermeditation。
5。Timetodurationisasplacetoexpansion。Timeingeneralistodurationasplacetoexpansion。Theyaresomuchofthoseboundlessoceansofeternityandimmensityasissetoutanddistinguishedfromtherest，asitwerebylandmarks；andsoaremadeuseoftodenotethepositionoffiniterealbeings，inrespectonetoanother，inthoseuniforminfiniteoceansofdurationandspace。
These，rightlyconsidered，areonlyideasofdeterminatedistancesfromcertainknownpoints，fixedindistinguishablesensiblethings，andsupposedtokeepthesamedistanceonefromanother。Fromsuchpointsfixedinsensiblebeingswereckon，andfromthemwemeasureourportionsofthoseinfinitequantities；which，soconsidered，arethatwhichwecalltimeandplace。Fordurationandspacebeinginthemselvesuniformandboundless，theorderandpositionofthings，withoutsuchknownsettledpoints，wouldbelostinthem；andallthingswouldliejumbledinanincurableconfusion。
6。Timeandplacearetakenforsomuchofeitherasaresetoutbytheexistenceandmotionofbodies。Timeandplace，takenthusfordeterminatedistinguishableportionsofthoseinfiniteabyssesofspaceandduration，setoutorsupposedtobedistinguishedfromtherest，bymarksandknownboundaries，haveeachofthematwofoldacceptation。
First，Timeingeneraliscommonlytakenforsomuchofinfinitedurationasismeasuredby，andco-existentwith，theexistenceandmotionsofthegreatbodiesoftheuniverse，asfarasweknowanythingofthem:andinthissensetimebeginsandendswiththeframeofthissensibleworld，asinthesephrasesbeforementioned，\"Beforealltime，\"or，\"Whentimeshallbenomore。\"Placelikewiseistakensometimesforthatportionofinfinitespacewhichispossessedbyandcomprehendedwithinthematerialworld；andistherebydistinguishedfromtherestofexpansion；thoughthismaybemoreproperlycalledextensionthanplace。Withinthesetwoareconfined，andbytheobservablepartsofthemaremeasuredanddetermined，theparticulartimeorduration，andtheparticularextensionandplace，ofallcorporealbeings。
7。Sometimesforsomuchofeitheraswedesignbymeasurestakenfromthebulkormotionofbodies。Secondly，sometimesthewordtimeisusedinalargersense，andisappliedtopartsofthatinfiniteduration，notthatwerereallydistinguishedandmeasuredoutbythisrealexistence，andperiodicalmotionsofbodies，thatwereappointedfromthebeginningtobeforsignsandforseasonsandfordaysandyears，andareaccordinglyourmeasuresoftime；butsuchotherportionstooofthatinfiniteuniformduration，whichweuponanyoccasiondosupposeequaltocertainlengthsofmeasuredtime；andsoconsiderthemasboundedanddetermined。For，ifweshouldsupposethecreation，orfalloftheangels，wasatthebeginningoftheJulianperiod，weshouldspeakproperlyenough，andshouldbeunderstoodifwesaid，itisalongertimesincethecreationofangelsthanthecreationoftheworld，by7640years:wherebywewouldmarkoutsomuchofthatundistinguisheddurationaswesupposeequalto，andwouldhaveadmitted，7640annualrevolutionsofthesun，movingattherateitnowdoes。Andthuslikewisewesometimesspeakofplace，distance，orbulk，inthegreatinane，beyondtheconfinesoftheworld，whenweconsidersomuchofthatspaceasisequalto，orcapabletoreceive，abodyofanyassigneddimensions，asacubicfoot；ordosupposeapointinit，atsuchacertaindistancefromanypartoftheuniverse。
8。Theybelongtoallfinitebeings。Whereandwhenarequestionsbelongingtoallfiniteexistences，andarebyusalwaysreckonedfromsomeknownpartsofthissensibleworld，andfromsomecertainepochsmarkedouttousbythemotionsobservableinit。Withoutsomesuchfixedpartsorperiods，theorderofthingswouldbelost，toourfiniteunderstandings，intheboundlessinvariableoceansofdurationandexpansion，whichcomprehendinthemallfinitebeings，andintheirfullextentbelongonlytotheDeity。Andthereforewearenottowonderthatwecomprehendthemnot，anddosooftenfindourthoughtsataloss，whenwewouldconsiderthem，eitherabstractlyinthemselves，orasanywayattributedtothefirstincomprehensibleBeing。Butwhenappliedtoanyparticularfinitebeings，theextensionofanybodyissomuchofthatinfinitespaceasthebulkofthebodytakesup。Andplaceisthepositionofanybody，whenconsideredatacertaindistancefromsomeother。Astheideaoftheparticulardurationofanythingis，anideaofthatportionofinfinitedurationwhichpassesduringtheexistenceofthatthing；sothetimewhenthethingexistedis，theideaofthatspaceofdurationwhichpassedbetweensomeknownandfixedperiodofduration，andthebeingofthatthing。Oneshowsthedistanceoftheextremitiesofthebulkorexistenceofthesamething，asthatitisafootsquare，orlastedtwoyears；theothershowsthedistanceofitinplace，orexistencefromotherfixedpointsofspaceorduration，asthatitwasinthemiddleofLincoln’sInnFields，orthefirstdegreeofTaurus，andintheyearofourLord1671，orthe1000thyearoftheJulianperiod。Allwhichdistanceswemeasurebypreconceivedideasofcertainlengthsofspaceandduration，-asinches，feet，miles，anddegrees，andintheother，minutes，days，andyears，&c。
9。Allthepartsofextensionareextension，andallthepartsofdurationareduration。Thereisonethingmorewhereinspaceanddurationhaveagreatconformity，andthatis，thoughtheyarejustlyreckonedamongstoursimpleideas，yetnoneofthedistinctideaswehaveofeitheriswithoutallmannerofcomposition:itistheverynatureofbothofthemtoconsistofparts:buttheirpartsbeingallofthesamekind，andwithoutthemixtureofanyotheridea，hinderthemnotfromhavingaplaceamongstsimpleideas。Couldthemind，asinnumber，cometososmallapartofextensionordurationasexcludeddivisibility，thatwouldbe，asitwere，theindivisibleunitoridea；byrepetitionofwhich，itwouldmakeitsmoreenlargedideasofextensionandduration。But，sincethemindisnotabletoframeanideaofanyspacewithoutparts，insteadthereofitmakesuseofthecommonmeasures，which，byfamiliaruseineachcountry，haveimprintedthemselvesonthememory(asinchesandfeet；orcubitsandparasangs；andsoseconds，minutes，hours，days，andyearsinduration)；-themindmakesuse，Isay，ofsuchideasasthese，assimpleones:andthesearethecomponentpartsoflargerideas，whichtheminduponoccasionmakesbytheadditionofsuchknownlengthswhichitisacquaintedwith。Ontheotherside，theordinarysmallestmeasurewehaveofeitherislookedonasanunitinnumber，whenthemindbydivisionwouldreducethemintolessfractions。Thoughonbothsides，bothinadditionanddivision，eitherofspaceorduration，whentheideaunderconsiderationbecomesverybigorverysmallitsprecisebulkbecomesveryobscureandconfused；anditisthenumberofitsrepeatedadditionsordivisionsthataloneremainsclearanddistinct；aswilleasilyappeartoanyonewhowilllethisthoughtslooseinthevastexpansionofspace，ordivisibilityofmatter。Everypartofdurationisdurationtoo；andeverypartofextensionisextension，bothofthemcapableofadditionordivisionininfinitum。Buttheleastportionsofeitherofthem，whereofwehaveclearanddistinctideas，mayperhapsbefittesttobeconsideredbyus，asthesimpleideasofthatkindoutofwhichourcomplexmodesofspace，extension，anddurationaremadeup，andintowhichtheycanagainbedistinctlyresolved。Suchasmallpartindurationmaybecalledamoment，andisthetimeofoneideainourminds，inthetrainoftheirordinarysuccessionthere。Theother，wantingapropername，IknownotwhetherImaybeallowedtocallasensiblepoint，meaningtherebytheleastparticleofmatterorspacewecandiscern，whichisordinarilyaboutaminute，andtothesharpesteyesseldomlessthanthirtysecondsofacircle，whereoftheeyeisthecentre。
10。Theirpartsinseparable。Expansionanddurationhavethisfurtheragreement，that，thoughtheyarebothconsideredbyusashavingparts，yettheirpartsarenotseparableonefromanother，nonoteveninthought:thoughthepartsofbodiesfromwhencewetakeourmeasureoftheone；andthepartsofmotion，orratherthesuccessionofideasinourminds，fromwhencewetakethemeasureoftheother，maybeinterruptedandseparated；astheoneisoftenbyrest，andtheotherisbysleep，whichwecallresttoo。
11。Durationisasaline，expansionasasolid。Butthereisthismanifestdifferencebetweenthem，-Thattheideasoflengthwhichwehaveofexpansionareturnedeveryway，andsomakefigure，andbreadth，andthickness；butdurationisbutasitwerethelengthofonestraightline，extendedininfinitum，notcapableofmultiplicity，variation，orfigure；butisonecommonmeasureofallexistencewhatsoever，whereinallthings，whilsttheyexist，equallypartake。
Forthispresentmomentiscommontoallthingsthatarenowinbeing，andequallycomprehendsthatpartoftheirexistence，asmuchasiftheywereallbutonesinglebeing；andwemaytrulysay，theyallexistinthesamemomentoftime。Whetherangelsandspiritshaveanyanalogytothis，inrespecttoexpansion，isbeyondmycomprehension:andperhapsforus，whohaveunderstandingsandcomprehensionssuitedtoourownpreservation，andtheendsofourownbeing，butnottotherealityandextentofallotherbeings，itisnearashardtoconceiveanyexistence，ortohaveanideaofanyrealbeing，withaperfectnegationofallmannerofexpansion，asitistohavetheideaofanyrealexistencewithaperfectnegationofallmannerofduration。Andtherefore，whatspiritshavetodowithspace，orhowtheycommunicateinit，weknownot。Allthatweknowis，thatbodiesdoeachsinglypossessitsproperportionofit，accordingtotheextentofsolidparts；andtherebyexcludeallotherbodiesfromhavinganyshareinthatparticularportionofspace，whilstitremainsthere。
12。Durationhasnevertwopartstogether，expansionaltogether。
Duration，andtimewhichisapartofit，istheideawehaveofperishingdistance，ofwhichnotwopartsexisttogether，butfolloweachotherinsuccession；anexpansionistheideaoflastingdistance，allwhosepartsexisttogether，andarenotcapableofsuccession。Andtherefore，thoughwecannotconceiveanydurationwithoutsuccession，norcanputittogetherinourthoughtsthatanybeingdoesnowexisttomorrow，orpossessatoncemorethanthepresentmomentofduration；yetwecanconceivetheeternaldurationoftheAlmightyfardifferentfromthatofman，oranyotherfinitebeing。Becausemancomprehendsnotinhisknowledgeorpowerallpastandfuturethings:histhoughtsarebutofyesterday，andheknowsnotwhattomorrowwillbringforth。Whatisoncepasthecanneverrecall；andwhatisyettocomehecannotmakepresent。WhatI
sayofman，Isayofallfinitebeings；who，thoughtheymayfarexceedmaninknowledgeandpower，yetarenomorethanthemeanestcreature，incomparisonwithGodhimselfFiniteoranymagnitudeholdsnotanyproportiontoinfinite。God’sinfiniteduration，beingaccompaniedwithinfiniteknowledgeandinfinitepower，Heseesallthings，pastandtocome；andtheyarenomoredistantfromHisknowledge，nofurtherremovedfromHissight，thanthepresent:theyalllieunderthesameview:andthereisnothingwhichHecannotmakeexisteachmomentHepleases。Fortheexistenceofallthings，dependinguponHisgoodpleasure，allthingsexisteverymomentthatHethinksfittohavethemexist。Toconclude:expansionanddurationdomutuallyembraceandcomprehendeachother；everypartofspacebeingineverypartofduration，andeverypartofdurationineverypartofexpansion。Suchacombinationoftwodistinctideasis，Isuppose，scarcetobefoundinallthatgreatvarietywedoorcanconceive，andmayaffordmattertofurtherspeculation。
ChapterXVI
IdeaofNumber1。Numberthesimplestandmostuniversalidea。Amongstalltheideaswehave，asthereisnonesuggestedtothemindbymoreways，sothereisnonemoresimple，thanthatofunity，orone:ithasnoshadowofvarietyorcompositioninit:everyobjectoursensesareemployedabout；everyideainourunderstandings；everythoughtofourminds，bringsthisideaalongwithit。Andthereforeitisthemostintimatetoourthoughts，aswellasitis，initsagreementtoallotherthings，themostuniversalideawehave。Fornumberappliesitselftomen，angels，actions，thoughts；everythingthateitherdothexist，orcanbeimagined。
2。Itsmodesmadebyaddition。Byrepeatingthisideainourminds，andaddingtherepetitionstogether，wecomebythecomplexideasofthemodesofit。Thus，byaddingonetoone，wehavethecomplexideaofacouple；byputtingtwelveunitstogether，wehavethecomplexideaofadozen；andsoofascore，oramillion，oranyothernumber。
3。Eachmodedistinct。Thesimplemodesofnumberareofallotherthemostdistinct；everytheleastvariation，whichisanunit，makingeachcombinationasclearlydifferentfromthatwhichapproachethnearesttoit，asthemostremote；twobeingasdistinctfromone，astwohundred；andtheideaoftwoasdistinctfromtheideaofthree，asthemagnitudeofthewholeearthisfromthatofamite。
Thisisnotsoinothersimplemodes，inwhichitisnotsoeasy，norperhapspossibleforustodistinguishbetwixttwoapproachingideas，whichyetarereallydifferent。Forwhowillundertaketofindadifferencebetweenthewhiteofthispaperandthatofthenextdegreetoit:orcanformdistinctideasofeverytheleastexcessinextension？
4。Thereforedemonstrationsinnumbersthemostprecise。Theclearnessanddistinctnessofeachmodeofnumberfromallothers，eventhosethatapproachnearest，makesmeapttothinkthatdemonstrationsinnumbers，iftheyarenotmoreevidentandexactthaninextension，yettheyaremoregeneralintheiruse，andmoredeterminateintheirapplication。Becausetheideasofnumbersaremorepreciseanddistinguishablethaninextension；whereeveryequalityandexcessarenotsoeasytobeobservedormeasured；
becauseourthoughtscannotinspacearriveatanydeterminedsmallnessbeyondwhichitcannotgo，asanunit；andthereforethequantityorproportionofanytheleastexcesscannotbediscovered；
whichisclearotherwiseinnumber，where，ashasbeensaid，91isasdistinguishablefromgoasfrom9000，though91bethenextimmediateexcessto90。Butitisnotsoinextension，where，whatsoeverismorethanjustafootoraninch，isnotdistinguishablefromthestandardofafootoraninch；andinlineswhichappearofanequallength，onemaybelongerthantheotherbyinnumerableparts:norcananyoneassignanangle，whichshallbethenextbiggesttoarightone。
5。Namesnecessarytonumbers。Bytherepeating，ashasbeensaid，theideaofanunit，andjoiningittoanotherunit，wemakethereofonecollectiveidea，markedbythenametwo。Andwhosoevercandothis，andproceedon，stilladdingonemoretothelastcollectiveideawhichhehadofanynumber，andgaveanametoit，maycount，orhaveideas，forseveralcollectionsofunits，distinguishedonefromanother，asfarashehathaseriesofnamesforfollowingnumbers，andamemorytoretainthatseries，withtheirseveralnames:
allnumerationbeingbutstilltheaddingofoneunitmore，andgivingtothewholetogether，ascomprehendedinoneidea，anewordistinctnameorsign，wherebytoknowitfromthosebeforeandafter，anddistinguishitfromeverysmallerorgreatermultitudeofunits。
Sothathethatcanaddonetoone，andsototwo，andsogoonwithhistale，takingstillwithhimthedistinctnamesbelongingtoeveryprogression；andsoagain，bysubtractinganunitfromeachcollection，retreatandlessenthem，iscapableofalltheideasofnumberswithinthecompassofhislanguage，orforwhichhehathnames，thoughnotperhapsofmore。For，theseveralsimplemodesofnumbersbeinginourmindsbutsomanycombinationsofunits，whichhavenovariety，norarecapableofanyotherdifferencebutmoreorless，namesormarksforeachdistinctcombinationseemmorenecessarythaninanyothersortofideas。For，withoutsuchnamesormarks，wecanhardlywellmakeuseofnumbersinreckoning，especiallywherethecombinationismadeupofanygreatmultitudeofunits；
whichputtogether，withoutanameormarktodistinguishthatprecisecollection，willhardlybekeptfrombeingaheapinconfusion。
6。Anotherreasonforthenecessityofnamestonumbers。ThisI
thinktobethereasonwhysomeAmericansIhavespokenwith，(whowereotherwiseofquickandrationalpartsenough，)couldnot，aswedo，byanymeanscountto1000；norhadanydistinctideaofthatnumber，thoughtheycouldreckonverywellto20。Becausetheirlanguagebeingscanty，andaccommodatedonlytothefewnecessariesofaneedy，simplelife，unacquaintedeitherwithtradeormathematics，hadnowordsinittostandfor1000；sothatwhentheywerediscoursedwithofthosegreaternumbers，theywouldshowthehairsoftheirhead，toexpressagreatmultitude，whichtheycouldnotnumber；
whichinability，Isuppose，proceededfromtheirwantofnames。TheTououpinamboshadnonamesfornumbersabove5；anynumberbeyondthattheymadeoutbyshowingtheirfingers，andthefingersofotherswhowerepresent。AndIdoubtnotbutweourselvesmightdistinctlynumberinwordsagreatdealfurtherthanweusuallydo，wouldwefindoutbutsomefitdenominationstosignifythemby；whereas，inthewaywetakenowtonamethem，bymillionsofmillionsofmillions，&c。，itishardtogobeyondeighteen，oratmost，fourandtwenty，decimalprogressions，withoutconfusion。Buttoshowhowmuchdistinctnamesconducetoourwellreckoning，orhavingusefulideasofnumbers，letusseeallthesefollowingfiguresinonecontinuedline，asthemarksofonenumber:v。g。
NonillionsOctillionsSeptillionsSextillionsQuintrillions857324162486345896437918423147
QuartrillionsTrillionsBillionsMillionsUnits248106235421261734368149623137
TheordinarywayofnamingthisnumberinEnglish，willbetheoftenrepeatingofmillions，ofmillions，ofmillions，ofmillions，ofmillions，ofmillions，ofmillions，ofmillions，(whichisthedenominationofthesecondsixfigures)。Inwhichway，itwillbeveryhardtohaveanydistinguishingnotionsofthisnumber。Butwhether，bygivingeverysixfiguresanewandorderlydenomination，these，andperhapsagreatmanymorefiguresinprogression，mightnoteasilybecounteddistinctly，andideasofthembothgotmoreeasilytoourselves，andmoreplainlysignifiedtoothers，Ileaveittobeconsidered。ThisImentiononlytoshowhownecessarydistinctnamesaretonumbering，withoutpretendingtointroducenewonesofmyinvention。
7。Whychildrennumbernotearlier。Thuschildren，eitherforwantofnamestomarktheseveralprogressionsofnumbers，ornothavingyetthefacultytocollectscatteredideasintocomplexones，andrangetheminaregularorder，andsoretainthemintheirmemories，asisnecessarytoreckoning，donotbegintonumberveryearly，norproceedinitveryfarorsteadily，tillagoodwhileaftertheyarewellfurnishedwithgoodstoreofotherideas:andonemayoftenobservethemdiscourseandreasonprettywell，andhaveveryclearconceptionsofseveralotherthings，beforetheycantelltwenty。
Andsome，throughthedefaultoftheirmemories，whocannotretaintheseveralcombinationsofnumbers，withtheirnames，annexedintheirdistinctorders，andthedependenceofsolongatrainofnumeralprogressions，andtheirrelationonetoanother，arenotablealltheirlifetimetoreckon，orregularlygooveranymoderateseriesofnumbers。Forhethatwillcounttwenty，orhaveanyideaofthatnumber，mustknowthatnineteenwentbefore，withthedistinctnameorsignofeveryoneofthem，astheystandmarkedintheirorder；forwhereverthisfails，agapismade，thechainbreaks，andtheprogressinnumberingcangonofurther。Sothattoreckonright，itisrequired，(1)Thattheminddistinguishcarefullytwoideas，whicharedifferentonefromanotheronlybytheadditionorsubtractionofoneunit:(2)Thatitretaininmemorythenamesormarksoftheseveralcombinations，fromanunittothatnumber；andthatnotconfusedly，andatrandom，butinthatexactorderthatthenumbersfollowoneanother。Ineitherofwhich，ifittrips，thewholebusinessofnumberingwillbedisturbed，andtherewillremainonlytheconfusedideaofmultitude，buttheideasnecessarytodistinctnumerationwillnotbeattainedto。
8。Numbermeasuresallmeasureables。Thisfurtherisobservableinnumber，thatitisthatwhichthemindmakesuseofinmeasuringallthingsthatbyusaremeasurable，whichprincipallyareexpansionandduration；andourideaofinfinity，evenwhenappliedtothose，seemstobenothingbuttheinfinityofnumber。ForwhatelseareourideasofEternityandImmensity，buttherepeatedadditionsofcertainideasofimaginedpartsofdurationandexpansion，withtheinfinityofnumber；inwhichwecancometonoendofaddition？Forsuchaninexhaustiblestock，number(ofallotherourideas)mostclearlyfurnishesuswith，asisobvioustoeveryone。Forletamancollectintoonesumasgreatanumberashepleases，thismultitude，howgreatsoever，lessensnotonejotthepowerofaddingtoit，orbringshimanynearertheendoftheinexhaustiblestockofnumber；wherestillthereremainsasmuchtobeadded，asifnoneweretakenout。Andthisendlessadditionoraddibility(ifanyonelikethewordbetter)ofnumbers，soapparenttothemind，isthat，Ithink，whichgivesustheclearestandmostdistinctideaofinfinity:ofwhichmoreinthefollowingchapter。
ChapterXVII
OfInfinity1。Infinity，initsoriginalintention，attributedtospace，duration，andnumber。Hethatwouldknowwhatkindofideaitistowhichwegivethenameofinfinity，cannotdoitbetterthanbyconsideringtowhatinfinityisbythemindmoreimmediatelyattributed；andthenhowthemindcomestoframeit。
Finiteandinfiniteseemtometobelookeduponbythemindasthemodesofquantity，andtobeattributedprimarilyintheirfirstdesignationonlytothosethingswhichhaveparts，andarecapableofincreaseordiminutionbytheadditionorsubtractionofanytheleastpart:andsucharetheideasofspace，duration，andnumber，whichwehaveconsideredintheforegoingchapters。Itistrue，thatwecannotbutbeassured，thatthegreatGod，ofwhomandfromwhomareallthings，isincomprehensiblyinfinite:butyet，whenweapplytothatfirstandsupremeBeingourideaofinfinite，inourweakandnarrowthoughts，wedoitprimarilyinrespecttohisdurationandubiquity；and，Ithink，morefigurativelytohispower，wisdom，andgoodness，andotherattributes，whichareproperlyinexhaustibleandincomprehensible，&c。For，whenwecalltheminfinite，wehavenootherideaofthisinfinitybutwhatcarrieswithitsomereflectionon，andimitationof，thatnumberorextentoftheactsorobjectsofGod’spower，wisdom，andgoodness，whichcanneverbesupposedsogreat，orsomany，whichtheseattributeswillnotalwayssurmountandexceed，letusmultiplytheminourthoughtsasfaraswecan，withalltheinfinityofendlessnumber。IdonotpretendtosayhowtheseattributesareinGod，whoisinfinitelybeyondthereachofournarrowcapacities:theydo，withoutdoubt，containinthemallpossibleperfection:butthis，Isay，isourwayofconceivingthem，andtheseourideasoftheirinfinity。
2。Theideaoffiniteeasilygot。Finitethen，andinfinite，beingbythemindlookedonasmodificationsofexpansionandduration，thenextthingtobeconsidered，is，-Howthemindcomesbythem。Asfortheideaoffinite，thereisnogreatdifficulty。Theobviousportionsofextensionthataffectoursenses，carrywiththemintothemindtheideaoffinite:andtheordinaryperiodsofsuccession，wherebywemeasuretimeandduration，ashours，days，andyears，areboundedlengths。Thedifficultyis，howwecomebythoseboundlessideasofeternityandimmensity；sincetheobjectsweconversewithcomesomuchshortofanyapproachorproportiontothatlargeness。
3。Howwecomebytheideaofinfinity。Everyonethathasanyideaofanystatedlengthsofspace，asafoot，findsthathecanrepeatthatidea；andjoiningittotheformer，maketheideaoftwofeet；andbytheadditionofathird，threefeet；andsoon，withoutevercomingtoanendofhisadditions，whetherofthesameideaofafoot，or，ifhepleases，ofdoublingit，oranyotherideahehasofanylength，asamile，ordiameteroftheearth，oroftheorbismagnus:forwhicheverofthesehetakes，andhowoftensoeverhedoubles，oranyotherwisemultipliesit，hefinds，that，afterhehascontinuedhisdoublinginhisthoughts，andenlargedhisideaasmuchashepleases，hehasnomorereasontostop，norisonejotnearertheendofsuchaddition，thanhewasatfirstsettingout:thepowerofenlarginghisideaofspacebyfurtheradditionsremainingstillthesame，hehencetakestheideaofinfinitespace。
4。Ourideaofspaceboundless。This，Ithink，isthewaywherebythemindgetstheideaofinfinitespace。Itisaquitedifferentconsideration，toexaminewhetherthemindhastheideaofsuchaboundlessspaceactuallyexisting；sinceourideasarenotalwaysproofsoftheexistenceofthings:butyet，sincethiscomeshereinourway，IsupposeImaysay，thatweareapttothinkthatspaceinitselfisactuallyboundless，towhichimaginationtheideaofspaceorexpansionofitselfnaturallyleadsus。For，itbeingconsideredbyus，eitherastheextensionofbody，orasexistingbyitself，withoutanysolidmattertakingitup，(forofsuchavoidspacewehavenotonlytheidea，butIhaveproved，asIthink，fromthemotionofbody，itsnecessaryexistence)，itisimpossiblethemindshouldbeeverabletofindorsupposeanyendofit，orbestoppedanywhereinitsprogressinthisspace，howfarsoeveritextendsitsthoughts。Anyboundsmadewithbody，evenadamantinewalls，aresofarfromputtingastoptothemindinitsfurtherprogressinspaceandextensionthatitratherfacilitatesandenlargesit。Forsofarasthatbodyreaches，sofarnoonecandoubtofextension；andwhenwearecometotheutmostextremityofbody，whatistherethatcanthereputastop，andsatisfythemindthatitisattheendofspace，whenitperceivesthatitisnot；nay，whenitissatisfiedthatbodyitselfcanmoveintoit？For，ifitbenecessaryforthemotionofbody，thatthereshouldbeanemptyspace，thougheversolittle，hereamongstbodies；andifitbepossibleforbodytomoveinorthroughthatemptyspace；-nay，itisimpossibleforanyparticleofmattertomovebutintoanemptyspace；thesamepossibilityofabody’smovingintoavoidspace，beyondtheutmostboundsofbody，aswellasintoavoidspaceinterspersedamongstbodies，willalwaysremainclearandevident:theideaofemptypurespace，whetherwithinorbeyondtheconfinesofallbodies，beingexactlythesame，differingnotinnature，thoughinbulk；andtherebeingnothingtohinderbodyfrommovingintoit。Sothatwhereverthemindplacesitselfbyanythought，eitheramongst，orremotefromallbodies，itcan，inthisuniformideaofspace，nowherefindanybounds，anyend；andsomustnecessarilyconcludeit，bytheverynatureandideaofeachpartofit，tobeactuallyinfinite。
5。Andsoofduration。As，bythepowerwefindinourselvesofrepeating，asoftenaswewill，anyideaofspace，wegettheideaofimmensity；so，bybeingabletorepeattheideaofanylengthofdurationwehaveinourminds，withalltheendlessadditionofnumber，wecomebytheideaofeternity。Forwefindinourselves，wecannomorecometoanendofsuchrepeatedideasthanwecancometotheendofnumber；whicheveryoneperceiveshecannot。Buthereagainitisanotherquestion，quitedifferentfromourhavinganideaofeternity，toknowwhethertherewereanyrealbeing，whosedurationhasbeeneternal。Andastothis，Isay，hethatconsiderssomethingnowexisting，mustnecessarilycometoSomethingeternal。Buthavingspokeofthisinanotherplace，Ishallsayherenomoreofit，butproceedontosomeotherconsiderationsofourideaofinfinity。
6。Whyotherideasarenotcapableofinfinity。Ifitbeso，thatourideaofinfinitybegotfromthepowerweobserveinourselvesofrepeating，withoutend，ourownideas，itmaybedemanded，-Whywedonotattributeinfinitytootherideas，aswellasthoseofspaceandduration；sincetheymaybeaseasily，andasoften，repeatedinourmindsastheother:andyetnobodyeverthinksofinfinitesweetness，orinfinitewhiteness，thoughhecanrepeattheideaofsweetorwhite，asfrequentlyasthoseofayardoraday？TowhichIanswer，-Alltheideasthatareconsideredashavingparts，andarecapableofincreasebytheadditionofanyequalorlessparts，affordus，bytheirrepetition，theideaofinfinity；because，withthisendlessrepetition，thereiscontinuedanenlargementofwhichtherecanbenoend。Butinotherideasitisnotso。FortothelargestideaofextensionordurationthatIatpresenthave，theadditionofanytheleastpartmakesanincrease；buttotheperfectestideaIhaveofthewhitestwhiteness，ifIaddanotherofalessorequalwhiteness，(andofawhiterthanIhave，Icannotaddtheidea)，itmakesnoincrease，andenlargesnotmyideaatall；
andthereforethedifferentideasofwhiteness，&c。arecalleddegrees。Forthoseideasthatconsistofpartsarecapableofbeingaugmentedbyeveryadditionoftheleastpart；butifyoutaketheideaofwhite，whichoneparcelofsnowyieldedyesterdaytooursight，andanotherideaofwhitefromanotherparcelofsnowyouseeto-day，andputthemtogetherinyourmind，theyembody，asitwere，andrunintoone，andtheideaofwhitenessisnotatallincreased；
andifweaddalessdegreeofwhitenesstoagreater，wearesofarfromincreasing，thatwediminishit。Thoseideasthatconsistnotofpartscannotbeaugmentedtowhatproportionmenplease，orbestretchedbeyondwhattheyhavereceivedbytheirsenses；butspace，duration，andnumber，beingcapableofincreasebyrepetition，leaveinthemindanideaofendlessroomformore；norcanweconceiveanywhereastoptoafurtheradditionorprogression:andsothoseideasaloneleadourmindstowardsthethoughtofinfinity。
7。Differencebetweeninfinityofspace，andspaceinfinite。
Thoughourideaofinfinityarisefromthecontemplationofquantity，andtheendlessincreasethemindisabletomakeinquantity，bytherepeatedadditionsofwhatportionsthereofitpleases；yetIguesswecausegreatconfusioninourthoughts，whenwejoininfinitytoanysupposedideaofquantitythemindcanbethoughttohave，andsodiscourseorreasonaboutaninfinitequantity，asaninfinitespace，oraninfiniteduration。For，asourideaofinfinitybeing，asIthink，anendlessgrowingidea，buttheideaofanyquantitythemindhas，beingatthattimeterminatedinthatidea，(forbeitasgreatasitwill，itcanbenogreaterthanitis，)-
tojoininfinitytoit，istoadjustastandingmeasuretoagrowingbulk；andthereforeIthinkitisnotaninsignificantsubtilty，ifIsay，thatwearecarefullytodistinguishbetweentheideaoftheinfinityofspace，andtheideaofaspaceinfinite。Thefirstisnothingbutasupposedendlessprogressionofthemind，overwhatrepeatedideasofspaceitpleases；buttohaveactuallyinthemindtheideaofaspaceinfinite，istosupposethemindalreadypassedover，andactuallytohaveaviewofallthoserepeatedideasofspacewhichanendlessrepetitioncannevertotallyrepresenttoit；whichcarriesinitaplaincontradiction。
8。Wehavenoideaofinfinitespace。This，perhaps，willbealittleplainer，ifweconsideritinnumbers。Theinfinityofnumbers，totheendofwhoseadditioneveryoneperceivesthereisnoapproach，easilyappearstoanyonethatreflectsonit。But，howclearsoeverthisideaoftheinfinityofnumberbe，thereisnothingyetmoreevidentthantheabsurdityoftheactualideaofaninfinitenumber。
Whatsoeverpositiveideaswehaveinourmindsofanyspace，duration，ornumber，letthembeeversogreat，theyarestillfinite；butwhenwesupposeaninexhaustibleremainder，fromwhichweremoveallbounds，andwhereinweallowthemindanendlessprogressionofthought，withoutevercompletingtheidea，therewehaveourideaofinfinity:which，thoughitseemstobeprettyclearwhenweconsidernothingelseinitbutthenegationofanend，yet，whenwewouldframeinourmindstheideaofaninfinitespaceorduration，thatideaisveryobscureandconfused，becauseitismadeupoftwoparts，verydifferent，ifnotinconsistent。For，letamanframeinhismindanideaofanyspaceornumber，asgreatashewill；itisplainthemindrestsandterminatesinthatidea，whichiscontrarytotheideaofinfinity，whichconsistsinasupposedendlessprogression。AndthereforeIthinkitisthatwearesoeasilyconfounded，whenwecometoargueandreasonaboutinfinitespaceorduration，&c。Becausethepartsofsuchanideanotbeingperceivedtobe，astheyare，inconsistent，theonesideorotheralwaysperplexes，whateverconsequenceswedrawfromtheother；asanideaofmotionnotpassingonwouldperplexanyonewhoshouldarguefromsuchanidea，whichisnotbetterthananideaofmotionatrest。Andsuchanotherseemstometobetheideaofaspace，or(whichisthesamething)
anumberinfinite，i。e。ofaspaceornumberwhichthemindactuallyhas，andsoviewsandterminatesin；andofaspaceornumber，which，inaconstantandendlessenlargingandprogression，itcaninthoughtneverattainto。For，howlargesoeveranideaofspaceI
haveinmymind，itisnolargerthanitisthatinstantthatIhaveit，thoughIbecapablethenextinstanttodoubleit，andsoonininfinitum；forthataloneisinfinitewhichhasnobounds；andthattheideaofinfinity，inwhichourthoughtscanfindnone。
9。Numberaffordsustheclearestideaofinfinity。Butofallotherideas，itisnumber，asIhavesaid，whichIthinkfurnishesuswiththeclearestandmostdistinctideaofinfinitywearecapableof。
For，eveninspaceandduration，whenthemindpursuestheideaofinfinity，ittheremakesuseoftheideasandrepetitionsofnumbers，asofmillionsandmillionsofmiles，oryears，whicharesomanydistinctideas，-keptbestbynumberfromrunningintoaconfusedheap，whereinthemindlosesitself；andwhenithasaddedtogetherasmanymillions，&c。，asitpleases，ofknownlengthsofspaceorduration，theclearestideaitcangetofinfinity，istheconfusedincomprehensibleremainderofendlessaddiblenumbers，whichaffordsnoprospectofstoporboundary。
10。Ourdifferentconceptionsoftheinfinityofnumbercontrastedwiththoseofdurationandexpansion。Itwill，perhaps，giveusalittlefurtherlightintotheideawehaveofinfinity，anddiscovertous，thatitisnothingbuttheinfinityofnumberappliedtodeterminateparts，ofwhichwehaveinourmindsthedistinctideas，ifweconsiderthatnumberisnotgenerallythoughtbyusinfinite，whereasdurationandextensionareapttobeso；whicharisesfromhence，-thatinnumberweareatoneend，asitwere:fortherebeinginnumbernothinglessthananunit，wetherestop，andareatanend；butinaddition，orincreaseofnumber，wecansetnobounds:andsoitislikealine，whereofoneendterminatingwithus，theotherisextendedstillforwards，beyondallthatwecanconceive。
Butinspaceanddurationitisotherwise。Forindurationweconsideritasifthislineofnumberwereextendedbothways-toanunconceivable，undeterminate，andinfinitelength；whichisevidenttoanyonethatwillbutreflectonwhatconsiderationhehathofEternity；which，Isuppose，willfindtobenothingelsebuttheturningthisinfinityofnumberbothways，aparteante，andapartepost，astheyspeak。For，whenwewouldconsidereternity，aparteante，whatdowebut，beginningfromourselvesandthepresenttimewearein，repeatinourmindstheideasofyears，orages，oranyotherassignableportionofdurationpast，withaprospectofproceedinginsuchadditionwithalltheinfinityofnumber:andwhenwewouldconsidereternity，apartepost，wejustafterthesameratebeginfromourselves，andreckonbymultipliedperiodsyettocome，stillextendingthatlineofnumberasbefore。Andthesetwobeingputtogether，arethatinfinitedurationwecallEternity:
which，asweturnourvieweitherway，forwardsorbackwards，appearsinfinite，becausewestillturnthatwaytheinfiniteendofnumber，i。e。thepowerstillofaddingmore。
11。Howweconceivetheinfinityofspace。Thesamehappensalsoinspace，wherein，conceivingourselvestobe，asitwere，inthecentre，wedoonallsidespursuethoseindeterminablelinesofnumber；andreckoninganywayfromourselves，ayard，mile，diameteroftheearth，ororbismagnus，-bytheinfinityofnumber，weaddotherstothem，asoftenaswewill。Andhavingnomorereasontosetboundstothoserepeatedideasthanwehavetosetboundstonumber，wehavethatindeterminableideaofimmensity。
12。Infinitedivisibility。Andsinceinanybulkofmatterourthoughtscanneverarriveattheutmostdivisibility，thereforethereisanapparentinfinitytousalsointhat，whichhastheinfinityalsoofnumber；butwiththisdifference，-that，intheformerconsiderationsoftheinfinityofspaceandduration，weonlyuseadditionofnumbers；whereasthisislikethedivisionofanunitintoitsfractions，whereinthemindalsocanproceedininfinitum，aswellasintheformeradditions；itbeingindeedbuttheadditionstillofnewnumbers:thoughintheadditionoftheone，wecanhavenomorethepositiveideaofaspaceinfinitelygreat，than，inthedivisionoftheother，wecanhavethe[positive]ideaofabodyinfinitelylittle；-ourideaofinfinitybeing，asImaysay，agrowingorfugitiveidea，stillinaboundlessprogression，thatcanstopnowhere。
13。Nopositiveideaofinfinity。Thoughitbehard，Ithink，tofindanyonesoabsurdastosayhehasthepositiveideaofanactualinfinitenumber；-theinfinitywhereofliesonlyinapowerstillofaddinganycombinationofunitstoanyformernumber，andthataslongandasmuchasonewill；thelikealsobeingintheinfinityofspaceandduration，whichpowerleavesalwaystothemindroomforendlessadditions；-yettherebethosewhoimaginetheyhavepositiveideasofinfinitedurationandspace。Itwould，I
think，beenoughtodestroyanysuchpositiveideaofinfinite，toaskhimthathasit，-whetherhecouldaddtoitorno；whichwouldeasilyshowthemistakeofsuchapositiveidea。Wecan，Ithink，havenopositiveideaofanyspaceordurationwhichisnotmadeupof，andcommensurateto，repeatednumbersoffeetoryards，ordaysandyears；
whicharethecommonmeasures，whereofwehavetheideasinourminds，andwherebywejudgeofthegreatnessofthissortofquantities。
Andtherefore，sinceaninfiniteideaofspaceordurationmustneedsbemadeupofinfiniteparts，itcanhavenootherinfinitythanthatofnumbercapablestilloffurtheraddition；butnotanactualpositiveideaofanumberinfinite。For，Ithinkitisevident，thattheadditionoffinitethingstogether(asarealllengthswhereofwehavethepositiveideas)canneverotherwiseproducetheideaofinfinitethanasnumberdoes；which，consistingofadditionsoffiniteunitsonetoanother，suggeststheideaofinfinite，onlybyapowerwefindwehaveofstillincreasingthesum，andaddingmoreofthesamekind；withoutcomingonejotnearertheendofsuchprogression。
14。Howwecannothaveapositiveideaofinfinityinquantity。Theywhowouldprovetheirideaofinfinitetobepositive，seemtometodoitbyapleasantargument，takenfromthenegationofanend；whichbeingnegative，thenegationofitispositive。Hethatconsidersthattheendis，inbody，buttheextremityorsuperficiesofthatbody，willnotperhapsbeforwardtograntthattheendisabarenegative:andhethatperceivestheendofhispenisblackorwhite，willbeapttothinkthattheendissomethingmorethanapurenegation。Norisit，whenappliedtoduration，thebarenegationofexistence，butmoreproperlythelastmomentofit。Butiftheywillhavetheendtobenothingbutthebarenegationofexistence，Iamsuretheycannotdenybutthebeginningisthefirstinstantofbeing，andisnotbyanybodyconceivedtobeabarenegation；andtherefore，bytheirownargument，theideaofeternal，aparteante，orofadurationwithoutabeginning，isbutanegativeidea。
15。Whatispositive，whatnegative，inourideaofinfinite。Theideaofinfinitehas，Iconfess，somethingofpositiveinallthosethingsweapplytoit。Whenwewouldthinkofinfinitespaceorduration，weatfirststepusuallymakesomeverylargeidea，asperhapsofmillionsofages，ormiles，whichpossiblywedoubleandmultiplyseveraltimes。Allthatwethusamasstogetherinourthoughtsispositive，andtheassemblageofagreatnumberofpositiveideasofspaceorduration。Butwhatstillremainsbeyondthiswehavenomoreapositivedistinctnotionofthanamarinerhasofthedepthofthesea；where，havingletdownalargeportionofhissounding-line，hereachesnobottom。Wherebyheknowsthedepthtobesomanyfathoms，andmore；buthowmuchthemoreis，hehathnodistinctnotionatall:andcouldhealwayssupplynewline，andfindtheplummetalwayssink，withouteverstopping，hewouldbesomethinginthepostureofthemindreachingafteracompleteandpositiveideaofinfinity。Inwhichcase，letthislinebeten，ortenthousandfathomslong，itequallydiscoverswhatisbeyondit，andgivesonlythisconfusedandcomparativeidea，thatthisisnotall，butonemayyetgofarther。Somuchasthemindcomprehendsofanyspace，ithasapositiveideaof:butinendeavouringtomakeitinfinite，-itbeingalwaysenlarging，alwaysadvancing，-theideaisstillimperfectandincomplete。Somuchspaceasthemindtakesaviewofinitscontemplationofgreatness，isaclearpicture，andpositiveintheunderstanding:butinfiniteisstillgreater。1。Thentheideaofsomuchispositiveandclear。2。Theideaofgreaterisalsoclear；butitisbutacomparativeidea，theideaofsomuchgreaterascannotbecomprehended。3。Andthisisplainlynegative:
notpositive。Forhehasnopositiveclearideaofthelargenessofanyextension，(whichisthatsoughtforintheideaofinfinite)，thathasnotacomprehensiveideaofthedimensionsofit:andsuch，nobody，Ithink，pretendstoinwhatisinfinite。Fortosayamanhasapositiveclearideaofanyquantity，withoutknowinghowgreatitis，isasreasonableastosay，hehasthepositiveclearideaofthenumberofthesandsonthesea-shore，whoknowsnothowmanytherebe，butonlythattheyaremorethantwenty。Forjustsuchaperfectandpositiveideahasheofaninfinitespaceorduration，whosaysitislargerthantheextentordurationoften，onehundred，onethousand，oranyothernumberofmiles，oryears，whereofhehasorcanhaveapositiveidea；whichisalltheidea，Ithink，wehaveofinfinite。Sothatwhatliesbeyondourpositiveideatowardsinfinity，liesinobscurity，andhastheindeterminateconfusionofanegativeidea，whereinIknowIneitherdonorcancomprehendallIwould，itbeingtoolargeforafiniteandnarrowcapacity。Andthatcannotbutbeveryfarfromapositivecompleteidea，whereinthegreatestpartofwhatIwouldcomprehendisleftout，undertheundeterminateintimationofbeingstillgreater。Fortosay，that，havinginanyquantitymeasuredsomuch，orgonesofar，youarenotyetattheend，isonlytosaythatthatquantityisgreater。Sothatthenegationofanendinanyquantityis，inotherwords，onlytosaythatitisbigger；andatotalnegationofanendisbutcarryingthisbiggerstillwithyou，inalltheprogressionsofyourthoughtsshallmakeinquantity；andaddingthisideaofstillgreatertoalltheideasyouhave，orcanbesupposedtohave，ofquantity。Now，whethersuchanideaasthatbepositive，Ileaveanyonetoconsider。
16。Wehavenopositiveideaofaninfiniteduration。Iaskthosewhosaytheyhaveapositiveideaofeternity，whethertheirideaofdurationincludesinitsuccession，ornot？Ifitdoesnot，theyoughttoshowthedifferenceoftheirnotionofduration，whenappliedtoaneternalBeing，andtoafinite；since，perhaps，theremaybeothersaswellasI，whowillowntothemtheirweaknessofunderstandinginthispoint，andacknowledgethatthenotiontheyhaveofdurationforcesthemtoconceive，thatwhateverhasduration，isofalongercontinuanceto-daythanitwasyesterday。If，toavoidsuccessioninexternalexistence，theyreturntothepunctumstansoftheschools，I
supposetheywilltherebyverylittlemendthematter，orhelpustoamoreclearandpositiveideaofinfiniteduration；therebeingnothingmoreinconceivabletomethandurationwithoutsuccession。Besides，thatpunctumstans，ifitsignifyanything，beingnotquantum，finiteorinfinitecannotbelongtoit。But，ifourweakapprehensionscannotseparatesuccessionfromanydurationwhatsoever，ourideaofeternitycanbenothingbutofinfinitesuccessionofmomentsofdurationwhereinanythingdoesexist；andwhetheranyonehas，orcanhave，apositiveideaofanactualinfinitenumber，Ileavehimtoconsider，tillhisinfinitenumberbesogreatthathehimselfcanaddnomoretoit；andaslongashecanincreaseit，Idoubthehimselfwillthinktheideahehathofitalittletooscantyforpositiveinfinity。
17。Nocompleteideaofeternalbeing。Ithinkitunavoidableforeveryconsidering，rationalcreature，thatwillbutexaminehisownoranyotherexistence，tohavethenotionofaneternal，wiseBeing，whohadnobeginning:andsuchanideaofinfinitedurationIamsureI
have。Butthisnegationofabeginning，beingbutthenegationofapositivething，scarcegivesmeapositiveideaofinfinity；which，wheneverIendeavourtoextendmythoughtsto，Iconfessmyselfataloss，andIfindIcannotattainanyclearcomprehensionofit。
18。Nopositiveideaofinfinitespace。Hethatthinkshehasapositiveideaofinfinitespace，will，whenheconsidersit，findthathecannomorehaveapositiveideaofthegreatest，thanhehasoftheleastspace。Forinthislatter，whichseemstheeasierofthetwo，andmorewithinourcomprehension，wearecapableonlyofacomparativeideaofsmallness，whichwillalwaysbelessthananyonewhereofwehavethepositiveidea。Allourpositiveideasofanyquantity，whethergreatorlittle，havealwaysbounds，thoughourcomparativeidea，wherebywecanalwaysaddtotheone，andtakefromtheother，hathnobounds。Forthatwhichremains，eithergreatorlittle，notbeingcomprehendedinthatpositiveideawhichwehave，liesinobscurity；andwehavenootherideaofit，butofthepowerofenlargingtheoneanddiminishingtheother，withoutceasing。A
pestleandmortarwillassoonbringanyparticleofmattertoindivisibility，astheacutestthoughtofamathematician；andasurveyormayassoonwithhischainmeasureoutinfinitespace，asaphilosopherbythequickestflightofmindreachit，orbythinkingcomprehendit；whichistohaveapositiveideaofit。Hethatthinksonacubeofaninchdiameter，hasaclearandpositiveideaofitinhismind，andsocanframeoneof1/2，1/4，1/8，andsoon，tillhehastheideainhisthoughtsofsomethingverylittle；butyetreachesnottheideaofthatincomprehensiblelittlenesswhichdivisioncanproduce。Whatremainsofsmallnessisasfarfromhisthoughtsaswhenhefirstbegan；andthereforehenevercomesatalltohaveaclearandpositiveideaofthatsmallnesswhichisconsequenttoinfinitedivisibility。
19。Whatispositive，whatnegative，inourideaofinfinite。
Everyonethatlookstowardsinfinitydoes，asIhavesaid，atfirstglancemakesomeverylargeideaofthatwhichheappliesitto，letitbespaceorduration；andpossiblyhewearieshisthoughts，bymultiplyinginhismindthatfirstlargeidea:butyetbythathecomesnonearertothehavingapositiveclearideaofwhatremainstomakeupapositiveinfinite，thanthecountryfellowhadofthewaterwhichwasyettocome，andpassthechanneloftheriverwherehestood:
Rusticusexpectatdumdefluatamnis，atilleLabitur，etlabeturinomnevolubilisoevum。
20。Somethinktheyhaveapositiveideaofeternity，andnotofinfinitespace。TherearesomeIhavemetthatputsomuchdifferencebetweeninfinitedurationandinfinitespace，thattheypersuadethemselvesthattheyhaveapositiveideaofeternity，butthattheyhavenot，norcanhaveanyideaofinfinitespace。ThereasonofwhichmistakeIsupposetobethis-thatfinding，byaduecontemplationofcausesandeffects，thatitisnecessarytoadmitsomeEternalBeing，andsotoconsidertherealexistenceofthatBeingastakenupandcommensuratetotheirideaofeternity；but，ontheotherside，notfindingitnecessary，but，onthecontrary，apparentlyabsurd，thatbodyshouldbeinfinite，theyforwardlyconcludethattheycanhavenoideaofinfinitespace，becausetheycanhavenoideaofinfinitematter。Whichconsequence，Iconceive，isveryillcollected，becausetheexistenceofmatterisnowaysnecessarytotheexistenceofspace，nomorethantheexistenceofmotion，orthesun，isnecessarytoduration，thoughdurationusedtobemeasuredbyit。AndIdoubtnotbutthatamanmayhavetheideaoftenthousandmilessquare，withoutanybodysobig，aswellastheideaoftenthousandyears，withoutanybodysoold。Itseemsaseasytometohavetheideaofspaceemptyofbody，astothinkofthecapacityofabushelwithoutcorn，orthehollowofanut-shellwithoutakernelinit:itbeingnomorenecessarythatthereshouldbeexistingasolidbody，infinitelyextended，becausewehaveanideaoftheinfinityofspace，thanitisnecessarythattheworldshouldbeeternal，becausewehaveanideaofinfiniteduration。Andwhyshouldwethinkourideaofinfinitespacerequirestherealexistenceofmattertosupportit，whenwefindthatwehaveasclearanideaofaninfinitedurationtocome，aswehaveofinfinitedurationpast？
ThoughIsupposenobodythinksitconceivablethatanythingdoesorhasexistedinthatfutureduration。Norisitpossibletojoinourideaoffuturedurationwithpresentorpastexistence，anymorethanitispossibletomaketheideasofyesterday，to-day，andto-morrowtobethesame；orbringagespastandfuturetogether，andmakethemcontemporary。Butifthesemenareofthemind，thattheyhaveclearerideasofinfinitedurationthanofinfinitespace，becauseitispastdoubtthatGodhasexistedfromalleternity，butthereisnorealmatterco-extendedwithinfinitespace；yetthosephilosopherswhoareofopinionthatinfinitespaceispossessedbyGod’sinfiniteomnipresence，aswellasinfinitedurationbyhiseternalexistence，mustbeallowedtohaveasclearanideaofinfinitespaceasofinfiniteduration；thoughneitherofthem，I
think，hasanypositiveideaofinfinityineithercase。Forwhatsoeverpositiveideasamanhasinhismindofanyquantity，hecanrepeatit，andaddittotheformer，aseasyashecanaddtogethertheideasoftwodays，ortwopaces，whicharepositiveideasoflengthshehasinhismind，andsoonaslongashepleases:
whereby，ifamanhadapositiveideaofinfinite，eitherdurationorspace，hecouldaddtwoinfinitiestogether；nay，makeoneinfiniteinfinitelybiggerthananother-absurditiestoogrosstobeconfuted。
21。Supposedpositiveideasofinfinity，causeofmistakes。Butyetifafterallthis，therebemenwhopersuadethemselvesthattheyhaveclearpositivecomprehensiveideasofinfinity，itisfittheyenjoytheirprivilege:andIshouldbeveryglad(withsomeothersthatIknow，whoacknowledgetheyhavenonesuch)tobebetterinformedbytheircommunication。ForIhavebeenhithertoapttothinkthatthegreatandinextricabledifficultieswhichperpetuallyinvolvealldiscoursesconcerninginfinity，-whetherofspace，duration，ordivisibility，havebeenthecertainmarksofadefectinourideasofinfinity，andthedisproportionthenaturethereofhastothecomprehensionofournarrowcapacities。For，whilstmentalkanddisputeofinfinitespaceorduration，asiftheyhadascompleteandpositiveideasofthemastheyhaveofthenamestheyuseforthem，orastheyhaveofayard，oranhour，oranyotherdeterminatequantity；itisnowonderiftheincomprehensiblenatureofthethingtheydiscourseof，orreasonabout，leadsthemintoperplexitiesandcontradictions，andtheirmindsbeoverlaidbyanobjecttoolargeandmightytobesurveyedandmanagedbythem。
22。Allthesearemodesofideasgotfromsensationandreflection。IfIhavedweltprettylongontheconsiderationofduration，space，andnumber，andwhatarisesfromthecontemplationofthem，-Infinity，itispossiblynomorethanthematterrequires；
therebeingfewsimpleideaswhosemodesgivemoreexercisetothethoughtsofmenthanthosedo。Ipretendnottotreatofthemintheirfulllatitude。Itsufficestomydesigntoshowhowthemindreceivesthem，suchastheyare，fromsensationandreflection；andhoweventheideawehaveofinfinity，howremotesoeveritmayseemtobefromanyobjectofsense，oroperationofourmind，has，nevertheless，asallourotherideas，itsoriginalthere。Somemathematiciansperhaps，ofadvancedspeculations，mayhaveotherwaystointroduceintotheirmindsideasofinfinity。Butthishindersnotbutthattheythemselves，aswellasallothermen，gotthefirstideaswhichtheyhadofinfinityfromsensationandreflection，inthemethodwehaveheresetdown。
