thoughts on man-第50章

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ear；　have　no　conclusive　evidence　to　convince　us；　that　we　may　not；　each　of　us；　for　aught　we　know；　be　the　only　thing　that　exists；　an　entire　universe　to　ourselves。

We　will　not　however　follow　these　ingenious　persons　to　the　startling　extreme　to　which　their　speculations　would　lead　us。　　But；　without　doing　so；　it　will　not　misbecome　us　to　be　cautious；　and　to　reflect　what　we　do；　before　we　take　a　leap　into　illimitable　space。


SECTION　II。

〃The　sun；〃　we　are　told；　〃is　a　solid　body；　ninety…five　millions　of　miles　distant　from　the　earth　we　inhabit；　one　million　times　larger　in　cubic　measurement；　and　to　such　a　degree　impregnated　with　heat；　that　a　comet；　approaching　to　it　within　a　certain　distance；　was　by　that　approximation　raised　to　a　heat　two　thousand　times　greater　than　that　of　red…hot　iron。〃

It　will　be　acknowledged；　that　there　is　in　this　statement　much　to　believe；　and　we　shall　not　be　exposed　to　reasonable　blame；　if　we　refuse　to　subscribe　to　it；　till　we　have　received　irresistible　evidence　of　its　truth。

It　has　already　been　observed；　that；　for　the　greater　part　of　what　we　imagine　we　know　on　the　surface　or　in　the　bowels　of　the　earth；　we　have；　or　may　have　if　we　please；　the　evidence　of　more　than　one　of　our　senses；　combining　to　lead　to　the　same　conclusion。　　For　the　propositions　of　astronomy　we　have　no　sensible　evidence；　but　that　of　sight；　and　an　imperfect　analogy；　leading　from　those　visible　impressions　which　we　can　verify；　to　a　reliance　upon　those　which　we　cannot。

The　first　cardinal　particular　we　meet　with　in　the　above　statement　concerning　the　sun；　is　the　term；　distance。　　Now；　all　that；　strictly　speaking；　we　can　affirm　respecting　the　sun　and　other　heavenly　bodies；　is　that　we　have　the　same　series　of　impressions　respecting　them；　that　we　have　respecting　terrestrial　objects　near　or　remote；　and　that　there　is　an　imperfect　analogy　between　the　one　case　and　the　other。

Before　we　affirm　any　thing；　as　of　our　own　knowledge　and　competence；　respecting　heavenly　bodies　which　are　said　to　be　millions　of　millions　of　miles　removed　from　us；　it　would　not　perhaps　be　amiss　that　we　should　possess　ourselves　of　a　certain　degree　of　incontestible　information；　as　to　the　things　which　exist　on　the　earth　we　inhabit。　　Among　these；　one　of　the　subjects　attended　with　a　great　degree　of　doubt　and　obscurity；　is　the　height　of　the　mountains　with　which　the　surface　of　the　globe　we　inhabit　is　diversified。　　It　is　affirmed　in　the　received　books　of　elementary　geography；　that　the　Andes　are　the　highest　mountains　in　the　world。　　Morse；　in　his　American　Gazetteer；　third　edition；　printed　at　Boston　in　1810＇46＇；　says；　〃The　height　of　Chimborazzo；　the　most　elevated　point　of　the　vast　chain　of　the　Andes；　is　20；280　feet　above　the　level　of　the　sea；　which　is　7102　feet　higher　than　any　other　mountain　in　the　known　world：〃　thus　making　the　elevation　of　the　mountains　of　Thibet；　or　whatever　other　rising　ground　the　compiler　had　in　his　thought；　precisely　13；178　feet　above　the　level　of　the　sea；　and　no　more。　　This　decision　however　has　lately　been　contradicted。　　Mr。　Hugh　Murray；　in　an　Account　of　Discoveries　and　Travels　in　Asia；　published　in　1820；　has　collated　the　reports　of　various　recent　travellers　in　central　Asia；　and　he　states　the　height　of　Chumularee；　which　he　speaks　of　as　the　most　elevated　point　of　the　mountains　of　Thibet；　as　nearly　30；000　feet　above　the　level　of　the　sea。

＇46＇　Article；　Andes。


The　elevation　of　mountains；　till　lately；　was　in　no　way　attempted　to　be　ascertained　but　by　the　use　of　the　quadrant）　and　their　height　was　so　generally　exaggerated；　that　Riccioli；　one　of　the　most　eminent　astronomers　of　the　seventeenth　century；　gives　it　as　his　opinion　that　mountains；　like　the　Caucasus；　may　have　a　perpendicular　elevation　of　fifty　Italian　miles＇47＇。　　Later　observers　have　undertaken　to　correct　the　inaccuracy　of　these　results　through　the　application　of　the　barometer；　and　thus；　by　informing　themselves　of　the　weight　of　the　air　at　a　certain　elevation；　proceeding　to　infer　the　height　of　the　situation。

＇47＇　Rees；　Encyclopedia；　article；　Mountains。


There　are　many　circumstances；　which　are　calculated　to　induce　a　circumspect　enquirer　to　regard　the　affirmative　positions　of　astronomy；　as　they　are　delivered　by　the　most　approved　modern　writers；　with　considerable　diffidence。

They　are　founded；　as　has　already　been　said；　next　to　the　evidence　of　our　senses；　upon　the　deductions　of　mathematical　knowledge。

Mathematics　are　either　pure　or　mixed。

Pure　mathematics　are　concerned　only　with　abstract　propositions；　and　have　nothing　to　do　with　the　realities　of　nature。　　There　is　no　such　thing　in　actual　existence　as　a　mathematical　point；　line　or　surface。　　There　is　no　such　thing　as　a　circle　or　square。　　But　that　is　of　no　consequence。　　We　can　define　them　in　words；　and　reason　about　them。　　We　can　draw　a　diagram；　and　suppose　that　line　to　be　straight　which　is　not　really　straight；　and　that　figure　to　be　a　circle　which　is　not　strictly　a　circle。　　It　is　conceived　therefore　by　the　generality　of　observers；　that　mathematics　is　the　science　of　certainty。

But　this　is　not　strictly　the　case。　　Mathematics　are　like　those　abstract　and　imaginary　existences　about　which　they　are　conversant。　　They　may　constitute　in　themselves；　and　in　the　apprehension　of　an　infallible　being；　a　science　of　certainty。　　But　they　come　to　us　mixed　and　incorporated　with　our　imperfections。　　Our　faculties　are　limited；　and　we　may　be　easily　deceived；　as　to　what　it　is　that　we　see　with　transparent　and　unerring　clearness；　and　what　it　is　that　comes　to　us　through　a　crooked　medium；　refracting　and　distorting　the　rays　of　primitive　truth。　　We　often　seem　clear；　when　in　reality　the　twilight　of　undistinguishing　night　has　crept　fast　and　far　upon　us。　　In　a　train　of　deductions；　as　in　the　steps　of　an　arithmetical　process；　an　error　may　have　insinuated　itself　imperceptibly　at　a　very　early　stage；　rendering　all　the　subsequent　steps　a　wandering　farther　and　farther　from　the　unadulterated　truth。　　Human　mathematics；　so　to　speak；　like　the　length　of　life；　are　subject　to　the　doctrine　of　chances。　　Mathematics　may　be　the　science　of　certainty　to　celestial　natures；　but　not　to　man。

But；　if　in　the　case　of　pure　mathematics；　we　are　exposed　to　the　chances　of　error　and　delusion；　it　is　much　worse　with　mixed　mathematics。　　The　moment　we　step　out　of　the　high　region　of　abstraction；　and　apply　ourselves　to　what　we　call　external　nature；　we　have　forfeited　that　sacred　character　and　immunity；　which　we　seemed　entitled　to　boast；　so　long　as　we　remained　inclosed　in　the　sanctuary　of　unmingled　truth。　　As　has　already　been　said；　we　know　what　passes　in　the　theatre　of　the　mind；　but　we　cannot　be　said　absolutely　to　know　any　thing　more。　　In　our　speculations　upon　actual　existences　we　are　not　only　subject　to　the　disadvantages　which　arise　from　the　limited　nature　of　our　faculties；　and　the　errors　which　may　insensibly　creep　upon　us　in　the　process。　　We　are　further　exposed　to　the　operation　of　the　unevennesses　and　irregularities　that　perpetually　occur　in　external　nature；　the　imperfection　of　our　senses；　and　of　the　instruments　we　construct　to　assist　our　observations；　and　the　discrepancy　which　we　frequently　detect　between　the　actual　nature　of　the　things　about　us　and　our　impressions　respecting　them。

This　is　obvious；　whenever　we　undertake　to　apply　the　processes　of　arithmetic　to　the　realities　of　life。　　Arithmetic；　unsubjected　to　the　impulses　of　passion　and　the　accidents　of　created　nature；　holds　on　its　course；　but；　in　the　phenomena　of　the　actual　world；　〃time　and　chance　happeneth　to　them　all。〃

Thus　it　is；　for　example；　in　the　arithmetical　and　geometrical　ratios；　set　up　in　political　economy　by　the　celebrated　Mr。　　Malthus。　　His　numbers　will　go　on　smoothly　enough；　1；　2；　4；　8；　16；　32；　as　representing　the　principle　of　population　among　mankind；　and　1；　2；　3；　4；　5；　6；　the　means　of　subsistence；　but　restiff　and　uncomplying　nature　refuses　to　conform　herself　to　his　dicta。

Dr。　　Price　has　calculated　the　produce　of　one　penny；　put　out　at　the　commencement　of　the　Christian　era　to　five　per　cent。　　compound　interest；　and　finds　that　in　the　year　1791　it　would　have　increased　to　a　greater　sum　than　would　be　contained　in　three　hundred　millions　of　earths；　all　solid　gold。　　But　what　has　this　to　do　with　the　world　in　which　we　live？　　Did　ever　any　one　put　out　his　penny　to　interest　in　this　fashion　for　eighteen　hundred　years？　　And；　if　he　did；　where　was　the　gold　to　be　found；　to　satisfy　his　demand？

Morse；　in　his　American　Gazetteer；　proceeding　on　the　principles　of　Malthus；　tells　us　that；　if　the　city　of　New　York　goes　on　increasing　for　a　century　in　a　certain　ratio；　it　will　by　that　time　contain　5；257；493　inhabitants。　　But　does　any　one；　for　himself　or　his　posterity；　expect　to　see　this　realised？

Blackstone；　in　his　Commentaries　on　the　Laws　of　England；　has　observed　that；　as　every　man　has　two　ancestors　in　the　first　ascending　degree；　and　four　in　the　second；　so　in　the　twentieth　degree　he　has　more　than　a　million；　and　in　the　fortieth　the　square　of　that　number；　or　upwards　of　a　million　millions。　　This　statement　therefore　would　have　a　greater　tendency　to　prove　that　mankind　in　remote　ages　were　numerous；　almost　beyond　the　power　of　figures　to　represent；　than　the　opposite　doctrine　of　Malthus；　that　they　have　a　perpetual　tendency　to　such　increase　as　would　infallibly　bring　down　the　most　tremendous　calamities　on　our　posterity。

Berkeley；　whom　I　have　already　referred　to　on　another　subject；　and　who　is　admitted　to　be　one　of　our　profoundest　philosophers；　has　written　a　treatise＇48＇　to　prove；　that　the　mathematicians；　who　object　to　the　mysteries　supposed　to　exist　in　revealed　religion；　〃admit　much　greater　mysteries；　and　even　falshoods　in　science；　of　which　he　alleges　the　doctrine　of　fluxions　as　an　eminent　example＇49＇。〃　　He　observes；　that　their　conclusions　are　established　by　virtue　of　a　twofold　error；　and　that　these　errors；　being　in　contrary　directions；　are　supposed　to　compensate　each　other；　the　expounders　of　the　doctrine　thus　arriving　at　what　they　call　truth；　without　being　able　to　shew　how；　or　by　what　means　they　have　arrived　at　it。

＇48＇　The　Analyst。　

＇49＇　Life　of　Berkeley；　prefixed　to　his　Works。


It　is　a　memorable　and　a　curious　speculation　to　reflect；　upon　how　slight　grounds　the　doctrine　of　〃thousands　and　thousands　of　suns；　multiplied　without　end；　and　ranged　all　around　us；　at　immense　distances　from　each　other；　and　attended　by　ten　thousand　times　ten　thousand　worlds；〃　mentioned　in　the　beginning　of　this　Essay；　is　built。　　It　may　be　all　true。　　But；　true　or　false；　it　cannot　be　without　its　use　to　us；　carefully　to　survey　the　road　upon　which　we　are　advancing；　the　pier　which　human　enterprise　has　dared　to　throw　out　into　the　vast　ocean　of　Cimmerian　darkness。　　We　have　constructed　a　pyramid；　which　throws　into　unspeakable　contempt　the　vestiges　of　ancient　Egyptian　industry：　　but　it　stands　upon　its　apex；　it　trembles　with　every　breeze；　and　momentarily　threatens　to　overwhelm　in　its　ruins　the　fearless　undertakers　that　have　set　it　up。

It　gives　us　a　mighty　and　sublime　idea　of　the　nature　of　man；　to　think　with　what　composure　and　confidence　a　succession　of　persons　of　the　greatest　genius　have　launched　themselves　in　illimitable　space；　with　what　invincible　industry　they　have　proceeded；　wasting　the　midnight　oil；　racking　their　faculties；　and　almost　wearing　their　organs　to　dust；　in　measuring　the　distance　of　Sirius　and　the　other　f