A Defence of FreeThinking in Mathematics.docx
《A Defence of FreeThinking in Mathematics.docx》由会员分享,可在线阅读,更多相关《A Defence of FreeThinking in Mathematics.docx(22页珍藏版)》请在冰点文库上搜索。
ADefenceofFreeThinkinginMathematics
ADefenceofFree-ThinkinginMathematicsADefenceofFree-ThinkinginMathematicsInanswertoaPamphletofPhilalethesCantabrigiensis,intituled,GeometrynoFriendtoInfidelity,oraDefenceofSirISAACNEWTON,andtheBRITISHMathematicians.AlsoanAppendixconcerningMr.WALTON'SVindicationofthePrincipleofFluxionsagainsttheObjectionscontainedintheANALYST.
WHEREIN
ItisattemptedtoputthisControversyinsuchaLightasthateveryReadermaybeabletojudgethereof.ByGeorgeBerkeley1.WhenIreadyour`DefenceoftheBritishMathematicians,'
Icouldnot,Sir,butadmireyourcourageinassertingwithsuchundoubtingassurancethingssoeasilydisproved.Thistomeseemedunaccountable,tillIreflectedonwhatyousay(p.32),when,uponmyhavingappealedtoeverythinkingreader,whetheritbepossibletoframeanyclearconceptionofFluxions,youexpressyourselfinthefollowingmanner,``Pray,Sir,whoarethosethinkingreadersyouappealto?
Aretheygeometricians,orpersonswhollyignorantofgeometry?
Iftheformer,Ileaveittothem:
ifthelatter,Iask,Howwellaretheyqualifiedtojudgeofthemethodoffluxions?
''Itmustbeacknowledgedyouseembythisdilemmasecureinthefavourofonepartofyourreaders,andtheignoranceoftheother.
Iamneverthelesspersuadedtherearefairandcandidmenamongthemathematicians.
Andforthosewhoarenotmathematicians,Ishallendeavoursotounveilthismystery,andputthecontroversybetweenusinsuchalightasthateveryreaderofordinarysenseandreflectionmaybeacompetentjudgethereof.
2.Youexpressanextremesurpriseandconcern,``thatIshouldtakesomuchpainstodepreciateoneofthenoblestsciences,todisparageandtraduceasetoflearnedmen,whoselabourssogreatlyconducetothehonourofthisisland(p.5);tolessenthereputationandauthorityofSirIsaacNewtonandhisfollowers,byshewingthattheyarenotsuchmastersofreasonastheyaregenerallypresumedtobe;andtodepreciatethesciencetheyprofess,bydemonstratingtotheworldthatitisnotofthatclearnessandcertaintyasiscommonlyimagined.''Allwhich,youinsist,``appearsverystrangetoyouandtherestofthatfamousUniversity,whoplainlyseeofhowgreatusemathematicallearningistomankind.''Henceyoutakeoccasiontodeclaimontheusefulnessofmathematicsintheseveralbranches,andthentoredoubleyoursurpriseandamazement(p.19and20).ToallwhichdeclamationIreply,thatitisquitebesidethepurpose.For,Iallow,andalwayshaveallowed,itsfullclaimofmerittowhateverisusefulandtrueinthemathematics:
butthatwhichisnotso,thelessitemploysmen'stimeandthoughtsthebetter.And,afterallyouhavesaidorcansay,Ibelievetheunprejudicedreaderwillthinkwithme,thatthingsobscurearenotthereforesacred;andthatitisnomoreacrimetocanvassanddetectunsoundprinciplesorfalsereasoningsinmathematicsthaninanyotherpartoflearning.
3.Youare,itseems,muchatalosstounderstandtheusefulness,ortendency,orprudenceofmyattempt.IthoughtIhadsufficientlyexplainedthisinthe`Analyst.'Butforyourfurthersatisfactionshallheretellyou,itisverywellknownthatseveralpersonswhoderideFaithandMysteriesinReligion,admitthedoctrineofFluxionsfortrueandcertain.Now,ifitbeshewnthatfluxionsarereallymostincomprehensiblemysteries,andthatthosewhobelievethemtobeclearandscientificdoentertainanimplicitfaithintheauthorofthatmethod:
willnotthisfurnishafairargumentumadhominemagainstmenwhorejectthatverythinginreligionwhichtheyadmitinhumanlearning?
Andisitnotaproperwaytoabatethepride,anddiscreditthepretensionsofthosewhoinsistuponclearideasinpointsoffaith,ifitbeshewnthattheydowithoutthemeveninscience.
4.Astomytimingthischarge;whynowandnotbefore,sinceIhadpublishedhintsthereofmanyyearsago?
SurelyIamobligedtogivenoaccountofthis:
ifwhathathbeensaidinthe`Analyst'
benotsufficient.SupposethatIhadnotleisure,orthatIdidnotthinkitexpedient,orthatIhadnomindtoit.Whenamanthinksfittopublishanything,eitherinmathematicsorinotherpartoflearning,whatavailsit,orindeedwhatrighthathanyonetoask,Whyatthisorthattime;
inthisorthatmanner;uponthisorthatmotive?
LetthereaderjudgeifitsufficenotthatwhatIpublishistrue,andthatIhavearighttopublishsuchtruthswhenandhowIpleaseinafreecountry.
5.Idonotsaythatmathematicians,assuch,areinfidels;orthatgeometryisafriendtoinfidelity,whichyouuntrulyinsinuate,asyoudomanyotherthings;whenceyouraisetopicsforinvective.
ButIsaytherearecertainmathematicianswhoareknowntobeso;andthatthereareotherswhoarenotmathematicianswhoareinfluencedbyaregardfortheirauthority.Some,perhaps,wholiveintheUniversity,maynotbeapprisedofthis:
buttheintelligentandobservingreader,wholivesintheworld,andisacquaintedwiththehumourofthetimesandthecharactersofmen,iswellawaretherearetoomanywhoderidemysteriesandyetadmirefluxions;whoyieldthatfaithtoameremortalwhichtheydenytoJesusChrist,whosereligiontheymakeittheirstudyandbusinesstodiscredit.Theowningthisisnottoownthatmenwhoreasonwellareenemiestoreligion,asyouwouldrepresentit:
onthecontrary,Iendeavourtoshewthatsuchmenaredefectiveinpointofreasonandjudgement,andthattheydotheverythingtheywouldseemtodespise.
6.Thereare,Imakenodoubt,amongthemathematiciansmanysincerebelieversinJesusChrist:
Iknowseveralsuchmyself:
butIaddressedmy`Analyst'toaninfidel;and,onverygoodgrounds,Isupposedthat,besideshim,therewereotherderidersoffaithwhohadneverthelessaprofoundvenerationforfluxions:
andIwaswillingtosetforththeinconsistenceofsuchmen.Iftherebenosuchthingasinfidelswhopretendtoknowledgeinthemodernanalysis,Iownmyselfmisinformed,andshallgladlybefoundinamistake;buteveninthatcase,myremarksonfluxionsarenotthelesstrue;norwillitfollowthatIhavenorighttoexaminethemonthefootofhumanscience,eventhoughreligionwerequiteunconcerned,andthoughIhadnoendtoservebuttruth.Butyouareveryangry(p.
13and14)thatIshouldenterthelistswithreasoninginfidels,andattackthemupontheirpretensionstoscience:
andhenceyoutakeoccasionstoshewyourspleenagainsttheclergy.IwillnottakeuponmetosaythatIknowyoutobeaMinutePhilosopheryourself;butIknowtheMinutePhilosophersmakejustsuchcomplimentsasyoudotoourchurch,andarejustasangryasyoucanbeatanywhoundertaketodefendreligionbyreason.Ifweresolveallintofaith,theylaughatusandourfaith:
andifweattempttoreason,theyareangryatus:
theypretendwegooutofourprovince,andtheyrecommendtousablindimplicitfaith.Suchistheinconsistenceofouradversaries.Butitistobehopedtherewillneverbewantingmentodealwiththemattheirownweapons;andtoshewtheyarebynomeansthosemastersofreasonwhichtheywouldfainpassfor.
7.Idonotsay,asyouwouldrepresentme,thatwehavenobetterreasonforourreligionthanyouhaveforfluxions:
butIsaythataninfidel,whobelievesthedoctrineoffluxions,actsaveryinconsistentpartinpretendingtorejecttheChristianreligionbecausehecannotbelievewhathedothnotcomprehend;orbecausehecannotassentwithoutevidence;orbecausehecannotsubmithisfaithtoauthority.Whethertherearesuchinfidels,Isubmittothejudgementofthereader.FormyownpartImakenodoubtofit,havingseensomeshrewdsignsthereofmyself,andhavingbeenverycrediblyinformedthereofbyothers.Nordoththischargeseemthelesscredible,foryourbeingsosensiblytouched,anddenyingitwithsomuchpassion.You,indeed,donotsticktoaffirm,thatthepersonswhoinformedmeare``apackofbase,profligate,andimpudentliars''(p.27).Howfarthereaderwillthinkfittoadoptyourpassions,Icannotsay;butIcantrulysay,thelatecelebratedMr.Addisonisoneofthepersonswhomyouarepleasedtocharacteriseinthesemodestandmannerlyterms.Heassuredmethattheinfidelityofacertainnotedmathematician,stillliving,wasoneprincipalreasonassignedbyawittymanofthosetimesforhisbeinganinfidel.NotthatIimaginegeometrydisposethmentoinfidelity:
butthat,fromothercauses,suchaspresumption,ignorance,orvanity,likeothermengeometriciansalsobecomeinfidels,andthatthesupposedlightandevidenceoftheirsciencegainscredittotheirinfidelity.
8.Youreproachmewithcalumny,detraction,andartifice(p.15).Yourecommendsuchmeansasareinnocentandjust,ratherthanthecriminalmethodoflesseningordetractingfrommyopponents(Ibid.).
Youaccusemeoftheodiumtheologicum,theintemperatezealofdivines,thatIdostaresuperviasantiquas(p.13);withmuchmoretothesameeffect.ForallwhichchargeIdependonthereader'scandour,thathewillnottakeyourword,butreadandjudgeforhimself.
Inwhichcasehewillbeabletodiscern(thoughheshouldbenomathematician)
howpassionateandunjustyourreproachesare,andhowpossibleitisforamantocryoutagainstcalumnyandpractiseitinthesamebreath.Consideringhowimpatientallmankindarewhentheirprejudicesarelookedinto,I
donotwondertoseeyourailandrageattherateyoudo.Butifyourownimaginationbestronglyshockedandmoved,youcannotthereforeconcludethatasincereendeavourtofreeascience,sousefulandorname