A Defence of FreeThinking in Mathematics.docx

A Defence of FreeThinking in Mathematics.docx

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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