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1、INTRODUCTIONTOMATHEMATICALPHILOSOPHYBertrandRussellDOVERPUBLICATIONS,INC.NewYorkBibliographicalNoteThisDoveredition,firstpublishedin1993,isanunabridgedandunalteredrepublicationofthesecondedition(1920)oftheworkfirstpublishedin1919byGeorgeAllen&Unwin,Ltd.,London,a
2、ndTheMacmillanCo.,NewYork.LibraryofCongressCatahging-in-PublicationDataRussell,Bertrand,r87z-rg7o.Introductiontomathematicalphilosophy/BertrandRussell.P.cm.Originallypublished:znded.London:G.AllenandUnwin;NewYork:Macmillan,r9r9.Includesinden.ISBNo-486-27724-0(pb
3、k.)r.Mathematics-Philosophy.I.Tifle.QA8.4.R87r993b5ro'.r-dczog3-2r477CIPManufacturedintheUnitedStatesofAmericaDoverPublications.Inc..31East2ndStreet,Mineola,N.Y.11501PREFACE('Introductionr"Tslsbookisintendedessentiallyasananddoesnotaimatgivinganexhaustivediscuss
4、ionoftheproblemswithwhichitdeals.Itseemeddesirabletoserforthcertainresults,hithertoonlyavailabletothosewhohavemasteredlogicalsymbolism,inaformofferingtheminimumofdifficultytothebeginner.Theutmostendeavourhasbeenmadetoavoiddogmatismonsuchquestionsasarestillopento
5、seriousdoubt,andthisendeavourhastosomeextentdominatedthechoiceoftopicsconsidered.Thebeginningsofmathematicallogicarelessdefinitelyknownthanitslaterportions,butareofatleastequalphilosophicalinterest.Muchofwhatissetforthinthefollowingchaptersisnotproperlytobecalle
6、d"philosophy,"thoughthemattersconcernedwereincludedinphilosophysolongasnosatisfactoryscienceofthemexisted.Thenatureofinfinityandcontinuity,forexample,belongedinformerdaystophilosophl,butbelongsnowtomathematics.Mathematicalphilosoplt!,inthestrictsense,cannot,perh
7、aps,beheldtoincludesuchdefinitescientificresultsashavebeenobtainedinthisregion;thephilosophyofmathematicswillnaturallybeex-pectedtodealwithquestionsonthefrontierofknowledge,astowhichcomparativecertaintyisnotyetattained.Butspeculationonsuchquestionsishardlylikely
8、tobefruitfulunlessthemorescientificpartsoftheprinciplesofmathematicsareknown.Abookdealingwithtfiosepartsfray,therefore,claimtobeanintroductiontomathematicalphilosophy
