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1、IntroductiontoMathematicalPhilosophybyBertrandRussellOriginallypublishedbyGeorgeAllen&Unwin,Ltd.,London.May1919.OnlineCorrectedEditionversion1:0(February5,2010),basedonthe“secondedition”(secondprinting)ofApril1920,incorporatingadditionalcorrections,markedingreen.[Ru
2、ssell’sblurbfromtheoriginaldustcover:]Thisbookisintendedforthosewhohavenoprevi-ousacquaintancewiththetopicsofwhichittreats,andnomoreknowledgeofmathematicsthancanbeacquiredataprimaryschoolorevenatEton.Itsetsforthinelementaryformthelogicaldefinitionofnumber,theanalysis
3、ofthenotionoforder,themoderndoctrineoftheinfinite,andthetheoryofdescriptionsandclassesassymbolicfictions.Themorecontroversialanduncertainaspectsofthesub-jectaresubordinatedtothosewhichcanbynowberegardedasacquiredscientificknowledge.Theseareexplainedwithouttheuseofsymbo
4、ls,butinsuchawayastogivereadersageneralunderstand-ingofthemethodsandpurposesofmathematicallogic,which,itishoped,willbeofinterestnotonlytothosewhowishtoproceedtoamoreseriousstudyofthesubject,butalsotothatwidercirclewhofeeladesiretoknowthebearingsofthisimportantmod-er
5、nscience.ContentsContents.....................ivPreface......................viEditor’sNote...................ixI.TheSeriesofNaturalNumbers...1II.DefinitionofNumber.........17III.FinitudeandMathematicalInduction32IV.TheDefinitionofOrder.......46V.KindsofRelations.....
6、......67VI.SimilarityofRelations........83VII.Rational,Real,andComplexNumbers101VIII.InfiniteCardinalNumbers......124IX.InfiniteSeriesandOrdinals.....144X.LimitsandContinuity........156XI.LimitsandContinuityofFunctions.171XII.SelectionsandtheMultiplicativeAx-iom......
7、..............187ivXIII.TheAxiomofInfinityandLogicalTypes..................210XIV.IncompatibilityandtheTheoryofDe-duction.................230XV.PropositionalFunctions.......248XVI.Descriptions..............267XVII.Classes.................289XVIII.MathematicsandLogic.
8、.......311Index.......................331Appendix:ChangestoOnlineEdition....338PrefaceThisbookisintendedessentiallyasan“Introduc-vtion,”an
