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1、18UnconventionalEssaysontheNatureofMathematics18UnconventionalEssaysontheNatureofMathematicsReubenHershEditorReubenHershDepartmentofMathematicsandStatisticsUniversityofNewMexicoAlbuquerque,NMUSACoverillustration:Photographsofthreecontributingauthors:AlfrédRényi,Gian-
2、CarloRota,andLeslieA.White.MathematicsSubjectClassificationMSC2000:01A0551–03LibraryofCongressControlNumber:2005925514ISBN-10:0-387-25717-9Printedonacid-freepaper.ISBN-13:978-0387-25717-4©2006SpringerScience+BusinessMedia,Inc.Allrightsreserved.Thisworkmaynotbetransla
3、tedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsincon-nectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinfor-mationstorageandretrieval,e
4、lectronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhethe
5、rornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.(SPI/EB)987654321springeronline.comContentsIntroductionbyReubenHersh...........................................................................viiAbouttheAuthors................................
6、.............................................................xviiChapter1ASocraticDialogueonMathematics................................................................1AlfrédRényiChapter2“Introduction”toFilosofiaematematica............................................
7、...............17CarloCellucciChapter3OnProofandProgressinMathematics.............................................................37WilliamP.ThurstonChapter4TheInformalLogicofMathematicalProof......................................................56AndrewAberdeinChapt
8、er5PhilosophicalProblemsofMathematicsintheLightofEvolutionaryEpistemology..........................................................
