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1、18UnconventionalEssaysontheNatureofMathematics18UnconventionalEssaysontheNatureofMathematicsReubenHershEditorReubenHershDepartmentofMathematicsandStatisticsUniversityofNewMexicoAlbuquerque,NMUSACoverillustration:Photographsofthreecontributingauthors:Alf
2、rédRényi,Gian-CarloRota,andLeslieA.White.MathematicsSubjectClassificationMSC2000:01A0551–03LibraryofCongressControlNumber:2005925514ISBN-10:0-387-25717-9Printedonacid-freepaper.ISBN-13:978-0387-25717-4©2006SpringerScience+BusinessMedia,Inc.Allrightsrese
3、rved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsincon-nectionwithreviewsorscholarlyanalysis.Useinconnectionwith
4、anyformofinfor-mationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifi
5、edassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.(SPI/EB)987654321springeronline.comContentsIntroductionbyReubenHersh.......................................................
6、....................viiAbouttheAuthors.............................................................................................xviiChapter1ASocraticDialogueonMathematics................................................................1AlfrédRényiChap
7、ter2“Introduction”toFilosofiaematematica...........................................................17CarloCellucciChapter3OnProofandProgressinMathematics.............................................................37WilliamP.ThurstonChapter4TheInformalL
8、ogicofMathematicalProof......................................................56AndrewAberdeinChapter5PhilosophicalProblemsofMathematicsintheLightofEvolutionaryEpistemology..........................................................
