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1、18UnconventionalEssaysontheNatureofMathematicsReubenHershEditorReubenHershDepartmentofMathematicsandStatisticsUniversityofNewMexicoAlbuquerque,NMUSACoverillustration:Photographsofthreecontributingauthors:AlfrédRényi,Gian-CarloRota,andLeslieA.White.MathematicsSubjectClassi
2、ficationMSC2000:01A0551–03LibraryofCongressControlNumber:2005925514ISBN-10:0-387-25717-9Printedonacid-freepaper.ISBN-13:978-0387-25717-4©2006SpringerScience+BusinessMedia,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionoft
3、hepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsincon-nectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinfor-mationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarm
4、ethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesof
5、America.(SPI/EB)987654321springeronline.comContentsIntroductionbyReubenHersh...........................................................................viiAbouttheAuthors.............................................................................................xviiChapte
6、r1ASocraticDialogueonMathematics................................................................1AlfrédRényiChapter2“Introduction”toFilosofiaematematica...........................................................17CarloCellucciChapter3OnProofandProgressinMathematics.......
7、......................................................37WilliamP.ThurstonChapter4TheInformalLogicofMathematicalProof......................................................56AndrewAberdeinChapter5PhilosophicalProblemsofMathematicsintheLightofEvolutionaryEpistemology........
8、...................................................................71YehudaRavChapter6TowardsaSe
