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1、PhilosophyofMathematicsandMathematicalPracticeintheSeventeenthCenturyThispageintentionallyleftblankPhilosophyofMathematicsandMathematicalPracticeintheSeventeenthCenturyPAOLOMANCOSUNewYorkOxfordOXFORDUNIVERSITYPRESS1996OxfordUniversityPressOxfordNewYorkAthensAu
2、cklandBangkokBombayCalcuttaCapeTownDaresSalaamDelhiFlorenceHongKongIstanbulKarachiKualaLumpurMadrasMadridMelbourneMexicoCityNairobiParisSingaporeTaipeiTokyoTorontoandassociatedcompaniesinBerlinIbadanCopyright©1996byPaoloMancosuPublishedbyOxfordUniversityPress,
3、Inc.198MadisonAvenue,NewYork,NY10016OxfordisaregisteredtrademarkofOxfordUniversityPressAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwis
4、e,withoutthepriorpermissionofOxfordUniversityPress.LibraryofCongressCataloging-in-PublicationDataMancosu,Paolo.Philosophyofmathematicsandmathematicalpracticeintheseventeenthcentury/PaoloMancosu.p.cm.Includesbibliographicalreferencesandindex.ISBN0-19-508463-21.
5、MathematicsEurope—Philosophy—History—17thcentury.I.Title.QA8.4.M361996510'.9'032--dc2095-47024135798642PrintedintheUnitedSlatesofAmericaonacid-freepaper.Tomyparents,AngelaandPorfidioThispageintentionallyleftblankPREFACEThepresentbookistheresultofseveralyears'w
6、orkinthehistoryofthephilosophyofmathematicsintheseventeenthcentury.WhiledoingresearchforitIhavecomeintocontactwithseveralscholarswhosehelpandencouragementitisapleasuretoacknowledgehere.IbeganworkonthissubjectwhileIwasagraduatestudentatStanfordUniversity.Atthat
7、timeIhadtheopportunitytotalkagreatdealwithWilburKnorr,NancyCartwright,andEzioVailati.Eziokindlyagreedtomyusingajointarticleinchapter5ofthisbook.IalsooweagreatdealtomyPh.D.advisor,SolomonFeferman.Althoughwerarelyspokeabouttheseventeenthcentury(weweretoobusydisc
8、ussingtheoriesofoperationsandclasses)hispointofviewonthefoundationsofmathematicshasgreatlyinfluencedmyoutlookonthesubject.Andthatinfluencegoesfarbeyondpurelytechnicalknowledge;Solh
