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1、SetTheoryanditsPhilosophyThispageintentionallyleftblankSetTheoryanditsPhilosophyACriticalIntroductionMichaelPotter33GreatClarendonStreet,OxfordOX26DPOxfordUniversityPressisadepartmentoftheUniversityofOxford.ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarshi
2、p,andeducationbypublishingworldwideinOxfordNewYorkAucklandBangkokBuenosAiresCapeTownChennaiDaresSalaamDelhiHongKongIstanbulKarachiKolkataKualaLumpurMadridMelbourneMexicoCityMumbaiNairobiSaoPauloShanghaiTaipeiTokyoToronto˜OxfordisaregisteredtrademarkofOxfordUniversityPressin
3、theUKandcertainothercountriesPublishedintheUnitedStatesbyOxfordUniversityPressInc.,NewYorkcMichaelPotter2004ThemoralrightsoftheauthorhavebeenassertedDatabaserightOxfordUniversityPress(maker)Firstpublished2004Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin
4、aretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthepriorpermissioninwritingofOxfordUniversityPress,orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriatereprographicsrightsorganizations.Enquiriesconcerningreproductionoutsidethescopeoftheaboveshouldbese
5、nttotheRightsDepartment,OxfordUniversityPress,attheaddressaboveYoumustnotcirculatethisbookinanyotherbindingorcoverandyoumustimposethesameconditiononanyacquirerBritishLibraryCataloguinginPublicationDataDataavailableLibraryofCongressCataloginginPublicationDataDataavailableISB
6、N0–19–926973–4(hbk.)ISBN0–19–927041–4(pbk.)13579108642TypesetbytheauthorPrintedinGreatBritainonacid-freepaperbyTJInternationalLtd.,Padstow,CornwallPrefaceThisbookwaswrittenfortwogroupsofpeople,philosophicallyinformedmathematicianswithaseriousinterestinthephilosophyoftheirsu
7、bject,andphilosopherswithaseriousinterestinmathematics.Perhaps,therefore,Ishouldbeginbypayingtributetomypublisherforexpressingnonervous-nessconcerningthesizeofthelikelyreadership.Frege(1893–1903,I,p.xii)predictedthattheformofhisGrundgesetzewouldcausehimtorelinquishasreaders
8、allthosemathematicianswho,iftheybumpintologicalexpres-sionssuchas‘concept’,‘relati