Philosophical Foundations of Set Theory 2011 (1)

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1、DefendingtheAxiomsThispageintentionallyleftblankDefendingtheAxioms:OnthePhilosophicalFoundationsofSetTheoryPenelopeMaddy13GreatClarendonStreet,Oxfordox26dpOxfordUniversityPressisadepartmentoftheUniversityofOxford.ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,schola

2、rship,andeducationbypublishingworldwideinOxfordNewYorkAucklandCapeTownDaresSalaamHongKongKarachiKualaLumpurMadridMelbourneMexicoCityNairobiNewDelhiShanghaiTaipeiTorontoWithofficesinArgentinaAustriaBrazilChileCzechRepublicFranceGreeceGuatemalaHungaryItalyJapanPolandPortugalSing

3、aporeSouthKoreaSwitzerlandThailandTurkeyUkraineVietnamOxfordisaregisteredtrademarkofOxfordUniversityPressintheUKandincertainothercountriesPublishedintheUnitedStatesbyOxfordUniversityPressInc.,NewYork#PenelopeMaddy2011ThemoralrightsoftheauthorhavebeenassertedDatabaserightOxfor

4、dUniversityPress(maker)Firstpublished2011Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthepriorpermissioninwritingofOxfordUniversityPress,orasexpresslypermittedbylaw,orundertermsagreedwiththeapprop

5、riatereprographicsrightsorganization.EnquiriesconcerningreproductionoutsidethescopeoftheaboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,attheaddressaboveYoumustnotcirculatethisbookinanyotherbindingorcoverandyoumustimposethesameconditiononanyacquirerBritishLibrary

6、CataloguinginPublicationDataDataavailableLibraryofCongressCataloginginPublicationDataDataavailableTypesetbySPIPublisherServices,Pondicherry,IndiaPrintedinGreatBritainonacid-freepaperbyMPGBooksGroup,BodminandKing’sLynnISBN978–0–19–959618–813579108642FortheCabalThispageintentio

7、nallyleftblankContentsPrefaceixIntroduction1I.TheProblem21.Anhistoricalreversal32.Howappliedmathematicsbecamepure63.Wherewearenow27II.ProperMethod381.Themeta-philosophy382.Someexamplesfromset-theoreticpractice413.Properset-theoreticmethod524.Thechallenge55III.ThinRealism601.I

8、ntroducingThinRealism612.WhatThinRealismisnot643.Thinepistemology714