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LOGICISM AND ITS PHILOSOPHICAL LEGACY Theideathatmathematicsisreducibletologichasalonghistory,but it was Frege who gave logicism an articulation and defense that transformeditintoadistinctivephilosophicalthesiswithaprofound influence on the development of philosophy in the twentieth century.Thisvolumeofclassic,revised,andnewlywrittenessaysby William Demopoulos examines logicism’s principal legacy for philosophy:itselaborationofnotionsofanalysisandreconstruction. The essays reflect on the deployment of these ideas by the principal figures in the history of the subject – Frege, Russell, Ramsey, and Carnap–andindoingsoilluminatecurrentconcernsaboutthenature ofmathematicalandtheoreticalknowledge.Issuesaddressedinclude thenatureofarithmeticalknowledgeinthelightofFrege’stheorem; thestatusofrealismaboutthetheoreticalentitiesofphysics;andthe proper interpretation of empirical theories that postulate abstract structuralconstraints. william demopoulos isProfessorofPhilosophyattheUniversity ofWesternOntario.Hehaseditedmanyvolumesonfoundationaland philosophicalissuesarisinginthesciences,includingPhysicalTheoryand itsInterpretation(withItamarPitowskyin2006),andFrege’sPhilosophyof Mathematics(1995). LOGICISM AND ITS PHILOSOPHICAL LEGACY WILLIAM DEMOPOULOS cambridge university press Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,SãoPaulo,Delhi,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,Cambridgecb28ru,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9781107029804 ©WilliamDemopoulos2013 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2013 PrintedandboundintheUnitedKingdombytheMPGBooksGroup AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Demopoulos,William. Logicismanditsphilosophicallegacy/WilliamDemopoulos. p. cm. Includesbibliographicalreferences(p.255)andindex. isbn978-1-107-02980-4 1. Logic,Symbolicandmathematical. 2. Mathematics–Philosophy. I. Title. qa9.d38 2013 511.3–dc23 2012023164 isbn978-1-107-02980-4Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. Dedicated to Rai, Billy, and Alexis, for whom my gratitude is beyond expression Contents Preface page ix Introduction 1 1 Frege’sanalysisofarithmeticalknowledge 8 2 Carnap’sthesis 28 3 Onextending“Empiricism,semanticsandontology”tothe realism−instrumentalismcontroversy 46 4 Carnap’sanalysisofrealism 68 5 BertrandRussell’sTheAnalysisofMatter:itshistoricalcontext andcontemporaryinterest(withMichaelFriedman) 90 6 Ontherationalreconstructionofourtheoreticalknowledge 108 7 Threeviewsoftheoreticalknowledge 140 8 Fregeandtherigorizationofanalysis 169 9 Thephilosophicalbasisofourknowledgeofnumber 185 10 The1910Principia’stheoryoffunctionsandclasses 210 11 Ramsey’sextensionalpropositionalfunctions 238 Bibliography 255 Index 266 vii