Wittgenstein’s philosophy of mathematics 1994

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1、WITTGENSTEIN’SPHILOSOPHYOFMATHEMATICSWITTGENSTEIN’SPHILOSOPHYOFMATHEMATICSPasqualeFrascollaLondonandNewYorkFirstpublished1994byRoutledge11NewFetterLane,LondonEC4P4EESimultaneouslypublishedintheUSAandCanadabyRoutledge29West35thStreet,NewYork,NY10001Thi

2、seditionpublishedintheTaylor&Francise-Library,2006.“TopurchaseyourowncopyofthisoranyofTaylor&FrancisorRoutledge’scollectionofthousandsofeBookspleasegotowww.eBookstore.tandf.co.uk.”©1994PasqualeFrascollaAllrightsreserved.Nopartofthisbookmaybereprintedo

3、rreproducedorutilizedinanyformorbyanyelectronic,mechanical,orothermeans,nowknownorhereafterinvented,includingphotocopyingandrecording,orinanyinformationstorageorretrievalsystem,withoutpermissioninwritingfromthepublishers.BritishLibraryCataloguinginPub

4、licationDataAcataloguerecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressCataloginginPublicationDataFrascolla,PasqualeWittgenstein’sphilosophyofmathematics/PasqualeFrascolla.Includesbibliographicalreferencesandindex.1.Mathematics–Philos

5、ophy.2.Wittgenstein,Ludwig,1889–1951.I.TitleQA8.4.F7199493-48039510'.1–dc20ISBN0-203-02246-7Mastere-bookISBNISBN0-203-17404-6(AdobeeReaderFormat)ISBN0–415–02483–8(PrintEdition)CONTENTSPrefaceviAbbreviationsviii1THEPHILOSOPHYOFARITHMETICOFTHETRACTATUS1

6、Preliminaries1Systematicexposition8The“knowledge”offorms:visionandcalculation23Foundationsofmathematics(I)332VERIFICATIONISMANDITSLIMITS:Theintermediatephase(1929–33)42Introduction42Finitecardinalnumbers:thearithmeticofstrokes44Mathematicalproposition

7、s54Themathematicalinfinite72Foundationsofmathematics(II)993FROMFACTSTOCONCEPTS:Thelaterwritingsonmathematics(1934–44)111Thecrisisofverificationism:rule-following111Mathematicalproofsasparadigms128Theproblemofstrictfinitism142Wittgenstein’squasi-revisi

8、onism157Notes174References185vPREFACEThisbookisintendedtobeanexposition,asunbiasedaspossible,oftheconceptionsonmathematicswhichwereprogressivelyelaboratedbyWittgensteinduringtheentirecourseofhisreflectionsonthesubject(fromtheTractatusupto1944)