Taking Frege at his Word PDF
Preview Taking Frege at his Word
Taking Frege at his Word Taking Frege at his Word JOAN WEINER 1 3 GreatClarendonStreet,Oxford,OX26DP, UnitedKingdom OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwide.Oxfordisaregisteredtrademarkof OxfordUniversityPressintheUKandincertainothercountries ©JoanWeiner2020 Themoralrightsoftheauthorhavebeenasserted FirstEditionpublishedin2020 Impression:1 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin aretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthe priorpermissioninwritingofOxfordUniversityPress,orasexpresslypermitted bylaw,bylicenceorundertermsagreedwiththeappropriatereprographics rightsorganization.Enquiriesconcerningreproductionoutsidethescopeofthe aboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,atthe addressabove Youmustnotcirculatethisworkinanyotherform andyoumustimposethissameconditiononanyacquirer PublishedintheUnitedStatesofAmericabyOxfordUniversityPress 198MadisonAvenue,NewYork,NY10016,UnitedStatesofAmerica BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressControlNumber:2020939200 ISBN978–0–19–886547–6 DOI:10.1093/oso/9780198865476.001.0001 Printedandboundby CPIGroup(UK)Ltd,Croydon,CR04YY LinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithand forinformationonly.Oxforddisclaimsanyresponsibilityforthematerials containedinanythirdpartywebsitereferencedinthiswork. ForMark Preface AlthoughthisbookisnotmeantasanintroductiontoFrege,Ihavetriedtomake it as readable by nonspecialists as I can. Since I presuppose that the reader is acquainted with the basic outlines of Frege’s career, I begin this preface with a briefdescriptionoftheseoutlines. Frege was engaged, for virtually all his career, in a single project: that of showing that the truths of arithmetic are truths of logic. He first mentions this project, and the gapless inferences it requires, in the preface to his 1879 mono- graph, Begriffsschrift. And he tells the reader that, in the process of trying to construct such proofs, he found natural language to be an impediment. He attempts to solve this problem in Begriffsschrift. In Begriffsschrift he offers us a logical language that is designed to be capable of expressing all content that has significanceforinference.Andheoffersusasystemofevaluationthatisdesigned to make it a mechanical task—once the inference is expressed in his new logical language—to identify inferences either as correct and gapless or as requiring additional premises. The resulting new logic was a major advance. In particular, Frege’slogic,unlikeBoole’s,allowsustoevaluatemathematicalinferenceswhose validitydependsonpolyadicrelationsandnestedquantification. Having introduced these logical tools, Frege turns, in his 1884 monograph, Foundations of Arithmetic, to the task of giving a detailed, but non-technical, description of his project. In Foundations he also discusses his reasons for thinking that the truths of arithmetic are analytic, that is, belong to logic. The next step was to give actual gapless proofs, in the logical language, of basic truthsofarithmeticfromlogicallaws.Intheprocessoftryingtoconstructthese proofs, however, Frege realized that substantial revisions to his logical system were necessary. In order to develop the new version of his logic, he needed to reconceive some of the basic notions of his logic, including the notions of function, concept, and object. The new version of his logic, and the descriptions ofthesereconceptions,arefirstpresentedinaseriesofthreeworks,Functionand Concept, “On Sinn and Bedeutung” and “On Concept and Object,” published in 1891 and 1892. In 1893 Frege published the first volume of Basic Laws of Arithmetic, which includes both an introduction to the new version of his logic and purely logical proofsofsomebasiclawsofarithmetic.In1903,whenthesecondvolumewasin press,Fregereceivedanow-famousletterfromBertrandRussell,inwhichRussell showedthatthelogicalsystemofBasicLawswasinconsistent.Theculpritwasone of Frege’s new logical laws, Basic Law V, a law that was crucial to the proofs viii needed to establish that arithmetic belongs to logic. Although Frege tried a number of alternative strategies after the discovery of the contradiction, none was successful. He wrote in a diary entry near the end of his life, “My efforts to becomeclearaboutwhatismeantbynumberhaveresultedinfailure.”¹ InspiteofthedramaticfailureofFrege’sgeneralproject,muchoftheworkhe didintheserviceofthisprojecthashadaprofoundinfluenceonthesubsequent developmentofphilosophyintheanalytictradition.Onepartofthisinfluencecan be found in his new logic. Another can be found in his treatment of language, natural as well as logically perfect. Indeed, virtually all philosophers who are trained in the analytic tradition read Frege’s writings in the context of an intro- ductiontothephilosophyoflanguage.Studentsaretaughtthat,inhispapers“On Sinn and Bedeutung” and ”Thoughts,” Frege means to be introducingthe begin- ningsofasemanticsortheoryofmeaning,atheorythat—evenifitisnotwidely acceptedtoday—setstheagendaformuchofthesubsequentphilosophicalwriting aboutlanguage.TheseviewsarepartofwhatIwillcalltheStandardInterpretation. Thecentraltenetsofthisinterpretationare: (1) ItwasFrege’saimtogiveatheoryofmeaning,oratheoryoftheworkings oflanguage,for(someversionof)naturallanguage.Thekindoftheoryin question is one that provides an account of how the truth of a sentence dependsonthesemanticfeaturesofitsparts. (2) On Frege’s view, the relevant semantic features of subsentential expres- sions (e.g., proper names, predicates) of a properly functioning language are determined by a reference relation that links them to extra-linguistic entities. And the reference relation is determined by something like the information content associated with the expression. A sentential expres- sioncanbesaidtohaveatruth-valueonlyifitsconstituentpropernames (predicates,etc.)alreadyrefertoextra-linguisticentities. (3) An important part of Frege’s logical theory is constituted by metatheore- ticalproofs.Hedefinesatruthpredicateforhislogicallanguageanduses this predicate to give a proto-soundness proof for his logical system: a metatheoretic proof that includes proofs of the basic laws and of the validityoftherules.Healsooffersaproof,byinductiononthecomplexity of a Begriffsschrift expression, that all expressions of his logical language refertoextra-linguisticentities. (4) Frege is a Platonist. He has an ontological theory on which there is a distinction between functions and objects and there is a “third realm” containing such non-perceivable, non-spatio-temporal entities as num- bers,functions,andthoughts. ¹ DiaryentryMarch23,1924,NS,p.282/PW,p.263. ix Many philosophers take the Standard Interpretation to be, not so much an interpretation of Frege’s statements, as a straightforward, uncontroversial report ofthosestatements.Andmanyphilosopherstakethesecondaryliteraturetobeof interestonlyinsofarasitelaboratesordeepenstheStandardInterpretation. Thisbookisdevotedtosettingoutaninterpretationthatisdeeplyatoddswith the Standard Interpretation. There are, however, aspects of the Standard Interpretation with which I have no dispute. Insofar as the enterprise of using naturallanguagetointroduce,discuss,orargueaboutfeaturesofaformalsystem countsasmetatheory,therecanbenodebate:Fregedoeshaveametatheory.What I deny is that Frege offers metatheoretic proofs that count as part of his logical theory.AndIdenythathemeanstoofferanythinglikeaproto-soundnessproof. Moreover,IdonotdenythatFregeisarealistinthefollowingsense:hebelieves that truth is independent of us and our thought. What I deny is that (to use MichaelDummett’swords),itis, because the expressions we use have such extra-linguistic correlates [referents] that we succeed in talking about the real world, and in saying things about it whicharetrueorfalseinvirtueofhowthingsareinthatworld.² And,finally,IdonotdenythatFregehasmuchtoteachusaboutnaturallanguage. WhatIdenyisthathemeanstodevelopsomethinglikeacompositionalsemantic theory. To deny these parts of the Standard Interpretation is to differ with this interpretationover,touseDummett’swords“fundamentalquestionsconcerning what Frege was about.”³ Dummett has argued that given the clarity of Frege’s writing, there is no reason for such divergence in interpretation. And Dummett mighthavebeenrightaboutthis,hadFregeexplicitlystated,forinstance,thathe meant to give a theory of how the truth-value of a sentence is determined by semantic features of its constituents. But no such statement appears in Frege’s writings.Infact,theproblemwiththeconceptionoftheStandardInterpretation asstraightforwardreportage,Iargue,isthatmuchofthereportagethatappearsin the writings of supporters of the Standard Interpretation is not accurate. And manyoftheviewstheStandardInterpretationattributestoFregeconflictwithhis explicit,repeatedstatementsaboutwhathisprojectisandwhatheistryingtodo. Moreover, on the Standard Interpretation, a number of the positions that, Frege claims explicitly, are central to his view are not just wrong but obviously wrong and even absurd. Contemporary interpreters of Frege’s work have overwhelm- inglyrespondedtotheseapparentlyabsurdstatementsbyengaginginwhatseem ² Dummett(1981a),p.198.TheexpressionsDummetthasinmindaresubsententialexpressions, sincehethinksitisamistaketotakesentencestohaveextra-linguisticcorrelates. ³ Dummett(1981b),pp.x–xi.
The list of books you might like
