Table Of ContentTaking Frege at his Word
Taking Frege at his Word
JOAN WEINER
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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
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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.
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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.
