Alfred Tarski: Philosophy of Language and Logic (History of Analytic Philosophy)

273 Pages·2012·2.63 MB·English

by  Douglas Patterson

HistoryofAnalyticPhilosophy
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Alfred Tarski: Philosophy
of Language and Logic
Douglas Patterson
VisitingScholar,UniversityofPittsburgh,Pittsburgh,PA
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10.1057/9780230367227 - Alfred Tarski: Philosophy of Language and Logic, Douglas Patterson
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©DouglasPatterson2012
Allrightsreserved.Noreproduction,copyortransmissionofthis
publicationmaybemadewithoutwrittenpermission.
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Contents
SeriesEditor’sForeword viii
0 Introduction 1 01
2-
0.1 Expressiveandrepresentationalsemantics 1 2-0
1
0.2 Thereceivedview 4 20
0.3 Themes 7 ct -
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1 IntuitionisticFormalism 12 C
e
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1.1 WhatwasIntuitionisticFormalism? 12 gra
1.1.1 Apuzzleaboutconceptsanddefinitions 12 Pal
1.1.2 Tarski,Les´niewskiandIntuitionisticFormalism 16 ey -
n
d
1.1.3 Formalism 19 y
S
1.2 Les´niewski 20 of
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1.2.1 Les´niewski’searlywork 20 sit
er
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1.2.2 Les´niewski’slaterwork 25 ni
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1.3 Kotarbin´ski 31 o
d t
1.4 Tarskiincontext 37 se
n
1.4.1 Theaxiomaticmethod 37 ce
1.4.2 Monismvstolerance 41 m - li
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1.4.3 Fivedoctrines 43 ct.c
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1.4.4 Tarski’sproject 49 nn
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2 TarskiasIntuitionisticFormalist 53 av
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2.1 Theearlymetamathematicalworks 53 al
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2.1.1 Axiomatizingconsequence 53 ww.
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2.1.2 Relativizationtoadeductivescience 55 m
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2.2 Explicitdefinition 62 al fr
2.2.1 Definingdefinition 63 eri
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2.2.2 Twoconceptionsofdefinition 65 m
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2.2.3 Padoa’smethod 67 yrig
2.3 Categoricityandcompletenessofterms 70 op
C
2.3.1 Provablemonotransformability 70
2.3.2 Absolutemonotransformability 76
2.4 Theoryandconcept 80
3 Semantics 84
3.1 Philosophicalresistance 85
v
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vi Contents
3.1.1 Thequantifier 86
3.1.2 Paradox 89
3.2 Mathematicalacceptance 91
3.3 IntuitionisticFormalismin“OnDefinableSets” 94
3.3.1 Theintuitivenotionofdefinability 95
3.3.2 Definingdefinablesetsvsdefining“Defines” 100
4 Truth 108
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4.1 ConventionT 109 2-
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4.1.1 Terminologicalnotes 109 12-
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4.1.2 TruthintheLvov–Warsawschool 111 ct -
4.1.3 Semanticconceptsinamathematicaltheory 114 ne
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4.1.4 T-sentences 117 C
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4.2 Tarski’sdefinitions 122 gra
4.2.1 Truthforthelanguageofthecalculusofclasses 122 Pal
4.2.2 Higherorderandpolyadicity 124 ey -
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4.2.3 Domainrelativizationandconsequence 128 y
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4.3 EvaluatingTarski’saccount 129 of
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4.3.1 Familiarquestions 129 sit
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4.3.2 TarskiandefinitionsandTarski’s“theory” 133 ni
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4.3.3 Reductionandphysicalism 138 o
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4.3.4 Correspondenceanddeflationism 140 se
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5 IndefinabilityandInconsistency 144 m - li
5.1 Indefinability 145 o
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5.1.1 Indefinabilitybefore1931 145 ect.
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5.1.2 TheoremI:textualissues 147 o
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5.1.3 TheoremIandIntuitionisticFormalism 155 av
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5.1.4 Axiomaticsemantics 158 al
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5.2 Inconsistencyineverydaylanguage 160 ww.
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5.2.1 InconsistentKotarbin´skianconventions 162 m
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5.2.2 TarskiafterKotarbin´ski 166 al fr
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6 Transitions:1933–1935 169 at
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6.1 The1935postscript 170 ht
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6.2 Carnaponanalyticityandtruth 174 yri
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6.3 Theestablishmentofscientificsemantics 179 C
7 LogicalConsequence 181
7.1 Tarski’sdefinition 182
7.1.1 Synopsis 182
7.1.2 ObjectionstoTarski’saccount 185
7.2 ConsequenceinLogicalSyntax 187
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Contents vii
7.2.1 L-consequenceandconditionF 187
7.2.2 TractarianismintheViennacircle 191
7.3 Theovergenerationproblemanddomainvariation 194
7.3.1 Domainvariation 194
7.3.2 ConsequenceinGödel’scompletenesstheorem 198
7.3.3 Tarski’sfixeddomain 201
7.4 Themodalityproblemand“Tarski’sFallacy” 203
7.4.1 Modalities 204 01
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7.4.2 Consequenceandtruth 206 2-0
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7.4.3 Tarski’s“must” 208 20
7.5 Theformalityproblemandthelogicalconstants 209 ct -
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7.5.1 Constantandconsequence 209 on
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7.5.2 Anachronisticreadings 211 ve
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7.5.3 Carnaponformality 213 algr
7.5.4 Theω-ruleandGödelsentences 214 y - P
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7.5.5 Antitractarianismandthenatureoflogic 215 dn
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7.6 EvaluatingTarski’saccount 219 of S
7.6.1 Theanalyticproblem 219 sity
7.6.2 Eliminatingtransformationrules 221 ver
ni
7.6.3 Epistemicandgeneralityconceptionsoflogic 223 U
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d t
8 Conclusion 227 se
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8.1 Paris1935andthereceptionofsemantics 227 ce
8.2 Finalremarks 232 m - li
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Notes 234 ect.
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Bibliography 249 ec
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Index 260 al
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Series Editor’s Foreword
Duringthefirsthalfofthetwentiethcenturyanalyticphilosophygradu-
allyestablisheditselfasthedominanttraditionintheEnglish-speaking
world,andoverthelastfewdecadesithastakenfirmrootinmanyother 01
2-
partsoftheworld.Therehasbeenincreasingdebateoverjustwhat‘ana- 2-0
1
lyticphilosophy’means,asthemovementhasramifiedintothecomplex 20
tradition that we know today, but the influence of the concerns, ideas ct -
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andmethodsofearlyanalyticphilosophyoncontemporarythoughtis on
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indisputable. All this has led to greater self-consciousness among ana- ve
a
lytic philosophers about the nature and origins of their tradition, and algr
P
scholarlyinterestinitshistoricaldevelopmentandphilosophicalfoun- y -
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dations has blossomed in recent years. The result is that history of dn
y
analytic philosophy is now recognized as a major field of philosophy of S
initsownright. sity
Themainaimoftheseriesinwhichthepresentbookappears–thefirst ver
ni
seriesofitskind–istocreateavenueforworkonthehistoryofanalytic U
o
philosophy, consolidating the area as a major field of philosophy and d t
e
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promotingfurtherresearchanddebate. The‘historyofanalyticphilos- n
e
c
ophy’isunderstoodbroadly, ascoveringtheperiodfromthelastthree m - li
decadesofthenineteenthcenturytothestartofthetwenty-firstcentury o
c
– beginning with the work of Frege, Russell, Moore and Wittgenstein, ect.
n
n
who are generally regarded as its main founders, and the influences o
c
e
upon them – and going right up to the most recent developments. In av
gr
allowingthe‘history’toextendtothepresent, theaimistoencourage al
p
engagementwithcontemporarydebatesinphilosophy–forexample,in ww.
w
showinghowtheconcernsofearlyanalyticphilosophyrelatetocurrent m
o
concerns.Infocusingonanalyticphilosophy,theaimisnottoexclude al fr
comparisonswithother–earlierorcontemporary–traditions,orconsid- eri
at
eration of figures or themes that some might regard as marginal to the m
ht
analytic tradition but which also throw light on analytic philosophy. yrig
Indeed,afurtheraimoftheseriesistodeepenourunderstandingofthe op
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broadercontextinwhichanalyticphilosophydeveloped,bylooking,for
example,attherootsofanalyticphilosophyinneo-KantianismorBritish
idealism, or the connections between analytic philosophy and phe-
nomenology,ordiscussingtheworkofphilosopherswhowereimportant
in the development of analytic philosophy but who are now often
forgotten.
viii
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SeriesEditor’sForeword ix
InthisbookDouglasPattersonprovidesthefirstfull-lengthaccountof
AlfredTarski’sphilosophy.TarskiwasborninWarsawin1901andgained
hisdoctorateinlogicattheUniversityofWarsawin1924,supervisedby
StanislawLes´niewski. Inthe1920sand1930shepublishedextensively
on logic and set theory, and as a representative of the so-called Lvov–
Warsaw School, maintained close links with Gödel, Carnap and other
membersoftheViennaCircle.WhenNaziGermanyinvadedPolandon
1 September 1939, Tarski was at a conference in the United States and 01
2-
was unable to return home. He stayed there throughout the war years, 2-0
1
teaching at Harvard, New York and Princeton before eventually being 20
given a permanent post at the University of California at Berkeley in ct -
e
n
1945,whereheremaineduntilhisdeathin1983.Tarskiwasthusoneof on
C
themanylogiciansandphilosophersfromCentralEuropewhomoved ve
a
to the United States as a result of the rise of Nazism in Germany, and algr
P
whosestoryispartofthebroaderstoryofthedevelopmentofanalytic y -
e
philosophy in North America, as the ideas of the Polish logicians and dn
y
thelogicalpositiviststookrootinnewsoil. of S
Tarski’stwomostfamouspapersare‘TheConceptofTruthinFormal- sity
ized Languages’, first published in Polish in 1933 (and in German in ver
ni
1935)and‘OntheConceptofLogicalConsequence’,publishedinboth U
o
Polish and German in 1936. In the first paper Tarski offers a definition d t
e
s
of truth for formal languages by introducing the notion of satisfaction n
e
c
andappealingtotherecursivestructureofformallanguages.Tarskifirst m - li
formulates his ‘T-schema’ here (famously exemplified in the statement o
c
that‘Snowiswhiteistrue’ifandonlyifsnowiswhite),andalsooffers ect.
n
n
asolutiontotheLiarparadoxbyinsistingthattruthforalanguagecan o
c
e
only be defined in a metalanguage. In the second paper Tarski offers av
gr
a corresponding semantic definition of logical consequence by utiliz- al
p
ing the idea of truth-under-an-interpretation introduced in his earlier ww.
w
paper.Thesetwopapershavebeenseenasestablishingthefoundations m
o
oftruth-conditionalsemantics,withTarskialsoregardedasakeyfigure al fr
inthedevelopmentofmodeltheory. eri
at
As Patterson argues in this book, however, Tarski’s actual views are m
ht
bothmorecomplexandmoreintriguingthantheyhavestandardlybeen yrig
takentobe.Pattersonbeginsbydistinguishingwhathecallsthe‘expres- op
C
sive’ conception of meaning from the ‘representational’ conception of
meaning. On the expressive conception, language expresses thoughts
andthenotionsofassertionandjustificationhaveprimacy.Ontherep-
resentational conception, language represents things in the world and
the notions of reference and truth have primacy. The former finds its
naturalhomeintheproof-theoreticconceptionoflogic,whilethelatter
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