Deflationism and Paradox

289 Pages·2006·1.69 MB·English

by  J. C. Beall

DEFLATIONISM AND PARADOX
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X
De ationism
and Paradox
Editedby
JC BEALL
and
BRADLEY ARMOUR-GARB
(cid:1)
CLARENDON PRESS OXFORD
3
GreatClarendonStreet,Oxfordox26dp
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Contents
ListofContributors vii
AShortIntroduction 1
JCBeallandBradleyArmour-Garb
PART I: DISQUOTATIONALISM AND PARADOX
1. TransparentDisquotationalism 7
JCBeall
2. IstheLiarSentenceBothTrueandFalse? 23
HartryField
3. SpikingtheField-Artillery 41
GrahamPriest
4. VariationsonaThemebyYablo 53
HartryField
PART II: MINIMALISM AND PARADOX
5. AMinimalistCritiqueofTarskionTruth 75
PaulHorwich
6. Minimalism,Epistemicism,andParadox 85
BradleyArmour-GarbandJCBeall
7. MinimalistsaboutTruthCan(andShould)BeEpistemicists,
anditHelpsifTheyAreRevisionTheoriststoo 97
GregRestall
8. Minimalism,DeXationism,andParadoxes 107
MichaelGlanzberg
PART III: OTHER DIRECTIONS
9. DotheParadoxesPoseaSpecialProblemforDeXationism? 133
AnilGupta
10. SemanticsforDeXationists 148
ChristopherGauker
11. HowSigniWcantIstheLiar? 177
DorothyGrover
12. TheDeXationist’sAxiomsforTruth 203
VolkerHalbachandLeonHorsten
vi Contents
13. NaiveTruthandSophisticatedLogic 218
AlanWeir
14. AnaphoricallyUnrestrictedQuantiWersandParadoxes 250
JodyAzzouni
Index 275
List of Contributors
Bradley Armour-Garb isAssistantProfessorofPhilosophy,theStateUniversity
of New York at Albany, and was a fellow of Wolfson College, Oxford. He works
primarilyonphilosophicallogic,thephilosophyoflanguage,andmetaphysics,and
has published articles on a constellation of issues, including truth, meaning, the
paradoxes,andthelike.Heiscoeditor,withJCBeall,ofDeflationaryTruth(Open
CourtPress,2005)andDeflationismandParadox(OxfordUniversityPress,2005).
Jody Azzouni is Professor of Philosophy, Tufts University. His books include
Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the
ExactSciences,KnowledgeandReferenceinEmpiricalScience,andDeflatingExistential
Commitment:ACaseforNominalism.
JC Beall is Associate Professor of Philosophy, University of Connecticut, and
ResearchAssociateattheAHRCArche´Centreforthephilosophyoflogic,language,
mathematics, and mind, at the University of St Andrews. In addition to papers on
truth-related topics and paradox, Beall is the editor of Liars and Heaps (Oxford
University Press, 2003), coauthor, with Bas C. van Fraassen, of Possibilities and
Paradox: An Introduction to Modal and Many-Valued Logic (Oxford University
Press,2003),andcoauthor,withGregRestall,ofLogicalPluralism(OxfordUniversity
Press, in press). Beall is currently finishing a monograph on truth and paradox
(OxfordUniversityPress,forthcoming).
Hartry Field isProfessorofPhilosophy,NewYorkUniversity.Hisbooksinclude
Science Without Numbers (Princeton University Press, 1980), Realism, Mathematics
andModality(Blackwell,1989),andTruthandTheAbsenceofFact(OxfordUniversity
Press,2001).Field’smainresearchareasincludemetaphysics,epistemology,philoso-
phy of logic, philosophy of mathematics, philosophy of science, and philosophical
logic; he has published on those topics in the Journal of Philosophy, Mind, Noˆus,
Philosophical Quarterly, Philosophical Review, Journal of Philosophical Logic, and
others.
Christopher Gauker isProfessorofPhilosophy,UniversityofCincinnati.Heis
the author of Thinking Out Loud: An Essay on the Relation between Thought and
Language (Princeton University Press, 1994), Words without Meaning (MIT Press,
2003) and Conditionals in Context (MIT Press, forthcoming). He is hoping for a
renaissanceinphilosophy.
MichaelGlanzbergisAssociateProfessorofPhilosophy,UniversityofCalifornia
atDavis.Heworksmainlyonlogicandthephilosophyoflanguage.Hehaspublished
articlesontruth, paradox, thesemantics/pragmaticsboundary, presupposition,and
demonstratives.
viii ListofContributors
Dorothy Grover isAdjunctProfessorofPhilosophy,Canterbury,andProfessor
Emeritus at the University of Illinois at Chicago. She has published extensively in
philosophicallogic,formallogicandistheoriginatoroftheprosententialtheoryof
truth.SheistheauthorofAProsententialTheoryofTruth(PrincetonUniversityPress).
AnilGuptaisDistinguishedProfessorofPhilosophy,UniversityofPittsburgh.His
research interests lie in logic, epistemology, and metaphysics. His publications on
theconceptoftruthinclude‘TruthandParadox’,‘ACritiqueofDeflationism’,and
TheRevisionTheoryofTruth(writtenwithNuelBelnap).
VolkerHalbachisFellowofNewCollegeandLecturer,UniversityofOxford.His
researchinterestsincludelogic,philosophyoflanguage,epistemologyandphilosophy
ofmathematics.Inparticular,hehasworkedonaxiomatictheoriesoftruth.Heisthe
authorofAxiomatischeWahrheitstheorienandarticlesinMind,theJournalofSymbolic
Logic, the Notre Dame Journal of Formal Logic, the Journal of Philosophical Logic,
Erkenntnis,Synthese,andotherjournals.
LeonHorstenisProfessorofPhilosophy,UniversityofLeuven.Hismainresearch
area is philosophical logic: truth and paradox, the paradox of the knower, and that
of provability. He has published on these subjects in journals including Journal
ofPhilosophicalLogic,NotreDameJournalofFormalLogic,JournalofSymbolicLogic,
Synthese,andErkenntnis.TogetherwithVolkerHalbach,hehaspublishedPrinciplesof
Truth(OntosVerlag,2004).Healsoworksonproblemsinmetaphysics,epistemol-
ogy,andphilosophyofmathematics.
Paul Horwich is Professor of Philosophy, New York University. His recent
publications include From a Deflationary Point of View (Oxford University Press,
2004)andReflectionsonMeaning(OxfordUniversityPress,2005).
GrahamPriestisBoyceGibsonProfessorofPhilosophy,UniversityofMelbourne,
andArche´ProfessorialFellow,DepartmentofLogicandMetaphysics,Universityof
St Andrews. His books include In Contradiction, Beyond the Limits of Thought,
IntroductiontoNon-ClassicalLogicandTowardsNon-Being(forthcoming).
Greg Restall isAssociateProfessorofPhilosophy,UniversityofMelbourne,and
FellowoftheAustralianAcademyofHumanities.Hismainresearchinterestsarein
logic,bothformalandphilosophical,andhehaspublishedpapersinthoseareas.His
booksincludeAnIntroductiontoSubstructuralLogics(Routledge),Logic(Routledge),
and Logical Pluralism (Oxford University Press, 2005). He is currently working in
prooftheoryanditsconnectionstomeaningtheory.
AlanWeirisSeniorLecturer,Queen’sUniversityBelfast,NorthernIreland.Hehas
alsotaughtattheUniversitiesofEdinburghandBirminghamandatBalliolCollege,
Oxford. He has published articles on logic and philosophy of mathematics in
anumberofjournalsincludingMind,PhilosophiaMathematica,NotreDameJournal
of Formal Logic, and Grazer Philosophische Studien, and contributed chapters in
anumberofvolumespublishedbyOxfordUniversityPress.
A Short Introduction
JCBealland Bradley Armour-Garb
Typicalintroductoryessays aimto dooneoftwothings (orboth):either providea
synopsis of the individual essays or provide suYcient background material for the
essays. This introductory essay is atypical. The essays in this volume are self-con-
tained,forthemostpart,andtherelevantbackgroundmaterialiscoveredelsewhere.
Accordingly,ourmodestaiminthisintroduction,asidefromprovidingreferencesfor
backgroundmaterial(see§4),istogiveabriefsketchofthemotivation:whyavolume
devotedtothenarrowtopicofdeXationismandparadox?
1. DEFLATIONARY THEORIES IN ONE BROAD STROKE
DeXationarytheoriesoftruth(andsemanticnotions,generally)aregenerallycharac-
terisednegatively,intermsofacontrastwithmoresubstantialtheoriesoftruth(and,
again,ofothersemanticnotions),whichtheyaimtodeXate.Forpresentpurposes,we
maycharacteriseadeXationarytheoryoftruthasembracingthefundamentalequiva-
lenceofTrue(A)andA.
What does ‘equivalence’mean here? DiVerent answers yield diVerent versions of
deXationism,andwewillnotheresurveytheWeld;however,attheveryleast,True(A)
and A are taken to be materially equivalent – each enjoying the same ‘semantic
status’.1
The givenequivalences are‘fundamental’inthatthey areboth conceptuallyand
explanatorilybasic.Tosaythattheyareconceptuallybasicistosaythatthereareno
‘deeperfacts’aboutthegivennotion(truth,denotation),intermsofwhichitcanbe
deWnedorintermsofwhichthegivenequivalencesthemselvescanbeexplained.
Conceptually,suchequivalencesarebrute.Theupshotofsuchconceptualfunda-
mentalityisthattheequivalencesaremoreorlessanalytic,aswellasbeingnecessary
and a priori. To say that they are explanatorily basic is to say that our ‘truth’-talk is
1 The same applies to other basic semantic notions, like denotation, where Denotes (b, c) is
‘equivalent’toTrue(b¼c).Thegivenequivalencewithrespectto‘denotation’may—andoften
will—bequaliWedwithanantecedentconditionconcerningexistence,orperhapssome‘free’version,
employingafreelogic,willbegiven.Thedetailsareirrelevant,forthisintroduction,astheindividual
essayscontainedinthisvolumeadequatelyelaborate,whenrelevant.