The Law of Non-Contradiction

452 Pages·2004·5.64 MB·English

by  Graham Priest

The Law of Non-Contradiction
New Philosophical Essays
editedby
GrahamPriest,JCBeall,
and
BradleyArmour-Garb
CLARENDON PRESS · OXFORD
3
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Contents
ListofContributors ix
Introduction:AttheIntersectionofTruthandFalsity 1
JCBeall
PartI: SettinguptheDebate
1. What’sSoBadAboutContradictions? 23
GrahamPriest
PartII: WhatistheLNC?
2. OntheFormalizationoftheLawofNon-Contradiction 41
RossT.Brady
3. WhatisaContradiction? 49
PatrickGrim
4. LawsofNon-Contradiction,Lawsofthe
ExcludedMiddle,andLogics 73
GregRestall
5. OptionNegationandDialetheias 85
R.M.Sainsbury
6. ConjunctionandContradiction 93
AchilleC.Varzi
PartIII: MethodologicalIssuesintheDebate
7. DiagnosingDialetheism 113
BradleyArmour-Garb
8. KnowledgeandNon-Contradiction 126
BrysonBrown
9. LogicalNon-Apriorismandthe‘Law’ofNon-Contradiction 156
OtávioBuenoandMarkColyvan
viii Contents
10. LetterstoBeallandPriest 176
DavidLewis
11. RevisingLogic 178
MichaelD.Resnik
PartIV: AgainsttheLNC
12. TrueandFalse—AsIf 197
JCBeall
13. ThePhilosophicalBasisofWhat?TheAnti-Realist
RoutetoDialetheism 217
JonCogburn
14. ‘ToPeeandnottoPee?’CouldThat BetheQuestion?
(FurtherReflectionsofTheDog) 235
JayGarfield
15. RealismandDialetheism 245
FrederickKroon
16. SemanticDialetheism 264
EdwinD.Mares
17. Ramsey’sDialetheism 276
VannMcGee
PartV: FortheLNC
18. TheBarber,Russell’sParadox,Catch-22,GodandMore:
ADefenceofaWittgensteinianConceptionofContradiction 295
LaurenceGoldstein
19. ACritiqueofDialetheism 314
GregLittmannandKeithSimmons
20. SimpleTruth,Contradiction,andConsistency 336
StewartShapiro
21. AnAnti-RealistCritiqueofDialetheism 355
NeilTennant
22. ThereAreNoTrueContradictions 385
AlanWeir
23. InDefenseoftheLawofNon-Contradiction 418
EdwardN.Zalta
Index 437
List of Contributors
Bradley Armour-Garb is Assistant Professor of Philosophy at the State Uni-
versity of New York at Albany. For as long as he can remember, he has had a
special fascination with paradoxes, although his chief research focuses on the
logic,language,andmetaphysicsof truth(andfalsity). Hehaspublishedpapers
inAnalysis,AustralasianJournalofPhilosophy,JournalofPhilosophicalLogic,Nouˆs,
andSynthese,amongstanumberofotherjournalsandcollections.
JCBeall isAssociate Professor of Philosophy at the University of Connecticut.
Hischief philosophicalinterestsincludetruth,logic,language,andmetaphysics,
andhehasanincessantpreoccupationwithparadoxes.Beall’sbooksincludeLiars
andHeaps(editor,2003),PossibilitiesandParadox:AnIntroductiontoModaland
Many-Valued Logic (with Bas van Fraassen, 2003), and Logical Pluralism (with
GregRestall,2004);heiscurrentlyworkingonamonographontruth,falsity,and
paradox(undercontractwithOxfordUniversityPress).
RossBradyisReaderandAssociateProfessorinPhilosophyatLaTrobeUniversity
inMelbourne,Australia.Hisresearchinterestsareinformallogic,especiallyrelev-
antlogic,andintheset-theoreticandsemanticparadoxes.Heisajointauthorof
RelevantLogicsandtheirRivals,vol.1(Ridgeview,1982),andtheeditorofRelevant
LogicsandtheirRivals,vol.2(Ashgate,2003).Hisbook,UniversalLogic(CSLI),is
forthcoming.
BrysonBrown is Professor and Chair of Philosophy at the University of Leth-
bridge.Hisphilosophicalinterestscentreonlogic,especiallyparaconsistentlogic,
and philosophy of science. He is co-author, with David Braybrooke and Peter
Schotch, of Logic on the Track of Social Change (1995). Recent articles include
‘Chunk and Permeate’ (co-authored with Graham Priest) in Journal of Philo-
sophical Logic, ‘The Pragmatics of Empirical Adequacy’ in Australasian Journal
of Philosophy, and ‘Notes on Hume and Skepticism of the Senses’ in Croatian
JournalofPhilosophy.
OtÁvio Bueno is Associate Professor of Philosophy at the University of South
Carolina. Hisresearchareasincludephilosophyof science,philosophyof math-
ematics, philosophy of logic and paraconsistent logic. He has published papers
inPhilosophyofScience,Synthese,JournalofPhilosophicalLogic,Analysis,Studies
inHistoryandPhilosophyof Science, Erkenntnis, HistoryandPhilosophyof Logic,
among many other journals and collections. He is the author of Constructive
Empiricism:ARestatementandDefenseandElementsofParaconsistentSetTheory
(withNewtondaCostaandJean-YvesBéziau).
x ListofContributors
JonCogburnisanAssistantProfessorofPhilosophyatLouisianaStateUniversity.
His philosophical interests include: realism/anti-realism debates, the computa-
tional theory of mind, vagueness, the sociology of cognitive science, and the
metaphysicsandaestheticsofvideogames.
MarkColyvanisProfessorof PhilosophyattheUniversityof Queensland. His
mainresearchinterestsareinphilosophyof mathematics,philosophyof science,
philosophy of logic and metaphysics. He is the author of The Indispensability of
Mathematics(OxfordUniversityPress,2001)andco-authorof EcologicalOrbits:
HowPlanetsMoveandPopulationsGrow(OxfordUniversityPress,2004).
Jay Garfield is Doris Silbert Professor in the Humanities and Professor of
Philosophy at Smith College, Professor in the graduate faculty of Philosophy
at the University of Massachusetts, Professorial Fellow at the University of
MelbourneandAdjunctProfessorofPhilosophyattheCentralInstituteofHigher
TibetanStudies. Hisinterestsincludethephilosophyof logic,thephilosophyof
mind,foundationsof cognitivescience,epistemology,Buddhistphilosophy,and
cross-cultural hermeneutics. His recent books inlcude Fundamental Wisdom of
the MiddleWay: Nagarjuna’s Mulamadhyamakakarika (Oxford University Press)
andEmptyWords:BuddhistPhilosophyandCross-CulturalInterpretation(Oxford
UniversityPress).
Laurence Goldstein is Professor of the Philosophy of Language and Mind
at the University of Hong Kong. His latest book is Clear and Queer Thinking:
Wittgenstein’sDevelopmentandhisRelevancetoModernThought;hisnextisThe
Liar,theBaldManandtheHangman.
Patrick Grim is SUNY Distinguished Teaching Professor at the State Univer-
sity of New York at Stony Brook. He is author of The Incomplete Universe and
ThePhilosophicalComputerandisfoundingco-editoroftwenty-fourvolumesof
ThePhilosopher’sAnnual.Grimworksinphilosophicallogic,contemporarymeta-
physics, ethics, and philosophy of religion. His current work in computational
modellingappearsinscholarlyjournalsacrossarangeofdisciplines.
Frederick Kroon is Associate Professor of Philosophy at the University of
Auckland.Hehaspublishedarticlesin,amongotherareas,computabilitytheory,
thetheoryofreference,thenatureofrationality,andthesemanticsoffiction.His
bookTheRoutesofReferencewillbepublishedbyOxfordUniversityPressin2005.
Greg Littmann has recently completed his Ph.D. at the University of North
Carolina at Chapel Hill, and is currently an Instructor in the Department of
PhilosophyattheSouthernIllinoisUniversityatEdwardsville(SIUE).
EdwinMares is a senior lecturer in Philosophy and member of the Centre for
Logic,LanguageandComputationatVictoriaUniversityofWellington.Heisthe
author of articles on various branches of logic and of the books Relevant Logic:
A Philosophical Introduction and (with Stuart Brock) Realism and Anti-Realism
(forthcoming).
ListofContributors xi
Graham Priest is Boyce Gibson Professor of Philosophy at the University of
Melbourne, and Arché Professorial Fellow at the University of St Andrews. His
philosophicalinterestsincludelogic,metaphysics,andthehistoryof philosophy
(WestandEast).HisbooksincludeInContradiction,BeyondtheLimitsofThought,
AnIntroductiontoNon-ClassicalLogicandTowardsNon-Being(forthcoming).
MichaelD.ResnikisaUniversityDistinguishedProfessorofPhilosophyatthe
University of North Carolina at Chapel Hill. He has written extensively in the
philosophyofmathematicsandthephilosophyoflogic.
GregRestallisAssociateProfessorofPhilosophyattheUniversityofMelbourne.
Hisacademicinterestsincludebothphilosophicallogicandformallogic,together
with the history of analytic philosophy and meaning theory. He has writ-
ten An Introduction to Substructural Logics (Routledge 2000), Logic (Routledge,
forthcoming)andLogicalPluralismwithJCBeall(Oxford,forthcoming).
R.M.SainsburyisProfessorof PhilosophyattheUniversityof TexasatAustin,
andSusanStebbingProfessoratKing’sCollege,London.HeistheauthorofRussell
(1979),Paradoxes(2ndedn.1995),LogicalForms(2ndedn.2000),DepartingFrom
Frege(2002)andReferenceWithoutReferents(forthcoming).
Stewart Shapiro is the O’Donnell Professor of Philosophy at The Ohio State
University and Arché Professorial Fellow at the University of St Andrews. His
major works include Foundations without Foundationalism (Oxford University
Press, 1991), which is an articulation and defence of second-order logic; Philo-
sophy of Mathematics: Structure and Ontology (Oxford University Press, 1997),
a presentation of structuralism; and his text in the philosophy of mathematics,
ThinkingaboutMathematics(OxfordUniversityPress,2000).
KeithSimmonsisProfessorofPhilosophyattheUniversityofNorthCarolinaat
ChapelHill.HeistheauthorofUniversalityandtheLiar,andeditor(withSimon
Blackburn) of Truth, in the series Oxford Readings in Philosophy. His published
articlesaremainlyinlogic,historyoflogic,philosophyoflanguage,metaphysics,
andethics.Heiscurrentlyatworkonamonographonthelogicalparadoxesand
(withDoritBar-On)amonographondeflationism.
NeilTennantisHumanitiesDistinguishedProfessorofPhilosophyandDistin-
guished University Scholar at the Ohio State University. His research interests
include mathematical, philosophical and computational logic, and the philo-
sophy of language, mind, mathematics, and science. His books include Natural
Logic; Philosophy, Evolution and Human Nature (with Florian von Schilcher);
Anti-RealismandLogic;Autologic;andTheTamingofTheTrue.
Achile C. Varzi is Associate Professor of Philosophy at Columbia University,
NewYork.Hismainresearchinterestsareinlogic,metaphysics,andthephilosophy
of language. His books include An Essay in Universal Semantics (Kluwer, 1999),
Parts and Places (with R. Casati, MIT Press, 1999), Theory and Problems of
Logic (with J. Nolt and D. Rohatyn, McGraw-Hill, 1998) and Holes and Other
xii ListofContributors
Superficialities(withR.Casati,MITPress,1994).Hispapersappearinseveralbooks
and journals, including Mind, Nouˆs, Philosophy and Phenomenological Research,
AustralasianJournalofPhilosophy,Philosophy,PhilosophicalStudies,Philosophical
Topics, Journal of Philosophical Logic, Notre Dame Journal of Formal Logic. Cur-
rentlyheisaneditorof TheJournalof Philosophyandanadvisoryeditorof The
MonistandofDialectica.
AlanWeirisaSeniorLectureratQueen’sUniversityBelfast,NorthernIreland.He
hasalsotaughtattheUniversitiesof EdinburghandBirmingham;andatBalliol
College, Oxford. He has published articles on logic and philosophy of math-
ematics in a number of collections and in journals including Mind, Philosophia
Mathematica,theNotreDameJournalofFormalLogicandAnalysis.
Edward N. Zalta <http://mally.stanford.edu/zalta.html> is a Senior Research
ScholaratStanfordUniversity’sCenterfortheStudyofLanguageandInformation.
Hisinterestsincludemetaphysicsandformalontology,philosophyof logic,and
philosophy of mathematics. He has published two books, Abstract Objects: An
IntroductiontoAxiomaticMetaphysicsandIntensionalLogicandtheMetaphysicsof
Intentionality.
Introduction: At the Intersection of
Truth and Falsity
JCBeall
‘Nowwewilltakeanotherlineofreasoning.Whenyoufollowtwoseparate
chains of thought, Watson, you will find some point of intersection which
shouldapproximatetothetruth.’—SherlockHolmes,in‘TheDisappearance
ofLadyFrancesCarfax’.
1. TOWARDS THE INTERSECTION
Suppose that we have (at least) two categories X and Y for any meaningful,
declarative sentence A of our language.É Pending further information about X
andY,thereseemtobefouroptionsforanarbitrarysentenceA:
» AisonlyinX
» AisonlyinY
» AisinbothXandY
» AisinneitherXnorY
Whether each such‘option’ is logically possible depends not only on our logic
(aboutwhichmorebelow)butonthedetailsofXandY.
Suppose that X comprises all (and only) sentences composed of exactly six
words,andYthosewithexactlynineteenwords.Inthatcase,onlythethirdoption
isruledout:XandYareexclusive—theirintersectionX∩Yisempty—sinceno
Acanbecomposedofexactlysixwordsandalsobecomposedofexactlynineteen
words.ÊDespitebeingexclusive,XandYarenotexhaustive—theirunionX∪Y
doesnotexhaustallsentences—sincesomeAmayfallintoneitherXnorY.(Just
consider‘MaxsatonAgnes’.)
Consideranotherexample.LetXcompriseallsentencesofyourfavouritenovel
andY yourall-timefavouritesentences. Inthatcase,exclusionisnotruledout;
theintersectionofXandYmaywellbenon-empty.(Supposethatyourfavourite
sentenceisthefirstsentenceofyourfavouritenovel.)Presumably,XandYarenot
É
Henceforth,‘sentence’isusedformeaningful,declarativesentences.
Ê
Actually,eventhisisabitcontentious,sincethereareinconsistent(butnon-trivial)arithmeticsin
which19and6‘collapse’.(See[29].)