Paradox and Paraconsistency : Conflict Resolution in the Abstract Sciences

381 Pages·2002·3.606 MB·English

by  John Woods

ParadoxandParaconsistency
ConflictResolutionintheAbstractSciences
In a world plagued by disagreement and conflict, one might expect
thattheexactsciencesoflogicandmathematicswouldprovideasafe
harbor. In fact, these disciplines are rife with internal divisions be-
tweendifferent,oftenincompatiblesystems.Dothesedisagreements
admit of resolution? Can such resolution be achieved without dis-
turbingassumptionsthatthetheoremsoflogicandmathematicsstate
objectivetruthsabouttherealworld?
In this original and historically rich book, John Woods explores
apparentlyintractabledisagreementsinlogicandthefoundationsof
mathematicsandsetsoutconflictresolutionstrategiesthatevadeor
disarm these stalemates. Among the conflicts to which these strate-
giesareappliedare:thedisagreementbetweenclassicalandrelevant
logicians;Quine’sattackonquantifiedmodallogic;disagreementas
towhetherdialethiclogichasanadequatemotivation;conflictsabout
how to understand the paradox of sets and the Liar paradox; the
vexedrelationshipbetweenmodernlogicandtheoriesofreasoning;
andconditionsunderwhichlogicallawsexhibitnormativeforce.
An important subtheme of the book is the extent to which plu-
ralisminlogicandthephilosophyofmathematicsunderminesrealist
assumptions.Woods’sresponseisanaccountoftruthinwhichrealism
isanirresistibleepiphenomenon.
Thisbookmakesanimportantcontributiontosuchareasofphilos-
ophyaslogic,philosophyoflanguage,andargumentationtheory,but
italsowillbeofinteresttomathematiciansandcomputerscientists.
JohnWoodsisDirectoroftheAbductiveSystemsGroup,University
ofBritishColumbia.

Paradox and Paraconsistency
Conflict Resolution in the Abstract Sciences
JOHN WOODS
UniversityofBritishColumbia
  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge  , United Kingdom
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridage.org/9780521810944
© John Woods 2003
This book is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2002
- 
isbn-13 978-0-511-07281-9 eBook (EBL)
- 
isbn-10 0-511-07281-3 eBook (EBL)
- 
isbn-13 978-0-521-81094-4 hardback
- 
isbn-10 0-521-81094-9 hardback
isbn--13 978-0-521-00934-8 paperback
- 
isbn-10 0-521-00934-0 paperback
Cambridge University Press has no responsibility for the persistence or accuracy of
s for external or third-party internet websites referred to in this book, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
InMemoryof
RichardSylvan(ne´ Routley),1936–1996.
RobGrootendorst,1944–2000.

Contents
Preface pageix
Prologue:PostmodernLogic xi
1 ConflictintheAbstractSciences 1
2 Modalities 40
3 ManagingInconsistency 80
4 SemanticIntuitions 120
5 SetsandTruth 155
6 Fiction 196
7 CurryingLiars 228
8 Normativity 277
Notes 327
Bibliography 341
Index 359
vii

Preface
Thisworkarisesfromaseriesoflecturesonparaconsistentlogicdeliveredat
theUniversityofGroningeninthespringtermof1988.Therefollowedayear
laterascheduleoflecturesonQuine’sphilosophyoflogic.Thefruitsofthese
endeavorscirculatedforawhileasTheGroningenLecturesonParaconsistent
Logic.Myeffortsweregracedbyexcellentstudentsandgenerouscolleagues.I
amespeciallygratefultoE.M.Barth,JeannePeijnenberg,ErikC.W.Krabbe,
andDavidAtkinsonforsharpcriticismandhelpfulsupport.In1990,aFellow-
shipattheNetherlandsInstituteforAdvancedStudymadeitpossibleforme
tojointheresearchgrouponFallaciesasViolationsofRulesforArgumenta-
tiveDiscourse.Iworkedthereonconflictresolutionstrategiesforintractable
disagreementsinquestionsofpublicpolicy.Onlytowardtheendofmystay
in Wassenaar did it occur to me that such strategies might be extended to
contentious issues in the philosophy of logic and related fields. I owe much
tothestimulationandencouragementofmyNIAScolleagues:projectleader
FransH.vanEemeren,thelateRobGrootendorst,SallyJackson,ScottJacobs,
Agne`svanRees,AgnesVerbeist,DouglasWalton,andCharlesWillard.
Thus was born a preoccupation with conflict resolution in the abstract
sciences, which became the main business of my University of Lethbridge
courseonDeviantLogicin1991and1992.Thedistractionsofotherresearch
projects and heavy administrative responsibilities entailed a postponement
of this one until an appointment as Visiting Scholar in the Department of
Philosophy at Stanford University in 1994 afforded me the stimulation and
leisuretoturnmymindagaintoconflictresolution.InthisIwasmuchhelped
byMichaelBratman,ChairoftheDepartment,JohanvanBenthem,Maurice
Finocchiaro,DavidGrover,andTimothySchroeder.Administrativedutiesne-
cessitatedafurtherpause,buttheprojectcametolifeagainandwascompleted
thankstoaVisitingProfessorshipintheDepartmentofDiscourseAnalysis,
ArgumentationTheory,andRhetoricattheUniversityofAmsterdaminthe
springtermof1998and1999.IamindebtedtotheDepartment’sHead,Frans
H.vanEemeren,andtohis(andmy)colleagues,thelateRobGrootendorst,
ix