Games: Unifying Logic, Language, and Philosophy

403 Pages·2009·2.513 MB·

by  Ondrej Majer, Ahti-Veikko Pietarinen, Tero Tulenheimo (eds.)

GAMES: UNIFYING LOGIC, LANGUAGE, AND PHILOSOPHY
LOGIC,EPISTEMOLOGY,ANDTHEUNITYOFSCIENCE
VOLUME 15
Editors
ShahidRahman,UniversityofLilleIII,France
JohnSymons,UniversityofTexasatElPaso,U.S.A.
EditorialBoard
JeanPaulvanBendegem,FreeUniversityofBrussels,Belgium
JohanvanBenthem,UniversityofAmsterdam,theNetherlands
JacquesDubucs,UniversityofParisI-Sorbonne,France
AnneFagot-LargeaultCollègedeFrance,France
BasvanFraassen,PrincetonUniversity,U.S.A.
DovGabbay,King’sCollegeLondon,U.K.
JaakkoHintikka,BostonUniversity,U.S.A.
KarelLambert,UniversityofCalifornia,Irvine,U.S.A.
GrahamPriest,UniversityofMelbourne,Australia
GabrielSandu,UniversityofHelsinki,Finland
HeinrichWansing,TechnicalUniversityDresden,Germany
TimothyWilliamson,OxfordUniversity,U.K.
Logic,Epistemology,andtheUnityofScienceaimstoreconsiderthequestionoftheunityof
scienceinlightofrecentdevelopmentsinlogic.Atpresent,nosinglelogical,semanticalor
methodologicalframeworkdominatesthephilosophyofscience.However,theeditorsofthis
seriesbelievethatformaltechniqueslike,forexample,independencefriendlylogic,dialogical
logics,multimodallogics,gametheoreticsemanticsandlinearlogics,havethepotentialto
castnewlightnobasicissuesinthediscussionoftheunityofscience.
Thisseriesprovidesavenuewherephilosophersandlogicianscanapplyspecifictechnical
insightstofundamentalphilosophicalproblems.Whiletheseriesisopentoawidevarietyof
perspectives,includingthestudyandanalysisofargumentationandthecriticaldiscussionof
therelationshipbetweenlogicandthephilosophyofscience,theaimistoprovideanintegrated
pictureofthescientificenterpriseinallitsdiversity.
Forothertitlespublishedinthisseries,goto
www.springer.com/series/6936
Games: Unifying Logic,
Language, and Philosophy
(cid:69)(cid:100)(cid:105)(cid:116)(cid:101)(cid:100)(cid:32)(cid:98)(cid:121)
Ondrej Majer
Czech Academy of Sciences, Czech Republic
Ahti-Veikko Pietarinen
University of Helsinki, Finland
Tero Tulenheimo
University of Helsinki, Finland
ABC
(cid:69)(cid:100)(cid:105)(cid:116)(cid:111)(cid:114)(cid:115)
Dr. Ondre j Majer Dr. Tero T ulenheimo
Academy of Sciences of the University of Helsinki
Czech Republic Department of Philosophy
Institute of Philosophy Siltavuorenpenger 20 A
Jilska 1 FI-00014 Helsinki
110 00 Prague 1 P.O. Box 9
Czech Republic Finland
[email protected] [email protected]
Dr. Ahti-V eikko Pietarinen
University of Helsinki
Department of Philosophy
Siltavuorenpenger 20 A
FI-00014 Helsinki
P.O. Box 9
Finland
[email protected]

Coverimage:AdaptationofaPersianastrolabe(brass,1712–13),fromthecollectionoftheMuseumofthe
HistoryofScience,Oxford.Reproducedbypermission.
ISBN978-1-4020-9373-9 e-ISBN978-1-4020-9374-6
LibraryofCongressControlNumber:2008938971
AllRightsReserved
(cid:176)c 2009 SpringerScience+BusinessMediaB.V.
Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby any means,
electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwritten permission from
thePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurposeofbeingenteredandexecuted
onacomputersystem,forexclusiveusebythepurchaserofthework.
Printedonacid-freepaper
9 8 7 6 5 4 3 2 1
springer.com
Contents
Introduction ix
Ondrej Majer, Ahti-Veikko Pietarinen, and Tero Tulenheimo
Part I Philosophical Issues
1 Why Play Logical Games? 3
Mathieu Marion
2 On the Narrow Epistemology of Game-Theoretic Agents 27
Boudewijn de Bruin
3 Interpretation, Coordination and Conformity 37
Hykel Hosni
4 Fallacies as Cognitive Virtues 57
Dov M. Gabbay and John Woods
Part II Game-Theoretic Semantics
5 A Strategic Perspective on IF Games 101
Merlijn Sevenster
6 Towards Evaluation Games for Fuzzy Logics 117
Petr Cintula and Ondrej Majer
7 Games, Quantification and Discourse Structure 139
Robin Clark
Part III Dialogues
8 From Games to Dialogues and Back 153
Shahid Rahman and Tero Tulenheimo
9 Revisiting Giles’s Game 209
Christian G. Fermu¨ller
v
vi Contents
10 Implicit Versus Explicit Knowledge in Dialogical Logic 229
Manuel Rebuschi
Part IV Computation and Mathematics
11 In the Beginning Was Game Semantics 249
Giorgi Japaridze
12 The Problem of Determinacy of Infinite Games
from an Intuitionistic Point of View 351
Wim Veldman
Symbol Index 371
Subject Index 373
Name Index 377
Contributing Authors
BoudewijndeBruin DovM.Gabbay
FacultyofPhilosophy DepartmentofComputerScience
UniversityofGroningen King’sCollegeLondon
OudeBoteringestraat 52 TheStrand
9712GLGroningen LondonWC2R2LS
TheNetherlands England
[email protected] UK
[email protected]
PetrCintula
HykelHosni
InstituteofComputerScience
ScuolaNormaleSuperiore
AcademyofSciences
PiazzadeiCavalieri
oftheCzechRepublic
56100Pisa
PodVodarenskou vezi2
Italy
18207Prague8
[email protected]
CzechRepublic
[email protected]
GiorgiJaparidze
DepartmentofComputingSciences
RobinClark VillanovaUniversity
DepartmentofLinguistics 800LancasterAvenue
619WilliamsHall Villanova,Pennsylvania 19085
UniversityofPennsylvania USA
Philadelphia, PA19104-6305 [email protected]
USA
[email protected] MathieuMarion
De´partementdephilosophie
ChristianG.Fermu¨ller Universite´ duQue´beca` Montre´al
TechnischeUniversita¨tWien Casepostale 8888,succursale
Favoritenstr. 9-11/E1852 Centre-ville
A-1040Wien Montre´al, Que´bec
Austria CanadaH3C3P8
[email protected] [email protected]
vii
viii Contributing Authors
MerlijnSevenster JohnWoods
PhilipsResearch DepartmentofPhilosophy
Prof.Holstlaan4 UniversityofBritishColumbia
5656AAEindhoven 1866MainMallE370
TheNetherlands Vancouver, BC
[email protected] CanadaV6T1Z1
[email protected]
ShahidRahman
[email protected]
U.F.R.dePhilosophie
DomaineUniversitaire“PontdeBois”
OndrejMajer
Universite´ LilleIII
Institute ofPhilosophy
59653Villeneuved’Ascq
AcademyofSciences
France
oftheCzechRepublic
[email protected]
Jilska´ 1,11000Prague
ManuelRebuschi CzechRepublic
Laboratoire d’Histoire des Sciences [email protected]
etdePhilosophie
ArchivesHenriPoincare´ Ahti-VeikkoPietarinen
UMR7117CNRS-Nancy-Universite´ DepartmentofPhilosophy
Universite´ Nancy2 P.O.Box9
23, Bd. Albert Ier-BP 3397. F-54015 00014UniversityofHelsinki
NANCYCedex Finland
France ahti-veikko.pietarinen@helsinki.fi
[email protected]
TeroTulenheimo
WimVeldman
DepartmentofPhilosophy
InstituteforMathematics,
AcademyofFinland
Astrophysics andParticlePhysics
P.O.Box9
RadboudUniversityNijmegen
00014UniversityofHelsinki
P.O.Box9010
Finland
6500GLNijmegen
tero.tulenheimo@helsinki.fi
TheNetherlands
[email protected]
Introduction
Ondrej Majer, Ahti-Veikko Pietarinen, and Tero Tulenheimo
1 Games and logic in philosophy
Recent years have witnessed agrowing interest in the unifying methodolo-
gies over what have been perceived as pretty disparate logical ‘systems’, or
else merely an assortment of formal and mathematical ‘approaches’ to philo-
sophical inquiry. This development has largely been fueled by an increasing
dissatisfaction to what has earlier been taken to be a straightforward outcome
of ‘logical pluralism’ or ‘methodological diversity’. These phrases appear to
reflect the everyday chaos of our academic pursuits rather than any genuine
attempt toclarify thegeneral principles underlying themiscellaneous waysin
whichlogicappearstous.
But the situation is changing. Unity among plurality is emerging in con-
temporary studies in logical philosophy and neighbouring disciplines. This is
a necessary follow-up to the intensive research into the intricacies of logical
systemsandmethodologies performed overtherecentyears.
Thepresent booksuggests onesuchpeculiar butveryunrestrained method-
ologicalperspectiveoverthefieldoflogicanditsapplications inmathematics,
language or computation: games. Anallegory for opposition, cooperation and
coordination, gamesarealsoconcrete objectsofformalstudy.
As a metaphor for argumentation Aristotle’s Topics and its reincarnations
suchasthescholasticArsObligatoriaaresetupasdialogicalduels(Pietarinen,
2003a). Logicsexploiting thisidearesurface inthetwentieth century attempts
to clarify the concepts of argument and proof. The game metaphor has re-
taineditsstrengthincontemporarytheoriesofcomputation(Pietarinen,2003b,
Japaridze,thisvolume),inwhichcomputationisrecastintermsofthesymbio-
sisbetweentheComputingSystem(‘Myself’)anditsEnvironment(‘Nature’).
Inmathematics, thebenefitsofdoing sowerenoteddecades agobyStanislaw
Ulam(1960),whowrotehowamusingitis“toconsiderhowonecan‘gamize’
ix