Applications of formal philosophy : the road less travelled

261 Pages·2017·4.02 MB·English

by  Payette, Gillman, Urbaniak, Rafal

Logic, Argumentation & Reasoning 14
Rafal Urbaniak
Gillman Payette Editors
Applications
of Formal
Philosophy
The Road Less Travelled
Logic, Argumentation & Reasoning
Interdisciplinary Perspectives from the Humanities
and Social Sciences
Volume 14
Series editor
Shahid Rahman
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(cid:129) Argumentation models and studies
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(cid:129) Reception of arguments, persuasion and the impact of power
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Rafal Urbaniak Gillman Payette
(cid:129)
Editors
Applications of Formal
Philosophy
The Road Less Travelled
123
Editors
RafalUrbaniak Gillman Payette
Institute of Philosophy, Department ofPhilosophy
SociologyandJournalism University of British Columbia
University of Gdańsk Vancouver, BC
Gdańsk Canada
Poland
and
Centrefor Logic andPhilosophy
ofScience
GhentUniversity
Ghent
Belgium
ISSN 2214-9120 ISSN 2214-9139 (electronic)
Logic, Argumentation & Reasoning
Interdisciplinary Perspectives from the Humanities andSocial Sciences
ISBN978-3-319-58505-5 ISBN978-3-319-58507-9 (eBook)
DOI 10.1007/978-3-319-58507-9
LibraryofCongressControlNumber:2017945681
©SpringerInternationalPublishingAG2017
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Contents
1 Applied Formal Philosophy: Some Reflections on the Program........ 1
Gillman Payette and Rafal Urbaniak
Part I Human Affairs
2 The Logic of Guilt, Innocence and Legal Discourse.... ..... .... 7
Andreas Kapsner
3 Counterfactuals, Logic Programming and Agent Morality ... .... 25
Luís Moniz Pereira and Ari Saptawijaya
4 The Wisdom of the Multitude: Diversity Versus Size... ..... .... 55
Peter C. Stone and Koji Kagotani
5 A Logic for Human Actions... .... .... .... .... .... ..... .... 73
Clayton Peterson
6 Reasoning with Comparative Moral Judgements:
An Argument for Moral Bayesianism ... .... .... .... ..... .... 113
Ittay Nissan-Rozen
Part II Epistemology
7 Is Theory Choice Using Epistemic Virtues Possible? ... ..... .... 139
Kit Patrick and Kate Hodesdon
8 Abduction Logics: Illustrating Pitfalls of Defeasible Methods . .... 169
Diderik Batens
9 A Multimodal Pragmatic Analysis of the Knowability Paradox....... 195
Massimiliano Carrara, Daniele Chiffi and Davide Sergio
v
vi Contents
Part III Closer to the Core
10 Philosophical Aspects of an Alleged Connection
Between the Axiom of Choice and Predicting the Future..... .... 213
Pawel Pawlowski
11 Counterpossibles, Impossible Worlds, and the Notion
of Similarity... .... .... ..... .... .... .... .... .... ..... .... 221
Maciej Sendłak
12 Grzegorczyk’s Non-Fregean Logics
and Their Formal Properties .. .... .... .... .... .... ..... .... 243
Joanna Golińska-Pilarek and Taneli Huuskonen
Chapter 1
Applied Formal Philosophy: Some
Reflections on the Program
GillmanPayetteandRafalUrbaniak
What is mathematical philosophy? How is it different from philosophy? How is it
applied? As to the first, in mathematical philosophy one uses mathematical tools
to shed light on philosophical questions. Conceived in that way, all mathematical
philosophyisapplied:mathematicalphilosophyisjustmathematicsappliedinphi-
losophy. The pressing question is how mathematical philosophy is really different
fromphilosophy?
Tobesuremathematicalphilosophyisakindofphilosophy.However,somemay
thinkthatitrepresentsaspecialkindofapproachtophilosophy.Andsomethinkthat
thespecial-nessmeansthatitisabetterkindofphilosophy,whileothersthinkthat
itsspecial-nessmeansthatitisinferior.Wewouldliketoofferacountertobothof
theseviews.
Bothoftheseviewstaketheirstartingpointfromthesametendencyinmathemat-
icalphilosophy.Oftenthemathematicaltoolsusedendupbeingveryinterestingin
themselvesandtaketheattentionofmathematicalphilosophers.Thisisonewayto
seewhathashappenedtologicattheendoftheXXthcentury.Thetoolsforstudying
logic became what logicians actually studied. That is what one might describe as
pure mathematical philosophy. Calling it ‘pure’ is not to deride or diminish such
programsofstudy;itprovidesanimportantservice,sinceitthoroughlyinvestigates
the limitations of tools that might be useful at some point. One example is that of
Bayesianepistemology:whileinitiallyonemightbetemptedtoapplyprobabilistic
methodsto(reformulationsof)questionsraisedbyclassicalepistemologists,amajor
stream of research in formal epistemology nowadays focuses on the issue of how
G.Payette
DepartmentofPhilosophy,UniversityofBritishColumbia,Vancouver,BC,Canada
e-mail:[email protected]
B
R.Urbaniak ( )
CentreforLogicandPhilosophyofScience,GhentUniversity,Ghent,Belgium
e-mail:[email protected]
R.Urbaniak
InstituteofPhilosophy,JournalismandSociology,UniversityofGdan´sk,Gdan´sk,Poland
©SpringerInternationalPublishingAG2017 1
R.UrbaniakandG.Payette(eds.),ApplicationsofFormalPhilosophy,
Logic,Argumentation&Reasoning14,DOI10.1007/978-3-319-58507-9_1
2 G.PayetteandR.Urbaniak
usingsuchmethodsistobejustifiedandwhatthebestprobabilisticprinciplesare,
ratherthanonapplyingthemtophilosophicalquestions.
Oneshouldneverbeobtusesoastodismisspure,basicresearch.Butthattendency
towardspureresearchhasgivenmathematicalphilosophyabad,albeitprestigious,
name.Someofthebestanalyticphilosophersofourtimearemathematicalphiloso-
phers.Sothefieldislookedonwithsomeadmirationinsomecircles.Butforothers
thattendencyhastheoppositeeffect.Mathematicalphilosophyspinsitswheelswith-
outeverdoinganycutting—tomixafewmetaphors.Butthatviewisalsomistaken.
Mathematicshasbeenusedtocutwithwildsuccessinanumberofareasofphilos-
ophy.BertrandRussell’sAnIntroductiontoMathematicalPhilosophywasprobably
one of the earliestattempts atapplication. Some mightsuggest thatitshould have
beenentitled“AnIntroductiontothePhilosophyofMathematics”,butitwasaptly
named. What it did was lay out the way to deal with philosophical problems with
mathematical precision. But the field that it then dealt with was mathematics, not
ethicsorepistemology—atleastnotdirectly.Whatearlymathematicalphilosophy
addedwasawaytoapproachphilosophybystatingphilosophicalproblemsprecisely;
itfirstusesmathematicallypreciselanguagestopreciselyreformulateproblems,and
thendeploysmathematicalmethods.
Theobviousthought,then,istofigureouthowtomakelanguagemathematically
precise,andsowegetformallogicanditsapplicationinthephilosophyoflanguage.
That precision was also soon directed toward the foundations of science, but still
undertheguiseofformallogic.Aftermetaphysicsbecameacceptableagain,thattoo
wasanareawherelogicaltoolswereappliedtomakethequestionsclearer.About
thesametimeonecouldseeethicsfinallyenterthecrosshairsoflogicalanalysis—
althoughlogicsforimperativeshadbeenaroundsincetheverybeginningsoflogical
analysis.Thus,mathematicalphilosophylookedlikeitmightbejustthat:applylogic
toanareaofphilosophicalstudy.Theresultwastolookatmathematicalphilosophyas
beingcoextensivewiththe“logicalanalysis”approachtophilosophy.Butthattakes
mathematicalphilosophytobeexhaustedbylogic,andwethinkthatisamistake.
Thereasonwethinkitisamistaketoseemathematicalphilosophyasexhausted
by logic is because that perspective tempts one to reject mathematical philosophy
onthebasisthatitsprogramistotreatlogicalanalysisastherightmethodologyfor
philosophy;itprobablyisn’t.Atoolshouldonlybeusedwhenitwillhelp.Sometimes
logical analysis doesn’t help; sometimes it makes things overly complicated. Or
worse,sometimesitleadsustooversimplifythingsinakindofprocrusteanmanner
andthendrawthewrongconclusions.
Whatwewanttodoinphilosophyis—paraphrasingWilfredSellars—understand
how things, in the most general sense, hang together, in the most general sense.
Logical analysis is very good in mathematics, but mathematics generally is better
suitedforphilosophy,generally.Howwewanttomodelthequestionsweareasking
is left wide open when we look to mathematics generally. But we are also left to
considerwhetherapplyingmathematicsreallyhelps.
Thekindsofanswerswegetwhenweapplymathematicstophilosophicalques-
tionstendtobeonesthatshapetheboundariesofinvestigation.WhenArrowasked:
1 AppliedFormalPhilosophy:SomeReflectionsontheProgram 3
iswelfareeconomicsactuallypossible?Hefoundanedgetothatfield.1 Andthatis
wherephilosophyshouldstarttoo,attheedges.Butthatdoesn’tmeanitistheonly
placeforphilosophy.
Indeed, when people say ‘applied philosophy’ the usual sense of ‘applied’ is
capturedbytheapplicationofphilosophicaltheoriestodiscussionswellwithinthe
boundaries.Appliedmathematicalphilosophyinthismoreusualsenseof‘applied’is
difficult.Theproblemsaremuchmorecomplexandconceptuallydifficultinthethick
ofthings,anddon’tlendthemselvestoclearexpressionwithmathematics.Howdo
characterandemotionaffectthenotionofcorrectmoralaction?Isracearealthing?
We don’t even know where to start with applying mathematics to those questions.
Buttheworkinghypothesisofmathematicalphilosophyisn’tthatweoughttofind
the mathematical tools to apply to such questions. The approach to mathematical
philosophyshouldbetostandreadywithmanytoolsathandwhenthosefieldshave
foundquestionswheremathematicsmighthelp.
That doesn’t mean that mathematical philosophers must sit about waiting for
theotherfieldstocometothem.Certainlynot;gooutandfindproblems.Butthat
kind of expedition must be guided by a kind of Hippocratic oath ‘First, do not
letmathematicsdoanyphilosophicalharm.’Sowecanfinallyanswerthepressing
question:howdoesmathematicalphilosophydifferfromphilosophy?Itisn’taspecial
kindofphilosophy.Itissimplythatsometimesinphilosophymathematicscanhelp
us answer the pressing philosophical questions we have. The hope is, dear reader,
thatyoufindtheessaysinthisbooktohavefollowedthatHippocraticoath.
Acknowledgments Gillman Payette would like to thank the Social Sciences and Humanities
ResearchCouncilofCanadaforsupportingthisworkthroughaBantingPostdoctoralFellowship.
1ThismaybeapoorexamplesinceArrowwasheavilyinfluencedbyoneofhis(undergraduate)
mathematicsteachers:AlfredTarski.Whatinfluencedhimwerenotionsinthelogicofrelations.