Vagueness in context

241 Pages·2006·1.185 MB·English

by  Shapiro, Stewart

VAGUENESS IN CONTEXT
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Vagueness in Context
STEWART SHAPIRO
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1.Vagueness(Philosophy) 2.Semantics(Philosophy) 3.Languageandlanguages—
Philosophy. I.Title.
B105.V33S532006 1210.68—dc22 2005026129
TypesetbyNewgenImagingSystems(P)Ltd.,Chennai,India
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ISBN0–19–928039–8 978–0–19–928039–1
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To my mother, Florence Feldman Shapiro.
There is no vagueness in her devotion and strength.
Preface
The purpose of this work is to develop a philosophical and a formal, model-
theoretic account of the meaning, function, and logic of vague terms in an
idealized version of a natural language like English. The essay has a dialectical
structure, typical of much work in logic and formal semantics. The first
chapterprovidesasimplified,perhapsnaive,accountofhowvaguenessarisesin
language, and is manifest in the use of language. It is a commonplace that the
extensions of vague terms vary with such contextual factors as the comparison
class and paradigm cases. A person can betall with respect to male accountants
and not tall (or even short) with respect to professional basketball players.
Apersoncanbewealthywithrespecttolocalbusinesstycoons,butnotwealthy
with respect to CEOs of major software companies. The main feature of the
present account is that the extensions (and anti-extensions) of vague terms also
vary in the course of a conversation, even after the external contextual features,
suchasthecomparisonclass,arefixed.Acentralthesisoftheviewisthat,insome
cases, a competent speaker of the language can go either way in the borderline
area of a vague predicate without sinning against the meaning of the words
and the non-linguistic facts. I call this open-texture, borrowing the term from
Friedrich Waismann.
Itisperhapsgettingcommontousetheterm‘‘contextualist’’forviewsthatthe
meanings of the terms in question—vague ones in this case—vary from context
tocontext.Nosuchclaimismadehere.Itseemsabsurdtosaythatthemeaning
of a vague term changes every time a borderline case is decided in the course
ofaconversation,butIdonothavesettledviewsonwhatcountsas‘‘meaning’’.
I continue to use the term ‘‘contextualist’’ to characterize the informal, philo-
sophicalelaborationofthepresentaccount.Nothingturnsonthis,however,and
I will be glad to give up the term.
Chapter2isashortintroductiononthepurposeandfunctionofformallogic.
Iadoptaperspectivethatmodeltheoryprovidesamathematicalmodelofcertain
aspectsofthecorrectuseofcertainterms,inroughlythesamesenseastheBohr
model is a model of the atom, and a point-mass is a model of an extended
physicalobject.Truthinamodelisamodeloftruth,or,tobeabitmoreprecise,
a model of the truth conditions of natural language sentences. Mathematical
models are rarely, if ever, perfect matches of what they are models of. In the
present case, artifacts are introduced from the fact that the model theory takes
placeinsettheory.Settheory,ofcourse,isnotvague,butitcanbeusedtomodel
thesemanticandpragmaticbehaviorofvagueterms.Insuchcases,onemustbe
careful not to draw conclusions about the phenomena being modeled from
artifacts of the model.
Preface vii
Chapter 3 begins to provide a technical model theory, using the resources of
mathematicallogic,forvaguenessinsomeformalizedlanguages.Thesystemhas
asimilarstructuretothesupervaluationistapproach,employingthenotionofa
sharpening (or precisification) of a base interpretation. In line with the philo-
sophicalaccount,however,thenotionofsuper-truthdoesnotplayacentralrole
inthedevelopmentofvalidity.ThemodeltheoryismuchlikethatoftheKripke
semanticsforintuitionisticlogic,exceptthatbothextensionsandanti-extensions
vary,inconcertwitheachother,throughoutagivenframe.Andthesystemdoes
not rely on completely sharp interpretations. In Ch. 4, various connectives and
quantifiersaredefined,andwesettleonalocalnotionofvalidity.Theultimate
goal, of course, is to delimit a plausible notion of logical consequence, and to
explore what happens with the sorites paradox.
Itmightbenotedthatthenotionof‘‘context’’doesnotappear,assuch,inthe
formal development. Several features of the deployment of vague terms can go
underthatname,andIseenoneedtocalloneofthemthecontextofutterance.
This might attenuate any misunderstandings of the philosophical term
‘‘contextualist’’.
Problems with the simplified account and some unnatural features of
the model theory lead to refinements of the philosophical account, the model-
theoretic semantics, and perhaps the logic as well. Chapter 5 deals with what
passes for higher-order vagueness—vagueness in the notions of ‘‘determinacy’’
and ‘‘borderline’’. The philosophical picture is developed, by extending and
modifying the account presented in Ch. 1. This is followed with the required
modifications to the model theory, and the central meta-theorems.
Up to that point in the book, the treatment concerns only predicates (or
properties). Chapter 6 deals with singular terms (or objects). Some physical
objects,suchastheNorthSea,seemtohavefuzzyboundaries.Ifyoupushthings,
perhaps every physical object has fuzzy boundaries. A second concern of this
chapteriswithapparentindeterminaciesinhowtocountcertainobjects.Dowe
have one cloud or two in the sky? One person or two in a given room? A third
itemofinterestareabstractterms,suchasincomegroupsandheights,thatalso
seem to be subject to sorites, since the underlying relation is not transitive. As
withCh.5,thephilosophicalaccountismodifiedtoaccommodatetheitemsin
question—vaguesingularterms—andthentheneededadditionsandchangesto
the model theory are sketched.
Chapter7beginswiththequestionofwhethervaguenessis(merely)alinguistic
phenomenon,concerninghowwedescribetheworld,orwhetheritistheworld
itselfthatisvague.Tobefrank,Iexpressfrustrationatthisissueofmetaphysical
vagueness,ratherthanadjudicatingitonewayortheother.AsIseeit,vaguenessis
a linguistic phenomenon, due to kinds of languages that humans speak. But
vaguenessisalsoduetotheworldwefindourselvesin,aswetrytocommunicate
featuresofittoeachother.Vaguenessisalsoduetothekindsofbeingsweare.Isee
no need to blame any one of these features for the pervasive phenomenon of
viii Preface
vagueness.ThesecondhalfofCh.7concernstheobjectivityofvaguediscourse.
Perhapsthisiswhatisatstakeintypicaldiscussionofmetaphysicalvagueness.
The book closes with a brief Appendix on Friedrich Waismann’s account of
open-texture and analyticity. His account of the openness of language lends
perspective to the present account of vagueness.
I have been working on this project, off and on, for several years. Along the
way,Iincurredmanyintellectualdebts,andamcertaintohaveforgottensomeof
them. But this does not excuse me from acknowledging at least some of them.
I was first introduced to the issues and some of the literature on vagueness
when I served on the Dissertation committees of Elizabeth Cohen and Rick
DeWitt.Theformerdefendedsupervaluationandthelatteramany-valuedlogic.
Intense conversations with them, and with their supervisor, George Schumm,
and watching the three of them interact, got me to see the strengths and, more
importantly,theweaknessesofthosetwoapproaches.Althougheachwasclearly
onto something, the solution had to lie elsewhere. I have learned a lot from
conversations with George over the years since.
My largest debt is to my colleague and friend Diana Raffman. Her original
(contextualist?) resolution of the sorites paradox shows how psychological and
pragmatic features go into fixing the extension of vague terms on any given
utterance(Raffman1994,1996).Theoverallstructureofherresolutioninspired
thepresentphilosophicalaccount,whichisformulatedintermsofconversations
ratherthanpsychologicalstates,anditsuggestedtheconcomitantmodeltheory.
Wetaughttwograduateseminarsonvaguenesstogether.Oneofthesefocusedon
the more or less standard literature (at the time), and the other delved into our
own evolving accounts. In both cases I benefited immensely from Diana’s pre-
sentations and from student participation. Diana is a wonderful critic, helping
me to see where I have gone wrong and, more importantly, helping me to see
howtoputthings.EvenwhenshethinksIamfundamentallymistaken,shehas
theabilitytodelveintohowIseethings(oramtryingtoseethings)andhelpme
explore the terrain. I could not have written this book without her, and I only
hope that I have been as useful to her own work as she has been to mine.
Turning to my second academic home, the Arche´ Research Centre at the
University of St Andrews has been extremely useful in this, and many other
projects. Over the past few years, I gave three or four series of seminars on this
project(depending onhowto countsuchthings).EventhoughIwentoverthe
samematerialseveraltimes,asitwasrefined,theaudiencesnevertiredofdelving
into the view, finding shortcomings, and helping me to formulate things
properly.Onecannotunderestimatethevalueofadedicatedgroupofcolleagues
whobecomefamiliarwiththebasicview,andthenuancesofitsmodeltheory,so
that we can explore its extensions together.
I owe much to Crispin Wright. Even though we approached the subject of
vagueness from rather different perspectives, our views have evolved together
Preface ix
overtheyears,totheextentthatwenowagreemorethanwedisagree.Crispin’s
influence on my view derives both from his voluminous and insightful pub-
lications on vagueness, and from countless hours of conversation, both in sem-
inar and in private. This will become apparent as the reader works through the
present book.
My former student Roy Cook, who spent four years at Arche´ as a post-
doctoral fellow in the philosophy of mathematics project, helped me to
formulate and elaborate the ‘‘logic as model’’ approach, and he helped me to
formulate and then clean up the model theory, preventing some embarrassing
errors.Theotherpost-doctoralfellowintheArche´mathematicsproject,Agust´ın
Rayo, has been the most persistent critic of this project. He pointed out many
shortcomingsandinfelicitiesintheproject,andhelpedmetoformulateitmore
forcefully. He also helped me to see where I agreed and where I disagreed
with various key claims in the literature, thus preventing many potential
misunderstandings.
I gave talks on the basic view, without the model theory, at a number of
conferences and colloquia. These include the University of Maryland, the
University of Florida, Union College, Hebrew University of Jerusalem,
UniversityofLondon,theBuffaloLogicColloquium,andtheconference‘‘Liars
and Heaps’’, held at the University of Connecticut. I am much indebted to the
audiences for helping me to sharpen the view, and to avoid errors. An early
versionofCh.1appearedas‘‘VaguenessandConversation’’intheproceedings,
Liars and Heaps (edited by JC Beall, Oxford, Oxford University Press, 2003).
Thanks especially to my commentator on that occasion, Rosanna Keefe. Her
remarks (published in the proceedings) helped me to reformulate some key
theses. Thanks also to Rosanna for many hours of conversation and corres-
pondenceoverthepastfewyears,concerningboththischapterandmuchofthe
rest of the book.
AversionofthebeginningofCh.5,onhigher-ordervagueness,isthesubject
ofaJointSessionsession,andappearsinthesupplementtotheProceedingsofthe
Aristotelian Society. Thanks to the respondent, my St Andrews colleague and
friend Patrick Greenough. Patrick was instrumental in the development of this
book, both in the aforementioned Arche´ seminars and in countless hours of
conversation.
Ihavebenefitedfromconversationandcorrespondencewithmanyothersover
the years. The list includes Louise Antony, Jack Arnold, Julius Barbanel, Julian
Cole, Mark Colyvan, Neil Cooper, Richard Dietz, Haim Gaifman, Katherine
Hawley, Robert Kraut, Joseph Levine, Kirk Ludwig, Fraser MacBride, Michael
Morreau, Sebastiano Moruzzi, Carl Posy, Graham Priest, Greg Ray, Georges
Rey,Stephen Schiffer, KeithSimmons, NicholasJ.Smith,MarkSteiner,Jamie
Tappenden,NeilTennant,BrianWeatherson,TimothyWilliamson,EliaZardini,
and several anonymous referees for OxfordUniversityPress. I apologize tothose