CONCEPT CALCULUS: MUCH BETTER THAN

Description

1 CONCEPT CALCULUS: MUCH BETTER THAN Harvey M. Friedman* May 4, 2009 revised August 28, 2009 revised October 31, 2009 ABSTRACT. This is the initial publication on Concept Calculus, which establishes mutual interpretability between formal systems based on informal commonsense concepts and formal systems for mathematics through abstract set theory. Here we work with axioms for better than and much better than, and the Zermelo and Zermelo Frankel axioms for set theory.

• basic facts about interpretation power
• equivalence relation
• t. interpretation
• t1 definable
• zf
• theory of strict linear orderings
• examples of incomparability between natural theories
• logic of informal concepts from common sense thinking
• proof

Sujets

• Alfred Tarski
• Relation
• Interprétation
• Linear
• Common
• Definable

Informations

• Publié par: edwui
• Nombre de lectures: 13

Extrait

WHATISIDENTITY(ASWENOWUSETHEWORD)?
JamesD.Fearon
DepartmentofPoliticalScience
StanfordUniversity
Stanford,CA94305
email:[e-mail]
DRAFT{Commentsappreciated
November3,1999ABSTRACT
Thepaperundertakesanordinarylanguageanalysisofthecurrentmeaningsof\iden-
tity,"acomplicatedandunclearconceptthatnonethelessplaysacentralroleinongoing
debatesineverysub eld ofpoliticalscience(forexample,debatesaboutnational,ethnic,
gender,andstateidentities).\Identity"aswenowknowitderivesmainlytheworkofpsy-
chologistErikEriksoninthe1950s;dictionaryde nitions havenotcaughtup,failingto
capturetheword’scurrentmeaningsineverydayandsocialsciencecontexts. Theanalysis
yieldsthefollowingsummarystatement. Asweuseitnow,an\identity"refertoeither
(a)asocialcategory,de ned bymembershiprulesand(alleged)characteristicattributesor
expectedbehaviors,or(b)sociallydistinguishingfeaturesthatapersontakesaspecialpride
inorviewsasunchangeablebutsociallyconsequential(or(a)and(b)atonce).Inthelatter
sense,\identity"ismodernformulationofdignity,pride,orhonorthatimplicitlylinksthese
tosocialcategories.Thisstatementdi ers fromandismoreconcretethanstandardglosses
o ered bypoliticalscientists;Iargueinadditionthatitallowsustobetterunderstandhow
\identity"canhelpexplainpoliticalactions,andthemeaningofclaimssuchas\identities
aresociallyconstructed."Finally,Iarguethatordinarylanguageanalysisisavaluableand
perhapsessentialtoolintheclari cation ofsocialscienceconceptsthathavestrongrootsin
everdayspeech,averycommonoccurrence.1 Introduction
Inrecentyears,scholarsworkinginaremarkablearrayofsocialscienceandhumanities
disciplineshavetakenanintenseinterestinquestionsconcerningidentity. Withinpolitical
science,forexample,we nd theconceptof\identity"atthecenteroflivelydebatesin
everymajorsub eld. StudentsofAmericanpoliticshavedevotedmuchnewresearchtothe
\identitypolitics"ofrace,genderandsexuality.Incomparativepolitics,\identity"playsa
centralroleinworkonnationalismandethniccon ict (Horowitz1985;Smith1991;Deng
1995;Laitin1999). Ininternationalrelations,theideaof\stateidentity"isattheheart
ofconstructivistcritiquesofrealismandanalysesofstatesovereignty(Wendt1992;Wendt
1999;Katzenstein1996;LapidandKratochwil1996;BierstekerandWeber1996). And
inpoliticaltheory,questionsof\identity"marknumerousargumentsongender,sexuality,
nationality,ethnicity,andcultureinrelationtoliberalismanditsalternatives(Young1990;
Connolly1991;Kymlicka1995;Miller1995;Taylor1989)
Comparedtorecentscholarshipinhistoryandthehumanities,however,politicalsci-
entistsremainlaggardswhenitcomestoworkonidentities.Duetoin uences rangingfrom
MichelFoucaulttothedebateonmulticulturalism,thehistoricalandculturalconstructionof
identitiesofallsortshaslatelybeenapreoccupationforbothsocialhistoriansandstudents
1ofliteratureandculture.
Despitethis vastlyincreased andbroad-ranginginterest in\identity," theconcept
itselfremainssomethingofanenigma.WhatPhillipGleason(1983)observed15yearsago
remainstruetoday:Themeaningof\identity"aswecurrentlyuseitisnotwellcapturedby
1SeeBrubakerandCooper(1999)forsomecitationstothisvoluminousliterature. Forameasureof
thespreadof\identity"inacademicdiscourse,Ichartedtheprogressofthewordindissertationabstracts,
whichcannowbesearchedon-linegoingbackto1981.Thenumberofdissertationabstractscontainingthe
word\identity"almosttripledbetween1981and1995,risingfrom709to1,911.Thisincreasehasoccurred
entirelyinthelasttenyears. Theaverageincreasewasabout12%peryearfor1986to1995,whileitwas
roughly at at-2.3%for1981to1985.Someofthisincreasecouldbeduetoanincreaseinthetotalnumber
ofdissertationsabstracted.Ihavebeenunabletogetthese gures, butIdidtrysearchingyear-by-yearfor
aneutral\controlword"{Iused\study"{togetaroughestimate. Bythismeasure,thetotalnumber
ofabstractedincreasedbyanaverageof.64%peryearfor1981-1985,and4.4%peryearfor
1986-1995.Thusthenumberofdissertationsabstractsusingtheword\identity"hasbeengrowingalmost
threetimesfasterthantherateforallabstracteddissertations.
1dictionaryde nitions, whichre ect oldersensesoftheword.Ourpresentideaof\identity"is
afairlyrecentsocialconstruct,andarathercomplicatedoneatthat.Eventhougheveryone
knowshowtousethewordproperlyineverydaydiscourse,itprovesquitedi cult togivea
shortandadequatesummarystatementthatcapturestherangeofitspresentmeanings.
Giventhecentralityoftheconcepttosomuchrecentresearch{andespeciallyinsocial
sciencewherescholarstakeidentitiesbothasthingstobeexplainedandthingsthathave
explanatoryforce{thisamountsalmosttoascandal.Ataminimum,itwouldbeusefulto
haveaconcisestatementofthemeaningofthewordinsimplelanguagethatdoesjusticeto
itspresentintension.
Thisisthemainpurposeofthispaper,todistillastatementofthemeaningof\iden-
tity"fromananalysisofcurrentusageinordinarylanguageandsocialsciencediscourse.
Themainresultsareeasilystated,althoughafairamountofworkonalternativepossibili-
tieswillberequiredtoreachthem. Iarguethat\identity"ispresentlyusedintwolinked
senses,whichmaybetermed\social"and\personal."Intheformersense,an\identity"
referssimplytoasocialcategory,asetofpersonsmarkedbyalabelanddistinguishedby
rulesdecidingmembershipand(alleged)characteristicfeaturesorattributes.Inthesecond
senseofpersonalidentity,anidentityissomedistinguishingcharacteristic(orcharacteris-
tics)thatapersontakesaspecialprideinorviewsassociallyconsequentialbutmore-or-less
unchangeable.
Thus,\identity"initspresentincarnationhasadoublesense. Itrefersatthesame
timetosocialcategoriesandtothesourcesofanindividual’sself-respectordignity.There
isnonecessarylinkagebetweenthesethings. Inordinarylanguage,atleast,onecanuse
\identity"torefertopersonalcharacteristicsorattributesthatcannotnaturallybeexpressed
intermsofasocialcategory,andinsomecontextscertaincategoriescanbedescribedas
\identities"eventhoughnooneseesthemascentraltotheirpersonalidentity.Nonetheless,
\identity"initspresentincarnationre ects andevokestheideathatsocialcategoriesare
boundupwiththebasesofanindividual’sself-respect. Arguablymuchoftheforceand
22interestofthetermderivesitsimplicitlinkageofthesetwothings.
Insection2belowIjustifytheenterpriseatgreaterlength,arguingthatforcontested,
complicated,orunclearsocialscienceconceptswithstrongrootsinordinarylanguage(i.e.,
mostofthem),acarefulanalysisofordinarylanguagemeaningsshouldprecedee orts to
legislateade nition forparticularresearchpurposes.Section3considerstheinadequacyof
dictionaryde nitions of\identity"andverybrie y tracesthehistoricalevolutionofitsnew
3setofmeanings. Section4beginstoaskaboutthecurrentmeaningof\identity"bytesting
possiblede nitions againstexamplesfromusage.Thetrailleads rst totheformulationof
aidentityasasocialcategory,and,insection6,toidentityasdistinguishingfeaturesofa
personthatformthebasisofhisorherself-respectordignity(andmore).Inbetween,section
5developsapotentiallyvaluabledistinctionbetweenroleand\type"identities. Sections7
and8drawoutsomeimplicationsoftheanalysisfortwoissuesofconcerntosocialscience
usersofconcept.Insection7Iusetheresultsoftheordinarylanguageanalysistoconsider
howidentitiesbearontheexplanationofactions(politicalandotherwise). Insection8I
brie y extendtheanalysisof\identity"appliedtoindividualstocorporateactorssuchas
statesand rms. Acentralargumentinrecentinternationalrelationstheoryholdsthatstate
interestsaredeterminedby\stateidentities."Themeaningofthisclaimobviouslydepends
onthemeaning\stateidentities,"whichIarguemightrefertoanyofseveraldi eren tthings.
Section9concludes.
2 Whybother?
Giventheintenseinterestinidentityandidentitiesacrossabroadspectrumofdisciplines,
onemightinitiallyexpectiteasyto nd simpleandclearstatementsofwhatpeoplemean
2Theaddedvalueofthisstatementofthecurrentmeaningof\identity"isnotthedistinctionbetween
\social"and\personal"sidesperse.Thereisalongtraditionofscholarsdrawingaofthissort,
contrastingvariousformulationsofindividualorpersonalidentity,ontheonehand,andsocialorgroupor
collectiveidentityontheother.Whatisnovelintheformulationderivedhereisthespeci c contentofthe
twosidesofthedistinction(whichcanbeandhasbeen lled inmanyways).
3Foranexcellentandmoredetailedsemantichistoriesof\identity,"seeGleason(1983)andMackenzie
(1978).
3whentheyusetheseconcepts.WhileIhavenotdoneanexhaustivesearch,Ihavenotfound
thistobethecase. Overwhelmingly,academicusersoftheword\identity"feelnoneedto
explainitsmeaningtoreaders.Thereaders’understandingissimplytakenforgranted,even
4when\identity"istheauthor’sprimarydependentorindependentvariable.
Thisisperhapsnotsosurprising. Inthe rst place,whiletheoriginsofourpresent
understandingof\identity"lieintheacademy,theconceptisnowquitecommoninpopular
discourse.Sinceweallknowhowtoemploythewordandweunderstanditinotherpeoples’
sentences,whybotherwithde nitions orexplanations?Second,inpopulardiscourseidentity
isoftentreatedassomethingine able andevensacred,whileintheacademyidentityisoften
5treatedassomethingcomplexandevenine able. Onehesitatestotrytode ne thesacred,
theine able, orthecomplex.
Ofcourse,onecan nd briefde nitions andclari cations inmanyplaces. Theserun
thegamut,fromsuggestiveglossestosomefairlycomplicatedandopaqueformulations.Here
aresomeexamples,culledmainlybutnotexclusivelyfromtheareasIreadmostin(political
science,internationalrelations):
1.Identityis\people’sconcepts