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Conditionals, Paradox,and Probability ThemesfromthePhilosophy ofDorothyEdgington LeeWaltersand JohnHawthorne
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Contents ListofTables vii
ListofContributors ix
.Introduction
LeeWalters
.PhilosophyandMe
DorothyEdgington
.ANoteonConditionalsandRestrictors
DanielRothschild
.ChasingHook:QuantifiedIndicativeConditionals
AngelikaKratzer
.NewParadigmPsychologyofConditionalReasoningandIts PhilosophicalSources
DavidOver
.CounterfactualstotheRescue
CleoCondoravdi
.CounterfactualsandProbability
RobertStalnaker
.GrammarMatters
SabineIatridou
.ConstructingtheImpossible
KitFine
.TheEpistemicUseof ‘Ought’
JohnHawthorne
.UndercuttingDefeatandEdgington’sBurglar
ScottSturgeon
.EdgingtononPossibleKnowledgeofUnknownTruth
TimothyWilliamson
.Prefaces,Sorites,andGuidestoReasoning
RosannaKeefe
.HysteresisHypotheses
AlanHájek
.VeritiesandTruth-values
NicholasK.Jones
BibliographyofworksbyDorothyEdgington
IndexofNames
IndexofTopics
ListofTables .The ‘defective’ , deFinettitablefor ifpthenq
..The generaldeFinettitablefor ifpthenq
.TheJeffreytablefor ifpthenq
ListofContributors C
C isProfessorofLinguisticsatStanfordUniversity.
D
E isWayn fleteProfessorofMetaphysicalPhilosophyEmeritus attheUniversityofOxford.
K
F isUniversityProfessorandSilverProfessorofPhilosophyandMathematics atNewYorkUniversity,andDistinguishedResearchProfessorattheUniversityof Birmingham.
A H ´ isProfessorofPhilosophyattheAustralianNationalUniversity.
J H isProfessorofPhilosophyattheUniversityofSouthern California.
S I isProfessorofLinguisticsattheMassachusettsInstituteof Technology.
N
K.J isOfficialFellowofStJohn’sCollegeandAssociateProfessorof PhilosophyattheUniversityofOxford.
R
K isProfessorofPhilosophyattheUniversityofSheffield.
A
K isProfessorEmeritaofLinguisticsattheUniversityof MassachusettsAmherst.
D
O isEmeritusProfessorofPsychologyatDurhamUniversity.
D
R isProfessorofPhilosophyatUniversityCollegeLondon.
R S isProfessorEmeritusofPhilosophyattheMassachusetts InstituteofTechnology.
S S isProfessorofPhilosophyattheUniversityofBirmingham.
L W isAssociateProfessorofPhilosophyattheUniversityofSouthampton.
T
W isWykehamProfessorofLogicattheUniversityofOxford.
Introduction LeeWalters
DorothyEdgington ’sworkhasbeenatthecentreofarangeofongoingdebatesin philosophicallogic,philosophyofmindandlanguage,metaphysics,andepistemology. Thisworkhasfocused,althoughbynomeansexclusively,ontheoverlappingareasof conditionals,probability,andparadox.Inwhatfollows,Ibrieflysketchsomethemes fromthesethreeareasrelevanttoDorothy’swork,highlightinghowsomeofDorothy’ s workandsomeofthecontributionsofthisvolume fitintothesedebates.
. Conditionals Oftenwefacedeep-rooteduncertainty,andsothebestwecandoistoestimatethe probabilitiesinvolved,ratherthanmakingoutrightjudgmentsastothetruthor falsityofaclaim.Forexample,therearetenballsinabag, fiveredand fivewhite; Priyapicksanunseenballfromthebagatrandom;hasPriyapickedaredball?The prudentanswerisnottoaffirmordenyoutrightthatPriyahaspickedaredball,but rathertosaythatitis %likelythatshehaspickedaredball(andconsequently, % likelythatshehasnot).
Thisretreattoprobabilisticjudgementsfromoutrightaffirmationsanddenialsis notlimitedtocategoricalclaimssuchasPriyapickedaredball.Itisalsopresentin ourconsiderationofconditionalstatements.So,addingtothepreviousexample,let’ s saythatthreeoftheredballshaveblackspots.Whatshouldourattitudebetothe claimthatifPriyapickedaredball,ithadablackspot?Well,asthreeofthe fivered ballshaveblackspots,theappropriateanswerseemstobethatitis %likelythatif Priyapickedaredball,ithadablackspot.
Considerationsofthissortmakeattractivetheclaimthattheprobabilityofa conditionalisequaltotheconditionalprobabilityofitsconsequentonitsantecedent.
*DorothyEdgington’sworkfaroutstripsthethreetopicsdiscussedabove.Andhercontributionstothe threedebatesmentionedaremorenumerousandoffermoreinsightthancanbediscussedhere. Nevertheless,fromthisbriefoverview,andfromthechapterscontainedintherestofthevolume,we canseetheingenuityandthebreadthofEdgington’swork,thedifficultyoftheproblemsthatshehas focusedon,andhowshehasadvancedourunderstandingofthem.
LeeWalters, Introduction In: Conditionals,Paradox,andProbability:ThemesfromthePhilosophyofDorothyEdgington Editedby:LeeWaltersandJohnHawthorne,OxfordUniversityPress(2021).©LeeWalters. DOI:10.1093/oso/9780198712732.003.0001
TheEquation:pðifA; CÞ¼ pðC=AÞ; wherepðC=AÞ¼ pðA&CÞ=pðAÞ,whenpðAÞ ¼ 0.
Sofar,sogood.TheproblemisthatDavidLewis()provedthattherecouldbeno propositionexpressedby ‘ifA,C’ thatsatisfiedTheEquation,andsoconditionals werenotevaluableastrueorfalse,ifTheEquationholds.Soshockingwasthisresult, giventheintuitivenessofTheEquation,thatRobertStalnakerdescribedLewis’ s resultasa ‘bombshell’ inalettertoBasvanFraassen.ThisisbecauseStalnakerwas tryingtogiveanaccountofthepropositionsexpressedbyconditionalstatements thatrespectedTheEquation.Inthefaceofthisdilemma,StalnakerrejectedThe Equationandmaintainedthatconditionalsexpresspropositions(see,interalia,his contributiontothisvolume).Others,likeEdgington,heldontoTheEquationand deniedthatconditionalsexpressedpropositions.
TheEquationisextremelyintuitive,sointhefaceofLewis’sproof,whynotgiveupthe assumptionthatconditionalsexpresspropositionsasEdgingtondoes?First,wecanask whatarepeopledoingwhentheyacceptandputforwardconditionals,ifnotbelieving andassertingthem?Thenon-propositionalistcanrespondthatweconditionallybelieve andconditionallyassertconditionals,wherethesenotionsmaynotbereducibleto furthermentalstatesorspeechacts.Fromapropositionalistperspectivethisresponse mayseemadhoc,but,asEdgingtonpointsout,therearenotonlywhat,fromher perspective,areconditionalassertions,butalsoconditionalcommands(ifitrains,takein thesunloungers)andconditionalquestions(ifLiverpoolscore first,willtheywin?), wherethesearenotobviouslyequivalenttooutrightimperativesandquestions.
Asecondobjectiontonon-propositionalismstatesthatwhereasonemightbeable toacceptthatindicativeconditionals(ifPriyatookaredball,ithasablackspot)do notexpresspropositions,itistoomuchtoacceptthatcounterfactualconditionals (ifPriyahadtakenaredball,itwouldhavehadablackspot)donotexpress conditionals.ButwhereasStalnakerreasonsfromtheclaimthatcounterfactuals expresspropositionstotheclaimthatindicativesalsoexpresspropositions, Edgingtonreasonsintheoppositedirectionprovidinganalogousreasonsforendorsingnon-propositionalismaboutcounterfactualsasshedoesforindicatives.
Perhapsthemainreasonforacceptingthatconditionalsexpresspropositionsis thatthealternativeappearstobesubjecttoaversionoftheFrege–Geachproblem thatplaguesexpressivism.¹Thatis,whatevernon-propositionalmeaningweassign toconditionalshastobeconsistentwiththemeaningofconditionalswhentheyare embeddedinmorecomplexlinguisticforms.Wecan,forexample,notonlyembed categoricalstatements,statementsthatstraightforwardlyexpresspropositions,in theconsequentsofconditionals,wecanalsoseeminglyembedconditionalsin theconsequentsofotherconditionals,resultinginstructuressuchas ‘ifA,thenif B,thenC’.Butifwhatisrequiredtobetheconsequentofaconditionalstatementisa propositionwhentheconsequentisacategoricalclaim,presumablyapropositionis requiredwhentheconsequentisitselfaconditional.Similarpointscanbemadewith otheroperatorssuchasconjunction,disjunction,negation,andmodaloperators.
¹SeeWilliamson’schapterinthisvolumefordiscussion.
Asimplewayofaccountingfortheembeddingofconditionalsinmorecomplex linguisticstructuresisintermsofpropositionalcontents.Butifwerejectthat conditionalsexpresspropositions,weneedto findsomeotherwayofaccounting forembeddingconditionals.Asitstands,thisisachallengetothosewhowant toholdontoTheEquation,ratherthanaproofthatTheEquationhastobe rejected.Still,theonusappearstobeonthosewhomaintainTheEquation,like Edgington,toprovideacompositionalaccountofthemeaningsofconditionals innon-propositionaltermsthatallowsthemtobeembedded.
Theaboveconstrualofthedialecticrestsontheassumptionthatwecanunproblematicallyembedconditionalsinmorecomplexlinguisticforms.Butthisisfarfrom obvious.Forexample,(i) ‘if A,thenif B, C’ seemsequivalentto(ii) ‘if(A&B), C’.But if(i)and(ii)areequivalent,thenasGibbard()hasshown, ‘ifA,C’ isequivalent to~AvCandsothefalsityofaconditional’santecedentissufficientforitstruth. Butthisconsequenceunacceptable.TotakeoneofEdgington’sexamples,fromthe factthatTheQueenisnotathome,itdoesnotfollowthatifTheQueenisathome, sheiswaitingformetotelephone!²
Moreover,asMcGee()argued,treatingembeddedconditionalsasexpressing propositionsseemsinconsistentwithmodusponens.Forexample,
.IfaRepublicanwins,thenifReagandoesnotwin,Andersonwill.
.ARepublicanwillwin.
Therefore,
.IfReagandoesnotwin,Andersonwill.
(
)seeminglyfollowsfrom()and()bymodusponens.Butwhereas()and() bothseemtrue,()doesnot(theDemocratCarterwasrunningsecondinthepolls, withAndersonadistantthird).McGeetakessuchcasestoshowthatmodusponens isindeedinvalid,butsuchaconclusionishardtoswallow.Thenon-propositionalist cannotethatshedoesnotrunintothisdifficulty,foronherconstrual,theargument aboveshouldbereplacedwith:
.IfaRepublicanwinsanditisnotReagan,thenAndersonwillwin.
.ARepublicanotherthanReaganwins.
.Andersonwillwin.
Andthisargumentisvalid.Thepropositionalist,then,needstoexplainwhyweare inclinedtoacceptthat(i)and(ii)areequivalentwhen,forhim,theyarenot.
Moregenerally,Edgingtonhasarguedthatembeddingsofconditionalsareproblematic,aresultthatissurprising,iftheyexpresspropositions.AngelikaKratzer (Chapter ,thisvolume)furthersthedebateonembeddingsofconditionalsby consideringwhataccountwecangiveofquanti fiedconditionalssuchas ‘ noone willpass,iftheygoofoff ’.Kratzerarguesthatsuchconditionalsdorepresenta
²Gibbardtakeshisprooftoshowthatindicativeconditionalsdonotexpresspropositions.Inthesame paper,healsopresentshisexampleofSlyPete,aso-called ‘Gibbardcase’ toreasontothesameconclusion. Edgington()argues,however,thattheproperlessonofsuchcasesisthatindicativeconditionalsare somehowepistemic,ratherthanthattheydonotexpresspropositions.
problemforapropositionalaccountofconditionalsandthatthereisnogeneral accountoftheembeddingsofconditionals.ThisismusictoEdgington’sears,but ratherthanrejectingpropositionalism,Kratzerappealstopragmaticstoaddressthe problem(seealsoChapter ,thisvolume,whereRothschildarguesthatbyadoptinga Kratzer-styletreatmentof ‘if ’ asarestrictor,propositionalistshavetheresourcesto respondtoanumberofargumentsfornon-propositionalism).
. TheParadoxofVagueness AsecondliteraturetowhichEdgingtonhasmadeimportantcontributionsandwhich isthefocusofseveralchaptersinthisvolume,istheparadoxofvagueness.Many conceptsexpressedinnaturallanguageappeartobevague,inthesensethatthey appeartolackpreciseapplicationconditionsandadmitofborderlinecases,cases whereitneitherseemsrighttosaytheconceptappliesnortosaythattheconcept doesnotapply.Forexample,considertheconcept bald.Althoughtherearepeople whoareclearlybaldandpeoplewhoareclearlynotbald,therearepeoplewhoare in-between,neitherclearlybaldnorclearlynotbald.Itwillnotdo,apparently,tosay thatsuchpeopleareneitherbaldnornotbald,since,plausibly,thisistocontradict oneself.Thetroubledoesnotendthere,however.
Itischaracteristicofvagueconcepts,unlikepreciseconcepts,thattheyappearto obeyaprincipleoftolerance,theiteratedapplicationofwhichleadstoabsurdities suchasthatsomeonewithamillionhairsontheirheadisbald.³Theparadoxical reasoningonlyrequirestwopremisesandmultipleapplicationsofmodusponens:
.Apersonwithzerohairsontheirheadisbald.
.Ifapersonwithn- hairsontheirheadisbald,apersonwithnhairsontheir headisbald.
Therefore,
.Apersonwithonehairontheirheadisbald.
(
)isanobviousapplicationoftheconcept bald;()isjustifiedbytheprincipleof tolerancethatappearstobecharacteristicofvagueconcepts;and()followsfrom ()and(),bymodusponens.Byitself,()doesnotrepresentaproblem.Butonce wehave(),wecancombinethiswith()toderivethatapersonwithtwohairson theirheadisbald,andso,byrepeatedapplicationsof(),wecandeducethat someonewithamillionhairsontheirheadisbald!
Howshouldwerespondtosuchparadoxicalreasoning?Edgington() approachestheparadoxofvaguenessbyarguingthatthereisanalogybetweenit andtheprefaceparadox.Inparticular,shethinksthatwecanlearnlessonsabout vaguenessbyconsideringthedegreeofbeliefresponsetotheprefaceparadox.
Theprefaceparadoxisasfollows.Acarefulauthorbelieveseachoftheclaimsshe makesinherbook,but,acknowledgingherfallibility,shestatesintheprefacethatsome
³Inourtoyexample,I’mignoringthefactthatwhethersomeoneisbalddependsnotonlyuponhow manyhairstheyhaveontheirhead,butalsouponthedistributionofthosehairs.
claimsshemakesinthebookareboundtobefalse.Theauthorappearstoberational, butwecanreasonfromanumberofclaimsthatshetakestobetrue(eachclaimshe makesinthebook)toaclaimthatsherejects,namelythatalltheclaimsinthebookare true.Whattodo?Thedegree-theoreticresponseistosaythattheauthorbelieveseach individualclaimshemakesinthebooktosomehighdegreelessthancertainty,butthat whensheconsidersthebookasawholeherindividualdoubtsaddup,sothatshe believestheentirebookonlywithalowdegreeofcertainty.Thisapproachcanbe formalizedbymodellingdegreesofbeliefprobabilisticallytoshowthattheprobability oftheconclusionofavalidargumentcanbelowerthantheprobabilityofanyofthe premises.Certainty,unliketruth,isnotpreservedbyvalidreasoning.
Edgington’saccountofvagueness,liketheaboveapproachtotheprefaceparadox, employsaprobabilisticdegree-theoreticstructurethatshecalls ‘verities’ or ‘degrees ofclosenesstocleartruth’.Howdoesthishelpwiththeparadoxofvagueness?Inthe paradoxicalreasoningabove,wemovefromaclearcaseofbaldness,astatementwith verity ,toaclearcaseofnon-baldness,astatementwithverity0.Theargumentis valid,andtheprincipleoftolerancelooksingoodshape.Edgington’sideaisthatas wemovealongthesequenceofpersonseachwithasinglemorehairontheirhead thanthepreviousone,wegraduallymoveawayfrompeoplewhoareclearlybald (verity ),throughthepeoplewhereitiscompletelyunclearwhethertheyarebald (verity0.),tothepeoplewhoareclearlynotbald(verity0).Butateverypointinthe sequence,therelevantconditionalthatisaninstanceoftheprincipleoftoleranceis extremelyplausible,becauseithasaverityjustshortof .ForEdgington,theverityof aconditionaljustistheconditionalverityoftheconsequentgiventheantecedent. Andtheconditionalverityofxisbald,giventhatyisbald,isthevaluetobeassigned toxisbaldonthehypotheticaldecisiontocountyasbald,adecisionthatisnot clearlywrong,giventhatyisaborderlinecaseofbaldness.Byemployingconditional verities,then,Edgingtonhopestoexplaintheplausibilityoftheinstanceofthe principleoftoleranceusedintheparadoxicalreasoning.
Edgington’sapproachtotheparadoxofvaguenessisintriguing,butitraisesmany questions(asdoallapproachestovagueness).Onesetofquestionsconcernsthe natureofveritiesthemselves.Edgingtonisclearthatveritiesarenotdegreesoftruth andsoarenotintendedtoreplacetheclassicalbivalenttruth-values.InChapter , NicholasJonesarguesthatEdgingtonismistakentothinkthatveritiesandtheclassical truth-valuesarenotincompetitionbecauseclassicalsemanticsisincompatiblewith plausibleprinciplesconcerningtherelationshipbetweenthetwoapproaches.Jones alsocastsdoubtonEdgington’sclaimthatveritiesarenotinfacttruth-values.
Howeverweultimatelyunderstandverities,Edgington’sapproachismotivatedby whatshetakestobeanalogiesbetweentheparadoxofvaguenessandthepreface paradox.InChapter AlanHájekarguesthatEdgingonwascorrecttodraw parallelsbetweenreasoningwithuncertaintyandreasoningwithvagueconcepts. Hájekpointstoexperimentsinwhichsubjectsaretakenalongaseriesofcoloured patches,wheresuchsubjectsdisplayso-called reversehysteresis intheirresponses.In theexperimentHájekdiscusses,subjectsarepresentedwithaseriesofcolourpatches rangingfromclearlyblue,throughbluey-greenpatchestothosethatareclearly green.Whathappensisthattherearepatchesthatsubjectslabelasgreenwhen approachingfromtheblue-endoftherangethattheylabelasbluewhenapproaching
fromthegreen-endoftherange.Hájektakessuchjudgmentstoberationaland arguesthatthebestexplanationofthisisthatthisisaversionofthePrefaceParadox, theProgressivePrefaceParadox.
RosannaKeefe,whilstnotwantingtodenysomeanalogiesbetweenthepreface paradoxandtheparadoxofvagueness,arguesinChapter thatthereareimportant disanalogiesbetweenreasoningwithvagueconceptsandtheprefaceparadoxand thatthisconstitutesacaseagainstEdgington’streatmentofvagueness.Inparticular, Keefearguesthatwhereasintheprefaceparadoxwebelieveallofthepremises individually,butnottheirconjunctionoruniversallyquanti fiedform,inthecaseof theparadoxofvaguenesswebelieveboththeindividualpremisesandtheirconjunctionanduniversallyquanti fiedform.Keefe,instead,arguesthatasupervaluationist treatmentofvaguenessisbetterequippedtotakeaccountofthesefacts.
. TheParadoxofKnowability Edgington’ s finalcontributiontobediscussedhere,ishernoveltakeontheso-called paradoxofknowability.Itisnowwidelyknownthataweakformofverificationism classically entailsanabsurdlystrongformofverificationism,givencertainseemingly minimalassumptions.Inparticular,reading ‘Kp’ aspisknownbysomeoneatsome timeorother,theweakformofverifictionism:
Knowability 8pðp ! ◊KpÞ
entailstheimplausiblystrongversionofverificationism:
Known 8pðp ! KpÞ.
Proof:
. q ∧ ¬Kq Assumethereisanunknowntruthforreductio;
. ðq ∧ ¬KqÞ! ◊K ðq ∧ ¬KqÞ InstanceofKnowability;
. ◊K ðq ∧ ¬KqÞ 10,11,modusponens;
. ◊ðKq ∧ K¬KqÞ 12,Knowledgedistributesoverconjunctions;
. ◊ðKq ∧ ¬KqÞ 13,TheFactivityofknowledge.
Butnocontradictionispossible,contra(),soouroriginalassumption,(),isfalse andtherearenounknowntruths.So,KnowabilityentailsKnown thatalltruthsare known.Butsincethelatterisunacceptable nooneknowshowmanyhairswereon myheadtwentyyearsago soisKnowability.Knowability,then,hastogo.
Aspresentedhere,theparadoxofKnowability(orFitch’sParadox,ortheChurchFitchParadox)is firsttakenasaproofthatKnowabilityentailsKnown,andsecond, giventhatKnownisfalse,thatKnowabilityisalsofalse.Butwhereistheparadoxin that?Rather,itseemsthatweshouldtaketheproofnotasa paradox butratherasa result showingthattherearecertainstructurallimitationsonknowledge(cf. Williamson(: .)Inparticular,theproofshowsthatwhereqisanunknown truth,thefactthatitisanunknowntruthcannotbeknown.Statedthisway,the falsityofKnowabilityseemsobvious.
Nevertheless,Edgingtonclaims ‘[t]hattruthswhichare[inprinciple] unknowable...shouldaboundintheformofthemostubiquitousandmundane
facts,suchthatnoonenoticeda flyontheceiling,orwhenthisleaffellfromthistree, strikesmanyasparadoxical’ (: ).Paradoxicalornot,Edgingtonargues ‘that thereisasenseinwhichonecanknowthat,asthingsactuallyare, p anditisnot knownthat p,butfromacounterfactualperspective asitwere,fromamodal distance ’ (: ).Edgington’sthoughtisthatthepossiblesituationoftheknower neednotbeidenticaltothepossiblesituationoftheunknowntruth.Ratherthan vindicatingKnowability,whatEdgingtonarguesforisthefollowing(where s and s* rangeoverpossiblesituations):
E-Knowability Williamson(,andChapter ,thisvolume)raisesachallengeforEdgington’ s defenceofE-Knowability,namely,howisthesituationofthetruth,s,specified? Itcannotbespecifiedbyasubjectofsomeothersituation,s*,byuseofthephrase ‘the actualsituation’,sincethisphrasewillpickouts*nots.Moregenerally,thereseems tobenowaythatthepotentialknowercanpickoutsviasomecausalreferential chain.Asubjectins*canpickoutsbydescription,though:sisthesituationinwhich p,q,r,...ButasWilliamsonnotes,thisrendersE-Knowabilitytrivial,whichwasnot Edgington’sintention,sincetheconsequentofE-Knowabilityistruesimplyof someoneknowingthatinthesituationinwhichp,q,r, ...obtain,pistrue. How,then,toallowthatasubjectins*canpickouts,withoutallowingthatthis istrivial?Edgington’sapproachistoinvokecounterfactualconditionals,but Williamsonarguesatlengththatthisapproachdoesnotwork,pressing,amongst otherobjections,theFrege–GeachworryforEdgington’sviewthatconditionals arenottruth-apt.
References Edgington,D.()OnConditionals, Mind : – Edgington,D.()VaguenessbyDegrees.InR.KeefeandP.(eds), Vagueness:AReader. Cambridge,MA:MITPress,pp. –
Edgington,D.()Truth,Objectivity,CounterfactualsandGibbard, Mind : –. Edgington,D.()PossibleKnowledgeofUnknownTruth, Synthese : – Gibbard,A.()TwoRecentTheoriesofConditionals.InW.L.Harper,R.,Stalnaker,and C.T.Pearce(eds), Ifs.Dordrecht:Reidel.
Lewis,D.()ProbabilitiesofConditionalsandConditionalProbabilities, Philosophical Review, : – McGee,V.()ACounterexampletoModusPonens, JournalofPhilosophy : –. Williamson,T.() KnowledgeandItsLimits.Oxford:OxfordUniversityPress.
PhilosophyandMe DorothyEdgington
Myearliestphilosophicalthought ortheearliestIrecall occurredattheageof threeorfour.Ihadbeentaught,parrot-fashion,togivetherightanswertoquestions like ‘What’ s and ?’ Thisskillwasbeingshownoffbymygrandparents(withwhom welivedduringthewar)tovisitors,whoweresuitablyimpressed.AndIwasvery puzzledabout why itwas ‘clever’ tosay asopposedto whatmadetheoneagood answerandtheotherbad.Thatturnsouttobeahardquestion.
Mynextphilosophicalmemoriesarenotuntilthe finalyearatschool,when,as preparationfortheGeneralPaperoftheOxfordandCambridgeentranceexams,we weregivenessaytopicsofaphilosophicalkind.Irecalloneonthejustificationof punishment;anotheronwhethertherecouldbetimewithoutchange.Idiscovered thatconsultinglargedictionariesoftenhelpedmetogetstarted.ThatyearIalsoread someRussellonthephilosophyofscience Ithinkitwas ABCofRelativity and dippedintoAdamSmith’ s TheWealthofNations.ButIhadonlythedimmest awarenessofphilosophyasasubject,anditneveroccurredtomethatitwaswhat Iwoulddo.Mathswasmyfavouritesubjectatschool,especiallygeometry,proofs givinggreatsatisfaction.
Neitherofmyparentswenttouniversity,noranyotherrelatives,exceptforone secondcousin,beforeme.BothmyparentsdidwellatForfarAcademy,theone secondaryschoolintown,andgotastringofScottishHighers.Bothregrettednot goingtouniversity.Soeducationmatteredtothemfortheironlychild:fromanearly ageitwastakenforgrantedthatIwouldgo indeed,toCambridge(assumedtobe thebest),thoughthatdidn’tcomeabout.Whatwouldhappenbeyonduniversitywas neverthoughtabout.
Iwasontrackateleven,atBoltonSchool(Girls’ Division).Thenwemovedto Lima,Peru,andforfouryearsIhadasomewhatspottyeducationatColegioSan Silvestre.Therewasnoscience,whichbotheredme.TherewasnoLatin,which botheredmymother,assheknewitwasrequiredforOxbridge.Sheendedup teaching,forayear,asmallclassherself,whichallowedmetoscrapethroughLatin O-level(aidedbysomeguessworkfromSpanish).AfterO-levelsIhadrunoutof schoolingthere,andwassenttoStLeonards,inStAndrews,tocatchupwithscience anddoA-levels.
IwasacceptedbyStHilda’sCollege,Oxford,toreadEngineering.Thiswasacrazy choice,thoughitmighthavehelpedmegetin:oneothergirlandIwerethe firsttodo
DorothyEdgington, PhilosophyandMe In: Conditionals,Paradox,andProbability:ThemesfromthePhilosophyof DorothyEdgington.Editedby:LeeWaltersandJohnHawthorne,OxfordUniversityPress(2021).©DorothyEdgington. DOI:10.1093/oso/9780198712732.003.0002
thisatStHilda’s(awomen’scollege therewerenomixedcollegesforundergraduatesthen).GirtonCollege,Cambridge,hadthegoodsensetoturnmedownforthe MechanicalSciencesTripos.(Itwasn’tjustthatIwasunsuitedtothesubject.Inthose days,Cambridge’sentranceexamswereawholetermafterOxford’s,andbythattime mymindhadstrayedfarfromacademicmatters.)SoOxforditwas.The firstyearwas disastrousacademically.IwantedtochangetoMaths,buttheMathstutordidn’t wantme.(Iwasnotworkingverywell.)Iwas,however,allowedtochangetoPPE Philosophy,PoliticsandEconomics.
Inmy firsttermofPhilosophyIhadtutorialswithagraduatestudent,Timothy Potts(laterofthePhilosophyDepartmentatLeeds).WefocusedonWittgenstein’ s Tractatus,andonFrege:arathernon-standardintroductiontothesubject,butone Ifoundfascinating.IalsoenjoyedmytutorialsinEconomicswithMargaretPaul, sisterofFrankRamsey,andwifeofanOxfordphilosopher,GeorgePaul,who,sadly, diedinasailingaccidentduringmysecondyear.
TherewaslittlechoiceinPPEinthosedays:twocompulsorypapersineachofthe threesubjects,andtwooptionalpapers.Stillfeelingamathematician manqué,my optionswereFormalLogic therelativelyadvancedspeciallogicpaper,takenby onlythreepeopleintheUniversityinmyyear;andthestatisticspaperinEconomics. IwastaughtlogicmainlybyE.J.Lemmon,beforeheleftforCaliforniawherehealso, alas,metanearlydeath,whilemountaineering.IenjoyedPPE,thoughneverknew whetherIwasdoingwellorbadly.InPhilosophy,J.L.Austin,thoughrecently deceased,wasstillverymuchalive,atleastwithmytutors,andIfoundthatthe pickierIwasaboutwhatthewordsintheessayquestionmightmean,themore Iseemedtopleasethem.
Stayingatuniversityaftergraduationhadn’toccurredtomeasapossibilityuntil, viaafriend,Igotsomecasualresearch-assistantworkforanAmericandoinga doctorateineconomicsatNuffieldCollege.Thatintroducedmetothegraduatestudentscene,andtheassumptionthatifyouweregoodenough,thatiswhatyoudid. Bywhatseemedlikea fluke,myFinalsresultmeantthatIwasgoodenough,soIwent toNuffieldtodoaB.Phil.inEconomics.(PlanBwastheStatisticalOfficeintheCivil Service,planCajobwithIBM.)
Wrongsubjectyetagain!Thistimeitwasn’tadisaster,andindeedthat firstyear aftergraduationIlearnedalotaboutprobability,whichbecameanabidinginterest. ButastheyearprogressedIfoundmyselfincreasinglyconsultingthePhilosophy lecturelist,especiallyforLogic,andattendingthoseclasseswithmoreenthusiasm thanthoseinEconomics.TowardstheendofthatyearIwenttoseemyold philosophytutor,SybilWolfram,toraisethepossibilityofchangingtoPhilosophy. SheswiftlyarrangedformetoseeGilbertRyleatMagdalen.Ryletreatedthe proposedchangeofsubjectasafaitaccompli:hewrotealetterthereandthen,in appallinghandwriting,tothefundingauthorities,insistingthatIshouldbefunded forthenexttwoyearsfortheB.Phil.inPhilosophydespitehavingalreadyhadone year ’sfundingfortheB.Phil.inEconomics.Hehandedthelettertomeandtoldme to ‘getittyped’ andsendtheoriginalwiththetypescript.OfcourseIhadtotypeit myself,butitworkedout.
Bothmyfalsestartswere,Ithink,theresultofafeelingthatIshoulddosomething ‘useful’.Andin Economicsdidseemusefulandimportant,withHarold
Wilson’ s ‘whiteheatofthetechnologicalrevolution’ onthehorizon.AfterWilson’ s election,OxfordeconomistswentbackandforthtoLondonagreatdeal,advisingthe government.Oneconsequencewasthatwegraduatestudentswereingreatdemand astutors,andIgotplentyofteachingexperiencethatyear.
Thatsummer, ,ImarriedJohnEdgington,whomIhadmetjustoverayear before,afewmonthsbeforeFinals.JohnhadjustcompletedaCambridgePh.D.in Physics(thoughmostofhisresearchwasdoneatHarwellandhehadlivedin Oxford);andhegotalectureshipatQueenMaryCollegeinLondon.Wecontinued toliveinOxford,rentingalovelycottage,GristCottageinIffley,frompeoplewho hadboughtitfortheirretirementafewyearson.
MostofmyworkinthenexttwoyearswaswithMichaelDummett agreat privilege.Therewasahistoricalpaper, ‘TheAuthoritiesfortheRiseofMathematical Logic’,mainlyonFrege,Russell,Hilbert,andBrouwer;andanotheradvancedlogic paper.Dummettwaswonderfullyilluminating,andIneverceasedtobeinaweofhim. TheDummettianlineofthoughtconnectingthetheoryofmeaning,classicallogic,and realismwouldoftencropup.Ifoundthisfascinating,andlaterfeltthatthosetwoyears gavemeaheadstartinunderstandingDummett’santi-realistchallenge.Mythird subjectwasMetaphysicsandtheTheoryofKnowledge,andIdon’trecalldoingmuch workforthat.AndIwroteathesisontheconceptofprobability.RamseyanddeFinetti weremyheroes.Carnap,Keynes,andvonMiseswerecriticized.(Ihadnotyetcome acrosspropensitytheoriesofobjectivechance.)Afewsuggestionsweremadeattheend thattheremightbemoreconstraintsonrationalitythanthesubjectivistsallowed,such asascribingthesameprobabilitytoeventsbetweenwhichonesawnorelevant difference.Iworkedonthethesisduringmy firsttermwithWilliamKneale surroundedbypackingcasesbecausehewasabouttoretire.AfterthatIhadno supervisiononthethesis.Itwaswritteninagreatrushinthelastavailablefew weeks,andmostlytypedupbyJohn.(FromaconversationyearslaterIlearnedthat atjustthattime,underjustthesamepressure,atHarvard,DavidLewiswastypingup hiswifeSteffi’smaster’sthesis,andSteffi’smemoriesofthetinkleofthetypewriter, interruptedbyexpletivescausedbytypos,werejustlikemine.)
Itwasnotthepractice,then,inphilosophyatOxfordtocontinuetoadoctorate aftertheB.Phil.Rather,onetriedtogetajob.OursonAlecwasbornafewmonths afterI finishedtheB.Phil.Ihadn’tappliedforjobs,becausetherewasaplanafootfor ustogotoNigeriaforayear,totheUniversityofIfe aspecialschemetoupgrade theteachingofphysicswitharotaofvisitors(andIthinkIwaslineduptoteach someeconomics).IndeedbeforehewasbornAlechadaplaneticketinthenameof ‘InfEdgington ’.HowevertheBiafrawarmadeusdecidethatthisventurewasunwise, especiallywithanewbornchild.DuringthenextyearIdidsometutoringand examiningforeconomicsA-level.(Itmatteredtometobeself-supporting.Beyond thatIwasnotveryambitious.)Ididthenapplyforafewjobs,andwaseventually offeredalectureshipinthePhilosophyDepartmentofBirkbeckCollege,London. Iknewalongergapwouldmakeitharder,ifnotimpossible,togetauniversityjob,let aloneoneinthesamecityasJohn’s,soIhadtoaccept evenifitwasabitscary,as Iwasexpectinganotherchild.Itwasaweightydecision,butanirresistibleone. WemovedtoLondoninthesummerof .Ifeltwemustlivenearmywork, andsowerenteda flatinMecklenburghSquare,Bloomsbury therentandrates
(i.e.counciltax)togethermatchedexactlymynetsalary.Justoverayearlaterwe movedtoalarger andcheaperbecauseshabbier flatinthesamesquare,inwhich welivetothisday.
BirkbeckwasthecollegeofLondonUniversitywhichcateredformature,part-time students.Mostwereolder,wiser,moreknowledgeable,andmoreconfidentthan Iwas.Mostofmylecturesrequiredlearningfromscratch.Oneofmylecturecourses wasonthehistoryofpoliticalphilosophy!OurdaughterFionawasborninMarch. Maternityleavehadnotbeeninvented.Lectureswentonwellintothesummer,the thirdtermrunningfromlateApriltoearlyJuly.Itwasa ‘make-or-break ’ sortofyear. Later,theKingswayCrèche London’soldestdaynursery andthelarger flat allowingforlive-inhelp,madelifealittleeasier.
Ididfeelabitoutonalimb,philosophically,atBirkbecktobeginwith,andoften feltIdidn’tunderstandwhatwasgoingonindiscussion.Logic(whichItaught)was notheldinhighregard.DavidHamlyn,ourHeadofDepartment,inhisintroductory talktonewstudents,givingthumbnailsketchesofhiscolleagues,likedtosay ‘Dorothydoessums’.Hewouldthenadd ‘Ifyoucan’tdothesums, don’tworry! They’rereallynotimportant!’
Butsoonthesubjectmovedmoreinmydirection mostnotablywiththe ‘Davidsonicboom’.Iwasneveracard-carryingDavidsonian, findingitimplausible thatthestructureofnaturallanguagecouldbecapturedinthestructureof first-order extensionallogic.Butitdidmeanthatacertainamountoflogicalmachinery satisfactionofpredicatesbysequents,etc. wasrequiredbyanyonewhowantedto understandthisproject,andlogicwasmoreinvogueoncemore.Newcolleagues, MarkPlattsandlaterIanMcFetridge,weremorecongenialphilosophically.
Itwasn’tjustDavidson.Muchmorewashappeningintheearly sthatengaged me.TherewasconsiderableinterestinRichardMontague’spossible-worldsemantics.(HansKamp,whohadbeenastudentofMontague’s,wasatUCLandthenat BedfordCollege.)TherewasDavidLewis’sandRobertStalnaker’sworkoncounterfactuals,andDummett’smagnificent Frege:ThePhilosophyofLanguage.Saul Kripke’slectures, NamingandNecessity,circulatedinbookletform.Noother philosophicalworkhaveIfoundsoriveting.Itwasaquiteexceptionalperiod.
– wasspentinVancouverattheUniversityofBritishColumbia,Johnto workatthenewcyclotron,andIhadavisitingpositioninthePhilosophy Department.Itwasagoodyear,andIbenefitedgreatlyfromtwoseminarsgiven byJonathanBennett,oneonadraftofhisbook LinguisticBehaviour, theotheronhis criticalnoticeofDavidLewis’ s Counterfactuals (CanadianJournalofPhilosophy, ).Jonathanfoundmeausefulcritic:Ihadcomefromasettingwherethethemes ofbothseminarsweremuchunderdiscussion.
Thecounterfactualsseminarisavividmemory.Theclassroom,likemanyatUBC, hadstunningviewsoversea,islands,andmountains.Thetime,unusually,waslate, aroundsunset.Ifyouarrivedearly,youdidn’tturnonthelight,youdidn’tspeak,you justlooked.Jonathanwouldthenarrivewithahugeurnofcoffee,tokeepusgoing lateintotheevening.
Jonathan’scriticalnoticewasinpress.Theseminarwasbasedlargelyonit,butalso conductedinthespiritofGoodmanvs.Lewis.JonathantendedtofavourGoodman (hehadsomeinterestingideasforcircumventingthechargeofcircularityconcerning
cotenability).Throughout,IdefendedLewis.Ididsowithsomesuccess.Then,early inthe finalclass,camethelethalobjection.Alleyeswereonme,expectantly.Isaid nothing.Afteralongpause,Jonathansaid ‘Ithinkwecan finishthere.’ Curtaindown.
ThelethalobjectionwasofapiecewithKitFine’sbetter-knownandperhapsmore memorableexample, ‘IfNixonhadpressedthebutton,therewouldhavebeena nuclearholocaust’ (fromFine’scriticalnoticeofLewis’sbookin Mind, ).By ordinarystandardsofsimilarity,themostsimilarworldstotheactualworldarenot alwaystheworldsthatwouldhavecomeabout,hadtheantecedentbeentrue.This was,ofcourse,beforeLewisrepliedthatitisnotordinarystandardsofsimilarity whichareatissue.Buttheexamplesconvincedmethatsimilaritytotheactualworld issimplynottherightnotiontodelimittherelevantworlds.Ironically,inlaterwork, BennettgravitatedtowardsaLewisiantheory,andIgravitatedaway.
Ialsoworkedonprobabilitythatyear.IreadJonDorling’sexcellentreviewarticle onMaryHesse’ s TheStructureofScience (BritishJournalforthePhilosophyof Science, ).IfoundacontradictioninhisanalysisofhowBayesianscouldsecure convergenceofopinionwhenevidence,onaverage,wentinthesamedirection.We correspondedaboutthisforabit,andjointlypublishedanotewhichwasineffecta correctiontothatpartofhisreview(BJPS, ).
YetanotherseminaratUBCmotivatedme,givenbyEdLevy,onquantumlogic. Ineverdidgetaverygoodunderstandingoftheissuesinquantumtheory.ButIcame toseehowclosetheconnectionwasbetweenclassicallogicandstandardprobability theory.Forinstance,usingjustprobabilitytheoryonecanprovethattheprobability of ¬¬A mustequaltheprobabilityof A,theprobabilityof A∨¬A isalways1, pððA&BÞ∨ðA&C ÞÞ¼ pðA&ðB∨C ÞÞ,etc.Anon-standardlogicrequiresanonstandardprobabilitytheory;and,assumingthiscanbedeveloped,thequestionarises whetherthenon-standardprobabilitytheoryisplausible,interesting,useful,and powerful.Ifnot,theremaybeargumentsforclassicallogicfromprobabilitytheory. Iworkedonthisinthelate1970s,anditledtoapaperonDummett ’schallengeto realism, ‘Meaning,BivalenceandRealism’ (ProceedingsoftheAristotelianSociety, 1980–81).IwasmotivatedbytworemarksofDummett’sinthelongandsubstantive Prefaceto TruthandOtherEngimas (1978): first,weshouldnotassumethatwecan ‘simplytransfertoempiricalstatementstheintuitionistaccountofmathematical ones,sinceobviouslythere(are)greatdissimilaritiesbetweenthem’ (p.xxix);second, ‘itismisleadingtoconcentratetooheavily,asIhaveusuallydone,onaformofantirealisttheoryofmeaninginwhichthemeaningofastatementisgivenintermsof whatconclusivelyverifiesit;oftensuchconclusiveverificationisnottobehad’ (p.xxxviii).InthepaperIarguedagainsttheintuitionistaccountsof ‘ or ’ and ‘not’ innon-mathematicalcontexts;andIshowedthatoncewehaveadmittednonconclusivejustificationsforasserting,accountscanbegivenofnegationanddisjunctionwhichmeetDummett’sconstraints,butdonotcastanydoubtsonthelawof excludedmiddleandbivalence.Probabilitytheorywasinthebackground,but certainlynotintheforeground:Ikeptmyassumptionsasweakandasintuitiveas possible.I find,onre-reading,thatIstillratherlikethatpaper!
DummettwasinthechairwhenIgavethepaperattheAristotelianSociety.Whilethe outcomewasnotonethathewelcomed,hedidsayhewaspleasedthatIwasaddressing hischallengehead-on;andhehad,asalways,manyinsightfulremarkstomake.
ActIIonconditionalsbegins,backinLondon,late orearly ,whenDavid Hamlyn,thenEditorof Mind,comesintomyofficewithtwobooksformetoreview. OneofthemisErnestAdams, TheLogicofConditionals.Readingitisarevelation. Twoofmyareasofinterest,probabilityandconditionals,joinup.Conditional judgementsareoftenuncertain.Theyareassessedbyconditionalprobability.Why hadn’tIthoughtofthat?
(Forwhatitisworth,beforereadingAdams,onindicativeconditionals,Ihadtried topersuadestudentsthattherewerestrongreasonstoacceptthetruth-functional account,althoughtherewerealsostrongreasonsagainstit;and,ratherhalfheartedly,IhadinvokedGricetotrytomitigatethecaseagainst.Oncounterfactuals, althoughIwasinitiallyverytakenbyLewis,Bennetthadpersuadedmethatsimilarity isnottherightnotion,andIhadalreadythoughtthatsomethinglike ‘themost probableworlds’ woulddobetter.)
Thecognoscenti Lewis,Stalnaker,Jackson hadbeenfamiliarwithAdams’ s articlesfromthemid-s,butIhadnot.OfcoursetherewasRamsey’ssuggestion longbeforehim()butnoonehadpaidmuchattentiontoit,beforeAdams.At theheartofAdams’sworkisaprobabilisticconsequenceofthenotionofavalid necessarilytruth-preserving argument.Considersuchanargument.Supposeyou think,butarenotsure,thatthepremisesaretrue.Whatshouldyourattitudebetothe conclusion?Calltheuncertaintyofapropositiononeminusitsprobability.Valid argumentshavethepropertythattheuncertaintyoftheconclusioncannotexceed thesumoftheuncertaintiesofthepremises.Inthatsense,validargumentspreserve probability:therecanbenomoreuncertaintyintheconclusionthanthereis distributedamongthepremises.Thisiseasilyproved.Itisquiteanintuitiveresult, butnotsointuitiveastobeobviouswithoutproof.Itexplainstheextenttowhichone canrelyonvalidargumentsinuncertaincontexts.Anditexplainswhatgoeswrong inthelotteryparadoxandtheparadoxofthepreface:averylargenumberof premises,thougheachveryclosetocertain,canyieldacertainlyfalseconclusion.
NowAdams’sinitialattitudewas:wehaven’tbeenableto findsatisfactorytruth conditionsforconditionals,butwehaveagoodideaofhowtoassessthemprobabilistically.Soletuscallthevalidargumentsinvolvingconditionalsthosewhich satisfytheaboveprobabilisticconstraint:theypreserve,inhissense,probabilityor conditionalprobability.Hethenshowshow,onthisconception, ‘If A, B’ doesnot followfrom ¬A,anddoesnotfollowfrom B.Moresurprisingly(atthetime), transitivity,contraposition,andstrengtheningoftheantecedentfail.
Adams’sworkhadgreatlyinfluencedStalnaker,who,withthenewandpowerful toolsofpossible-worldssemantics,aimedattruthconditionsforconditionalssuch thattheprobabilityoftheirtruthistheconditionalprobabilityofconsequentgiven antecedent.Alas,itcouldnotbedone.Lewis’sprooftothateffect()isthemost famous.ButAdamshadhisownproof,earlier.Indeed,theresultwasintuitedby Ramseyin : ‘Manysentencesexpresscognitiveattitudeswithoutbeing propositions....Thisiseventrueoftheordinaryhypothetical.’ Itwasalsorealized bydeFinetti,theotherfounderofsubjectiveprobabilitytheory,in ,whenhe developedhisowntheoryofconditionalsconstruedasjudgementsofconditional probability.AndIhavefoundthattheresultcauseslesssurpriseamongstprobability theoriststhanitdoesamongstphilosophers:aconditionalprobabilityisnotthe
probabilitythatsomethingisthecase, simpliciter,buttheprobabilitythatsomething, B,isthecase undertheassumptionthat somethingelse, A isthecase.Thereason wehaven’tbeenableto findsatisfactorytruthconditionsforconditionalsisthat theydon’thaveany:theyarenottobethoughtofaspropositions,trueorfalseas thecasemaybe.
Allthistookalotofgettingtothebottomof.PerhapsIwaseasedintoaccepting thelackoftruthconditionsbyhavingpreviouslyreviewedJ.L.Mackie’ s Truth, ProbabilityandParadox,wherehedefendsasuppositionalviewofconditionals anddeniesthattheyarestraightforwardlytrueorfalse.Ididn’tmuchliketheview atthetime,anddidn’tthinkMackiehadadequatereasonsforthedenial,butit wasatleastsomethingIhadcomeacrossandthoughtabout.Iworkedaloton tryingtogettheargumentsagainsttruthconditionsassimpleandintuitively compellingasIcould.
Leapingaheadnearlyadecade,IgaveacourseonconditionalsattheInstitutode InvestigacionesFilosóficasinMexicoCity,inthesummerof .Myfriendand colleaguefromBirkbeck,MarkPlatts,hadgonetoworkthere.Ihadalreadyvisited him.Ihadsurprisedhiscolleaguesthere,andhadsurprisedmyself,by findingthat IcouldstillspeaktheSpanishIlearnedinPeruasachild.Igavethecoursein Spanish,whichwasgreatfun.Intheaudiencewasarecentlyarrivedphilosopher fromArgentina,RaúlOrayen.Havingeachcomeabout milesfromopposite directions,itwassometimesuncannyhowsimilarlywethoughtabouttopicsin philosophyandlogic.RaúlwantedapaperonthismaterialfortheMexicanjournal Crítica.Almostwithoutexception,publicationsneedtobesqueezedoutofme.Raúl pesteredagreatdeal,and ‘DoConditionalsHaveTruthConditions?’ appearedin Crítica, .Ayearortwolater,backinLondon,inmyroleasHonorarySecretary andEditoroftheAristotelianSociety,IwascorrespondingwithFrankJacksonabout hiscontributiontoaJointSession,andenclosedacopyoftheconditionalspaper.He selecteditforthecollectiononconditionalshewaseditingfor OxfordReadingsin Philosophy ()andsothepaperhadawiderreadershipthanIhadthoughtit would.(Ididmessthingsupabitbyaddingtotheoriginalversionafewparagraphs towardstheend,aboutStalnaker’ s ‘IndicativeConditionals’,andmakinganerror (aboutaraindance).Othershaveconvincedmethatthereisneverthelessagood pointtobesalvagedfromtheerror.)
Iwas,fromthestart,verytakenwithAdams’sideasaboutcounterfactuals,but we ’llleavethattopicuntillater.Ithinkitwasinthelate sthatIwas firststruck byananalogybetweenthelotteryparadoxandthesoritesparadox.Themessageof theformer,asIsaidabove,isthatasufficientlylargenumberofpremises,eachvery closetocertain,canlead,byvalidreasoning,toacertainlyfalseconclusion,because theuncertaintiesofeachpremisecanmountup.Similarlyinthecaseofvagueness, Icametobelieve,alargenumberofpremiseseachveryclosetoclearlytruecanlead onebyvalidreasoningtoaclearlyfalseconclusion.IndeedIargue,somewhat unorthodoxly,thatdegreesofclosenesstoclearcases,idealizedsoastoberepresentedbynumbers,haveaprobabilisticstructure,andsoyetanotherapplicationfor probabilitytheoryistothephenomenonofvagueness.Mymostworkedoutpaperon thatthemeis ‘VaguenessbyDegrees’ inRosannaKeefeandPeterSmith, Vagueness: AReader ().
Itmusthavebeenintheearly swhen,workingonDummett,Icameacross Fitch’sparadox:theargumentfrom ‘alltruthsarepossibleobjectsofknowledge’ to ‘alltruthsareknown’.Forsupposethereisatruth, p,whichisneverknowntobetrue. Thenthereisatruth, ‘p anditisneverknownthat p’,whichitisimpossibletoknow. Itoccurredtome suddenly,oneevening,onmybicycle thattherewasaway roundthisargument:the ‘world’ oftheknowledgedoesnothavetobethe ‘world’ of thetruth.Justaswecanhaveknowledgeofotherpossiblesituations,so,inother possiblesituations,wecanhaveknowledgeofotherpossiblesituations,someof whichareactualsituations.JustasIcanknowthatifIhadn’tnoticed, p wouldnever havebeenknown,so,whenIdidn’tnotice,inthepossiblesituationinwhichIdid, Icanthinkoftheactualsituationandknowthatinit, p istrueandunknown.Allthis neededalotofmakinggood,buttryingtodosowasinterestingandfun.Threebrief comments: first,Iuse ‘knowledge’ forsimplicity,butitwouldbesafertostatethe wholeargumentintermsofreasonablebelief.Second,themodalentitiesofwhichwe haveknowledgeshouldnotbethoughtofasfullyspecific fine-grainedworlds,replete witheverydetail,butascoarse-grainedpossibilities,likethepossibilitythatitwill raininLondontomorrow thesortofpossibilitieswereferto,talk,think,and reasonabout.Thereismuchtobesaid,independentlyofFitch’sargument,for takingtheseasbasic.Andthird,oneneedstosaysomethingaboutwhatmakesthe possibleknowledgelatchontotheactualsituation,ratherthansomeothersituation inwhich p
In ,preparingaJointSessionpaperforasymposiumwithAnthonyAppiah onDummettianthemes,IfoundIneededtorefertothisphenomenon,so Isubmittedmy ‘ParadoxofKnowability’ paperto Mind,whereitwaspublishedin thesameyear.TwocriticalresponsesbyTimothyWilliamsonappearedpromptly, andwerelaterreworkedinhisbook KnowledgeandItsLimits.Pressedtorespondto hiscriticismsthen,Itriedtodosoin Synthese, ,whereItriedtodoabetterjobof sayingwhatmakesamerelypossiblepieceofknowledgerefertotheactualsituation. Thedebatecontinues.
Iwasnotmotivatedbyanurgetodefendantirealism,althoughthisargumentdid seemtometodefeatittooeasily.Itwasratheranengagingproject,tryingtomake senseofan ‘outsideviewlookingin’,ratherthanan ‘insideviewlookingout’,at modalreality,toputitmetaphorically.
In IspenttheautumntermasaVisitingFellowatPrinceton,whereIenjoyed somegreatseminars:DavidLewisonmodality,SaulKripkeonidentityandDick Jeffreyonprobability.BasvanFraassenwasonleave,butbackintownoccasionally, andIhadsomegoodconversationswithhimaboutbeliefrevision.(Theonly downsidetothevisitwasabrokenjawandruinedteethastheresultofabicycle accident.)
ImadetwovisitstoPragueinthe s,givingundergroundlectures,underthe auspicesoftheJanHusFoundation.The firstwerepartofacourseonFregeand Russell,thesecondpartofacourseonKant(theAesthetic,andtheTranscendental Deduction) allideologicallydangerousintheeyesoftheregime.Theaudiences consistedofhighlyintelligentandculturedstreet-sweepersandthelike.Alecture wentlikethis:Ihadascript,andsodidtheorganizer.Iwouldreadasentence. Hewouldtranslateit.Thereoftenensuedadiscussionorargumentaboutthe
translation,andIwouldthenbeconsulted:isthis,orthat,abetterrenderingofwhat Isaid?TherewouldfollowadiscussionaboutwhetherIwasright.Onlywhenthe sentencehadbeenunderstoodandevaluatedbyeveryonedidweproceedtothenext sentence.Ittookalongtime,butneverhaveIhadsuchanattentiveaudience.The firstlectureIgaveonmyreturn,backinLondon,Ilookedaroundindismayand wonderedwhatproportionofwhatIsaidwasbeingtakenin!
In IlecturedagaininMexico,andwentontoBuenosAirestogivesome lecturesattheArgentinianSocietyforAnalyticPhilosophy,SADAF.The Argentinianphilosopherswereveryableandkeen.Theyhadrecentlysuffereda periodnotunlikethatinPrague:duringthetimeoftheColonels,analyticphilosophy wasdeemeddangerousandSADAFwasbanned,andhadgoneunderground.That wasatimeofespeciallyintensephilosophicalactivity,theysaid.Nowthatdemocracy wasrestored,oneofitsmembers,CarlosNino,wasMinisterforJustice.
SADAFoccupiedapleasanttownhousealittlenorthofthecentreofBuenosAires. TheorganizationconsidereditselftobemodelledontheAristotelianSociety(which Iwasrunningatthetime).Iwasaskedmorethanonce,whereinLondonisthe AristotelianSociety?Theirimagewasofanimpressivebuilding,sotheyweremost disappointedtolearnthatwehiredaroomonceafortnightforourmeetings,and apartfromthat,itwaslocatednowhere!(Iwasabletoarrangeforthemtoreceivefree copiesofthe Proceedings.)
ItaughtatUBCinVancouveragainin and ,onesemestereachtime.On thesecondoccasionIwastold,ratherapologetically,thatwhatwasrequiredwasan introductorycourseonnon-conclusivereasoning:twosections,eachmeetingthree timesaweek,anddoingweeklyhomework.Thisturnedouttobemostenjoyable loadsofprobabilisticpuzzles,andmuchbesides.Ihavenotesexceeding pages. Ifoundtheexperienceofdoingthesamecoursetwiceover,tomysurprise,avery goodwayofimprovingthecourse.BackinLondon,inwhatwasstillthefederal degree,thereweredaytimelecturesforUCLandKing’sstudentsandeveninglectures forBirkbeckstudents.Isuggestedthatthosewhowishedcouldmeettheirlecturing requirementsbygivingthesamecourse,onceinthedayandonceintheevening, ratherthantwoseparatecourses.Manylikedtodothis,thoughsomedidn’t,andit cametobeknownastheEdgingtonplan,and flourishedforwelloveradecade.Alas, thefederaldegreeisnomoreandthereislittleopportunityforco-operationbetween thecollegesthesedays.
AlsoperhapsworthacommentisamethodofdistributingnoteswhichIlearned fromJonathanBennett:Iwouldgivethelecture,thenIwouldwriteupthenotes alwaysagoodleadintopreparingthenextlecture andtheywouldbedistributedat thenextmeeting,aftertheevent.IdidthislaterwhenteachingatOxford(mainly logicandlanguage,alsoepistemology)andmoststudentslikedit certainly,Ihad requestsforcopiesofthenotesforyearsafterIleftOxford.
In Johnhadanoverduesabbaticalcomingupafteranexceptionallylongstint asHeadofDepartment,IappliedforandgotaBritishAcademyResearch Readership,andwespenttheacademicyear – firstattheUniversityofTexas atAustin,andthenatBerkeley.AtBerkeleywewereluckytorentDonaldDavidson’ s house,ashighonthehillasthehousesgo.AndatBerkeleyI finallymetErnest Adams,andweworkedtogetheralot notonlyonconditionals,butalsoonthe
