Topics of thought the logic of knowledge belief imagination francesco berto

Topics of Thought. The Logic of Knowledge, Belief, Imagination

Francesco Berto

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TopicsofThought

TheLogicofKnowledge,Belief,Imagination

FrancescoBerto

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Tothememoryofmydad

Acknowledgments

Thisbookisonemainoutcomeofthe2017-2022research project TheLogicofConceivability:ModellingRationalImaginationwithNon-NormalModalLogics,fundedbytheEuropeanResearchCouncil(ERC)undertheHorizon2020 ResearchandInnovationProgramme,GrantAgreementNo. 681404,andco-hostedbytheDepartmentofPhilosophy attheUniversityofStAndrewsandbytheInstitutefor Logic,LanguageandComputation(ILLC)attheUniversity ofAmsterdam.Iamgratefultomycolleaguesatboth institutionsforsurroundingmewithtwoperfectacademic environmentsduringmyresearch.Atthebeginningof2014, ImovedfromScotlandtoAmsterdam:IarrivedattheILLC withlittleknowledgeofepistemiclogicandnointerestin epistemology.Bytheendof2018,whenIreturnedtomy belovedScotlandtojoinStAndrews,myexposuretothe ILLC’sgreattraditioninepistemiclogichadcausedmy intereststoexpandinwaysthisbookmakesapparent.

MybiggestdebtistotheLogicofConceivabilityGang,for helpingmetoshapemostoftheideasthebookplayswith: PeterHawkeandAyb¨uke ¨ Ozg¨un(whohavealsoco-authored itsChapters2and4and,respectively,7and8),Karolina Krzy˙zanowska,TomSchoonen,AnthiaSolaki,ChrisBadura, andThomasFerguson.

In2020Ipresentedmostofthebook’scontentstwice, intwoseriesofseminarsdeliveredonline(youknowwhy) toheroicaudiences,duringmyhonoraryChaireMercier Lectures‘at’theUniversit´eCatholiquedeLouvain,and‘at’ the9thSummerSchoolinPhilosophyoftheUniversityof

Hamburg.Between2016and2021,Ipresentedindividual Chapters,orthepaperstheyarebasedon,inanumber ofvenues:theseminaroftheArch´eLogicGroupatthe UniversityofStAndrews;theNon-CategoricalThinking WorkshopattheCenterforLogicLanguageandCognition, UniversityofTurin;theKyotoWorkshoponParaconsistency andDialetheismattheUniversityofKyoto;theTokyoForum forAnalyticPhilosophyattheUniversityofTokyo;the workshoponImaginationandModalityattheUniversity ofPadua;theconferenceonConceivabilityandModality attheUniversityofRome-LaSapienza;the9thEuropean ConferenceofAnalyticPhilosophyattheUniversityof Munich;theworkshoponDoxasticAgencyandEpistemic LogicattheRuhrUniversityofBochum;theconferenceon thePhilosophyofImagination,againattheUniversityof Bochum;theConferenceonReasoninginSocialContextsat theRoyalNetherlandsAcademyofArtsandSciences;the PhilosophyofLanguageandLogicSeminarattheUniversity ofMilan;aseminarattheDalleMolleInstituteforArtificialIntelligenceinLugano;theLogica2018conferencein theCzechRepublic;theconferenceonModelsofBounded ReasoninginIndividualsandGroupsattheLorentzCenter inLeiden;the41stInternationalWittgensteinSymposium inKirchbergamWechsel;aconferenceattheRoyalSociety ofEdinburgh;thePhilosophySeminarattheUniversityof Stirling;aseminarfortheMUMBLEResearchGroupat theUniversityofTurin;thePhilosophicalReflectoriumat theUniversityofStAndrews;aseminarattheInstituteof Philosophy,UniversityofLondon.

Asyoumayhaveguessedfromsuchalonglist,waytoo manypeoplehavecomeupwithgoodquestions,suggestions, andcriticisms,formetobeabletothankeveryoneindividually.I’llgiveitatry,withapologiestothoseIhave forgotten:ArifAhmed,MariaAloni,HolgerAndreas,Sergei Artemov,MagdalenaBalcerak-Jackson,AlexandruBaltag, JohanvanBenthem,CorineBesson,SarahBroadie,JessicaBrown,ClaudioCalosi,IlariaCanavotto,MaxCarrara, JoanCasasRoma,RobertoCiuni,DamianoCosta,Aaron Cotnoir,EnzoCrupi,MarcelloD’Agostino,JohnDivers, MikeDunn,MarieDuˇz´ı,PaulEgr´e,PetervanEmdeBoas,

JorgeFerreira,CamilleFouch´e,LelloFrascolla,AleGiordani, MartinGlazier,ValeriaGiardino,MattGreen,PatrickGreenough,DavideGrossi,KatherineHawley,LevinHornischer, HykelHosni,AndreaIacona,LucaIncurvati,ManuelGustavo Isaac,BrunoJacinto,MarkJago,BjørnJespersen,Amir Kiani,AmyKind,StephanKr¨amer,MichielvanLambalgen,DanLassiter,MiguelLeonUntiveros,HannesLeitgeb, MartinLipman,JiqiLiu,TitoMagri,DiegoMarconi,Neri Marsili,PeterMilne,SanjayModgil,SarahMoss,Bence Nanay,AntonioNegro,DanielNolan,SebastianObrist,Sergei Odintsov,HitoshiOmori,NaomiOsorio-Kupferblum,David Over,WalterPedriali,MatteoPlebani,GrahamPriest,Simon Prosser,ThomasRandriamahazaka,StephenRead,Fran¸cois Recanati,GregRestall,FlorisRoelofsen,RobertvanRooij, StefanRoski,GillRussell,BenSachs,PierreSaint-Germier, PaoloSavino,KevinScharp,BenSchnieder,KatrinSchulz, SonjaSmets,JustinSnedegar,RoySorensen,BeppeSpolaore, MargotStrohminger,MichaelStuart,NeilTennant,Peter Verdee,AlbertoVoltolini,HeinrichWansing,ZachWeber, TimWilliamson,CrispinWright,SteveYablo.Iamalso gratefultothestaffatOxfordUniversityPress;toPeter Momtchiloff,forbeingsuchawiseeditorandforproviding terrificanonymousreviewers(thankstoyou,too!)forthe bookmanuscript;andtoMarkJago(again)forallowingme toformatthisbookusinganelegantLaTeXtemplateofhis design.

Variouspartsofthebookrelyonpreviouswork.Chapter1 isnew.Chapter2ismostlynew,butalsousesmaterialfrom anunpublishedmanuscriptco-authoredwithPeterHawke andLevinHornischer.Chapter3ismostlynew,butalso includes(arecapof)ideasthatshowedupinpaperson whichthefollowingChapters4to6arebased.Thesego asfollows:Chapter4isbasedon‘KnowabilityRelativeto Information’, Mind 2021(withPeterHawke).Chapter5is basedon‘EquivalenceinImagination’,in EpistemicUses ofImagination (Routledge2021,editedbyAmyKindand ChrisBadura),thoughitalsoincludesideastakenfromthe older‘AboutnessinImagination’, PhilosophicalStudies 2017. Chapter6includesideasfrom‘SimpleHyperintensionalBelief Revision’, Erkenntnis 2018,aswellasnewmaterial,and

fixessomeclaimsfromthat2018paperwhich,Inowthink, werenotquiteright.Chapter7isbasedonanunpublished manuscript,provisionallytitled‘TheLogicofFramingEffects’ andco-authoredwithAyb¨uke ¨ Ozg¨un.Chapter8isbased on‘IndicativeConditionals:ProbabilitiesandRelevance’, PhilosophicalStudies 2021,co-authoredwithAyb¨ukeagain. Iamgratefultoalltheeditorsandpublishersforpermission tore-usematerialfromthepublishedworks.

Finally:thanksmum,dad,Val,andMabel,forkeepingme fromthinkingtoomuchabout thinkingabout.

WhatThoughtsAreAbout

Wethinkaboutthisandthat:whenonethinksthatMary ishappy,one’sthoughtisabouthowMaryisdoing.When onesupposesthatthemarketswillfall,one’ssuppositionis aboutwhatwillhappenwiththemarkets.Whenonebelieves thatJohnistallandhandsome,one’sbeliefisaboutJohn’s heightandlooks.Whatisthelogicofsuchthoughts?This bookbeginstoexploretheideathat,toanswerthequestion, onehastotakethat‘about’atfacevalue.

Aboutnessis‘therelationthatmeaningfulitemsbearto whateveritisthattheyare on or of orthatthey address or concern’(Yablo 2014,1).Thisistheir subjectmatter or,asI willalsosay,their topic.Researchonaboutnessandsubject matterhasbeenburgeoninginthelastdecades,thanksto theworksofphilosophersandlogicianslikeDavid Lewis (1988a,b),Ken Gemes (1994, 1997),Lloyd Humberstone (2008),StephenYablo,Kit Fine (2016a, 2017),Peter Hawke (2018),Friederike Moltmann (2018),Arthur Schipper (2018, 2020),andmore.

Suchworksaddressaboutnessmostly,thoughnotonly, asafeatureofthosemeaningfulitemswhicharepieces oflanguage–inparticular,declarativesentences.However, mentalstatescanbemeaningful,too.Onetraditionalname forsuchmeaningfulnessis‘intentionality’:thefeaturethat someofourmentalstateshave,ofbeingdirectedtowards objects,situations,orstatesofaffairs.Thebookdealswith

TopicsofThought:TheLogicofKnowledge,Belief,Imagination. FrancescoBerto,OxfordUniversityPress.©FrancescoBerto2022. DOI:10.1093/oso/9780192857491.003.0001

propositionalor dedicto intentionalstates:statesofthemind whicharegenerally,thoughnotuniversally,understoodby philosophersashavingpropositionsastheircontents,andas beingdirectedtowardsthesituationsthepropositionsare concernedwith.Thus,suchmentalstatesareoftencalled ‘propositionalattitudes’:theyarerecordedlinguisticallyby verbstakingsententialcomplements,suchas‘believes(that)’, ‘knows(that)’,‘imagines(that)’,‘supposes(that)’,‘isinformed(that)’,usedtoascribeattitudestowardspropositions, ortowardswhatmakesthepropositionstrue.Iwilloftenuse theterm‘thoughts’asacover-allforsuchstates.1

Thebookexploresanewapproachtothelogicofthought –anew,unifiedwayofansweringthequestion:giventhat onethinks(believes,knows,etc.)that ϕ,whatother ψsdoes onethink(believe,know,etc.)bythelogicofone’sthought? Underwhichlogicaloperationsisone’sthought closed ?

Whileaddressingthequestion,thebookalsotriestoshow thatsuchanapproachhasalottogivetophilosophy,in areasthatrangefrommainstreamepistemology(dogmatism, scepticism,fallibilism),tosuppositionalthinkingandthe cognitiveroleofimagination,tobeliefmanagementand revision,probabilisticthinking,andconditionality.

1 ItwouldhavebeenniceifI’dhadsomethingtosayontheconnections betweenaboutness,topicality,and dere intentionalmentalstates–states directedtowardsobjects,andrecordedlinguisticallybyverbstakingnounphrasecomplements:‘PaullovesPeter’,‘MaryadmiresFrodo’,‘Carlosimagines thewingedhorse’,‘TheGreeksworshippedZeus’.However,theconnections betweentopicalityand dedicto intentionalitygavemeplentyofworkalready foraninitialexploration.Besides, dere intentionalitymaybeespeciallyrelated tothetopicalityofthesubsententialcomponentsofsentences,andIthinkit isfairtosaythatthisiscurrentlyalessdevelopedareaofaboutnessresearch, thoughsee,e.g., Hawke (2018), Badura (2021b),forpromisingideas.Notorious puzzlesofintentionalityinthe dere ballparkinvolveputativefailuresofthe SubstitutivityofIdentity(or,moreaccurately,Substitutivityof(Rigid)CoReferentialTerms:DavefearsJacktheRipper,butDavedoesn’tfearhis neighbourJohn;unbeknownsttohim,JohnisJacktheRipper);andproblems concerningexistenceandexistentialgeneralization(MaryadmiresFrodo;does thereexist,therefore,someonewhomMaryadmires?).I(still)thinkthatthe bestwaytoaddressthelatterkindofissueistogoMeinongianandadmit nonexistentobjects:see Zalta (1988); Berto (2012); Crane (2013); Priest (2016).

Themostwell-knownlogicalanswertothequestionof closurecomesfromstandardepistemiclogicinthetradition of Hintikka (1962):wetreatnotionslike knows,believes, isinformedthat,usingnormalmodallogic.Werepresent attitudeascriptionsviaoperatorsinterpretedasquantifiers overpossibleworlds(waysthingsasawholecouldbeor havebeen),restrictedfromtheviewpointofagivenworld byabinaryaccessibilityrelation, R.Weread R indifferent ways,dependingontheoperator:evidentialindiscernibility, consistencywithone’sbeliefs,etc.‘Xϕ’(‘Theagent Xsthat ϕ’,where‘X’canascribeknowledge,belief,etc.)istrueat world w justincase ϕ istrueatabunchofworldsaccessible viatherelation R from w.Byimposingsimpleconditions on R,wecanthenvalidatevariousprinciplescharacteristic ofdifferentmodalsystems,andwhichsupposedlycapture featuresoftherelevantattitudes.Someconditionson R aremorecontentiousthanothers.Wegenerallyagreethat R shouldbereflexivefor‘X’tobereadas‘knows’,given thatknowledgeisfactive(onecanonlyknowtruethings);it shouldn’t,forittobereadas‘believes’(onecanhavefalse beliefs).Butwedebateonwhether R shouldbetransitive,for wedisagreeonwhetherPositiveIntrospectionshouldholdfor knowledgeorbelief:does Xingthat ϕ entailthatone Xsthat one Xsthat ϕ?

Whateverconstraints R maysatisfy,thissettingdelivers unrestrictedclosure,i.e.,fullclosureunderlogicalconsequenceorentailment,for X qua normalmodality:one Xs whateverisentailedbywhatone Xs.That’sbecause,if one Xsthat ϕ,then ϕ mustbetrueatallpossibleworlds accessiblevia R.Butthat ϕ entails ψ isunderstoodas meaningorimplyingthatanyworldmaking ϕ true(inany modelofourlogic)willalsomake ψ true.Andsoonewill also X that ψ.Inparticular,onealwayshasthesameattitude towards‘intensional’,logicalornecessaryequivalents:if ϕ and ψ aretrueatthesamepossibleworlds(ofallmodelsofour logic),one Xsthat ϕ iffone Xsthat ψ.

Thisrepresentshighlyidealized,logicallyomniscientagents (Faginetal. 1995,ch.9)that,forinstance,canneverretain

inconsistentbeliefswithouttriviallybelievingeverything. ThesamehappensinthemainstreamAGMapproachto beliefrevision(Alchourr´onetal. 1985),aswellasinepistemic logicsthatrecaptureAGMinamodalsetting(VanDitmarsch etal. 2008).Additionally,thestandardHintikkanframework istypicallymonotonic,inthatitdoesn’tstraightforwardly model,e.g.,theideathatmoreinformationmayresultinless knowledge(Harman 1973; Brown 2018).

Asharedfeatureoftheoperatorsintroducedinthisbook, instead,isthattheyfailfullclosure:onesometimes Xsthat ϕ without Xingalogicallyentailedornecessarilyequivalent ψ.Thisistiedtowhatthepropositionsthat ϕ andthat ψ are(and,arenot)about,andthereforeone’sthoughtis (and,isnot)about.Theaboutnessofa dedicto intentional state, Xingthat ϕ,shouldbesuitablyrelatedtothatof theproposition, P ,whichmakesforthecontentof ϕ.And thisbookmarketstheideathat P maybeunderstood,not justasthesetofpossibleworldswhereitistrue,butalso intermsofwhatitisabout:itssubjectmatter,ortopic.2 Therefore,thelogicofintentionalitymustbetopic-sensitive: topicsexplicitlyfeatureinthesemanticsoftheoperatorsthat representattitudeascriptions.Duetosuchtopic-sensitivity, theoperatorsarehyperintensional(BertoandNolan 2021): substitutionoflogicalornecessaryequivalentsintheirscope

2

Isaidabovethatthecontentsofattitudeslikebelieforknowledgearenot universallyunderstoodbyphilosopherstobepropositions.Sarah Moss (2018) hasrecentlyadvancedtheoriginalproposalthattheybetaken,instead,as setsofprobabilityspaces,calledprobabilisticcontents(roughly:aprobability spaceisasetofpossibleworldswithanalgebraofpropositions,takenassetsof worldsintheirturn,andaprobabilitymeasureontheelementsofthealgebra). Whenit’saboutattitudessuchasfull(asopposedtograded)beliefs–the kindofattitudeswewillfocusonforthemostpartinourbook–thereisa correspondencebetweenpropositionsandcertainsimpleprobabilisticcontents: onecanassociatetoeachproposition P thesetofprobabilityspacessuchthat P istrueateachworldintheirdomain.Probabilitiesareidleforsuchprobabilistic contents,forwhattheyreallyrepresentisonlyadistinctionbetweenpossible worlds(Moss 2018,14).Buteveninthiscase,forMossafullbeliefascription doesn’tascribebeliefinthatsimplecontent:‘John(fully)believesthatMaryis happy’isusedtoconveythatJohnhasaprobabilisticbeliefthat’srelevantly similartothebeliefthatit’scertainthatMaryishappy(Moss 2019).Itwould beaninterestingtask,althoughit’snotonepursuedinthisbook,toinvestigate howMoss’viewmayconnecttotopic-sensitiveconceptionsofpropositional content.

cansometimesfailtopreservetruth.

Ontheotherhand,theoperatorsintroducedinthebook arenotlogicallyanarchic.Touseterminologygoingback, Ithink,to Dretske (1970),theyare semi-penetrating:they penetratethrough,orareclosedunder,someentailmentsor logicalconsequences,althoughtheydon’tfullypenetrate.One whoadvertisessuchoperators,therefore,mayendupinthe uncomfortablepositionoffacingbothchargesofexcessiveand ofinsufficientclosure.Forinstance,defendersoffullepistemic closure,i.e.,fullclosurefortheknowledgeattitude,willstress thatcorrect,competentlycarriedoutlogicaldeductionisthe safestwaytopreserveknowledge.Onecannotbechargedof committingthefallacyoflogicaldeduction, Kripke (2011a) protests.

Viceversa,enemiesoflogicalidealizationwillfindcounterexamplestoanyresidualclosurefeaturebylookingat ordinaryagents.Ifthepointofavoidinglogicalomniscience istorepresentrealisticreasoners,whystopshortofcomplete logicalanarchy?Can’tJoeBloggsevenfailtobelievethat ϕ whilehebelievesthat ϕ ∧ ψ becauseheis,onoccasion, cognitivelyincapacitated,otherwisebusy,orso?Insofaras deductionhappensintime,onecouldalwaysgetdistracted andfailwhileinthebusinessofapplyingConjunctionElimination.3

Defendingthespecificvaliditiesandinvaliditiesinvolving varioustopic-sensitiveoperatorsisonetaskcarriedout throughoutthisbook.Herefollow,instead,somegeneral considerationsconcerningidealization.

3 See Williamson (2000),282(hespeaksofsuddendeath;Iwentforthe lessdrasticdistraction). HarmanandSherman (2004)criticizeWilliamsonfor assumingthat‘deductionisakindofinference,somethingonedoes’,andclaim thatthis‘confusesquestionsofimplicationwithquestionsofinference’(495). Asremarkedby Holliday (2012),weuse‘deduction’,notonlytoreferto(what onemighttakeas)abstract,perhapsstructured,objectsoutsideofspacetime, butalsotorefertoahumanactivity(asin‘SherlockHolmeshadmadethe rightdeductiononemoretime’):thementalprocessofdrawingconclusions frompremisesinacertainway;andIthinkit’sthislattersensethatisrelevant forWilliamson’sremark.

1.2LogicalOmniscience

Debatesonlogicalomniscienceinepistemiclogicareattimes phrasedintermsofarigidnormative/descriptivedichotomy: isonedealingwithidealagentsrepresentinganormative standard,orisonedescribingordinarythinkers?Iftheformer, whynotfullclosure?Ifthelatter,whyanyclosureatall?I thinkthiswayofputtingthingsismisleadinginanumberof ways.Here’sone:itconfusesidealizationwithnormativity. Thatlogicallyomniscient,idealizedagentsareontopof certainlogicalconsequencesoftheirthoughtsdoesn’tmean that we shouldbe. ϕ entails ϕ ∨ ψ, ϕ ∨ ψ ∨ χ,andsoon,and sologicallyomniscientagentswhobelievethefirstitemin theseries,believethewholeseries.Butgiventhatoneof us believesthatitisraining,oneishardlyrationallycommitted tocomingtobelievethateitheritisrainingorthere’slife onKepler-442b;thateitheritisrainingorthere’slifeon Kepler-442borpigscanfly;andsoon.Limitedaswearein ourtime,attention,memory,andcomputationalpowers,we shouldn’twasteourresourcesbyengaginginsuchastupid sequenceofdeductivemoves.Asargued,e.g.,by Cherniak (1986), Harman (1986),rationalthinkersmustnot‘clutter theirmind’withpointlessinferences.

Here’sanotherconfusionweneedtoavoid:weshould notforgetthatwefailtobelogicallyomniscientforvery diverseandoftenorthogonalreasons.Sometimeswefail tohavetherightattitudetowardssomenecessarytruths simplybecausewelacksomerelevantempiricalinformation: oneisnotinformedthatone’sneighbourJohnisJackthe RipperalthoughonehasnodoubtsonJohn’sself-identity. Wesometimesknowsomenecessarytruthsbecausetheywere easytoprove,whereaswedon’tknowothertruthswhichare necessary(ofthesamesortofnecessity)becausetheyare difficulttoproveor,moregenerally,theyinvolvesophisticated reasoningweareunabletocarryout:onecanknowfrom elementaryschoolthat7+5=12withoutknowingthat xn + yn = zn hasnosolutionsinpositiveintegersfor n> 2. Onecaninstantlyseethat ϕ ⊃ ϕ isalogicaltruthwithout knowingthatalongandcomplicatedpropositionaltautology is.

Next,sometimeswethinkthat ϕ withoutthinkingthat ψ, although ϕ entails ψ,becausewelacksomeconceptneeded tograspthepropositionthat ψ,andonecannothavesuch attitudesasknowledge,belief,orevensupposition,towardsa contentonecannotgrasp.Onecan,forinstance,believethat ϕ withoutbelievingthat ϕ ∧ (ϕ ∨ ψ)althoughthetwoare logicallyequivalentinclassicalandinvariousnon-classical logics,foronelackssomeconceptwhichisneededinorder tograsp ψ’scontent.Perhapsonecannotevenseethat ϕ if onelacksconceptsrequiredtograspthepropositionthat ϕ, althoughonecanseeasituationinwhich ϕ (Barwiseand Perry 1983; Williamson 2000):onecanseeasituationin whichGretaisplayingGo,butonecannotseethatGreta playsGoifonehasnoideaofwhatGois.

Next,sometimesit’stheintrinsicnatureofthestatethat standsinthewayoffullclosure,evenfor‘ideallyastute logicians’(Dretske 1970,1010)who,inaddition,havethefull repertoireofconceptsattheirdisposal.Somepropositional attitudesfailfullclosureinanobviousway:onedesiresor hopesthatone’sheadachegoesaway,andthisentailsthat onehasaheadache;butonedoesn’tdesireorhopethatone hasaheadache,evenasanideallogician(supposingsuch logicianscanstillhaveheadaches).

Finally,otherattitudesmayfailfullclosureinaless obviousway.Fullepistemicclosureisattimescontested alsoforaccommodatinginterpretationsof‘Xϕ’,e.g.,not assayingthatoneknows ϕ,but,roughly,thatoneisina positiontoknowitbracketingcontingentobstaclesaswellas cognitiveandcomputationallimitations.Somephilosophers haveseriouslyentertainedtheideathatperfectreasonersmay knowthattheyhavehands,withoutbeingpositionedtoknow thattheyarenorecentlyenvattedhandlessbrains,although thehavingofhandsentailsthatoneisnohandlessbrainina vat.

Whatweneed,istobeclearonwhatweareafterin ourmodellingactivities.Wemaywanttoidealizeinone dimension,withoutthisimplyingthatweaimatgiving anormativeaccountforthatdimension.Itmayturnout thattheagentswemodel,idealizedincertainrespects,also happentorepresentsomesortofnormativestandardforthose

respects.Butthat’snotthemainreasonwhyweidealize: wedoitchieflyinordertohaveasimpleandmanageable settingtoworkwiththere,whileweexaminetheeffects ofde-idealizationinanother,orthogonaldimension,which isthefocusofourmodellingaims.Idealizationisforus justusefulsimplificationhere.Forinstance:wemaywant torepresentagentswithalimitedconceptualrepertoire, butwhoserelevantattitudesareperfectlyclosedwithrespecttoanypropositiongraspabletothem,tostudyhow conceptuallimitationsworkina‘pure’setting,i.e.,onein whichlimitationsofotherkindsdon’tgetintheway.Or, wemaywanttorepresentagentswhoaredeductively and conceptuallyunbounded,butwhoseepistemicpositionis defeasiblebecausetheyoperateonlimitedandpotentially misleading,evenwhentruthful,information.Or,wemaywant tograntsuchagentsattitudeswhicharenotfullyclosed,just becausewethinkthat’stheintrinsicnatureoftherelevant attitudes.4 Asthestorytoldinthisbookunfolds,thehope (thoughImayhavefailedtoliveuptoitthroughoutallof thework)isthatitisclearenoughwhatkindsofidealizations andde-idealizationsareinplaceinitsvariousparts.

What’sinthestory?Thefollowingsectiongivesachapterby-chapteroverview.Itdeferstosubsequentchaptersfor defensesofthemainclaims,butit’shopefullydetailedenough forafirstpass.

4 Someexamplesofworksthatidealizeinonedimensioninordertobetter focusonanother: Williamson (2000)highlightstheopportunityofassuming logicalomnisciencetostudytheeffectsoflimitedpowersofdiscrimination onagents,andadvocatesfailureofintrospectiveprinciplesforsuchagents (theydon’talwaysknowthattheyknow). Holliday (2012)focuseson‘ideally astutelogicians’`alaDretske,who‘knowalllogicallyvalidprinciplesand[...] believeallthelogicalconsequencesofwhattheybelieve’(92)tostudypossible failuresofepistemicclosureforthem–thus,closurefailureswhicharenotdue todeductivelimitationsofthemodelledagents.Presentingawarenesslogics, Schipper (2015)proposesafullS5modallogicforepistemicoperators,thus representingfullypositivelyandnegativelyintrospectiveepistemicagents(not onlyaretheylogicallyomniscient:also,theyalwaysknowbothwhattheydoand whattheydon’tknow),inordertoinvestigatetheconsequencesoflimitations inconceptualawareness.

1.3What’sintheBook

Thecoreideaisthatthetopic-sensitivityof dedicto thoughts pivotsontheoneofthepropositionsmakingfortheircontents.

Nowchapter 2 developstheviewthatpropositionscanbe usefullyseenasfeaturing(atleast)twoconstituents:(1) truthconditionsand(2)subjectmatterortopic.Tosay thesamething–toexpressthesamecontent–sentences ϕ and ψ mustcoincideinbothtruthconditionsandtopic. Thechaptercalls two-component (2C) semantics theview thatsuchconstituentsarenotonlyusefullyrepresented asdistinct,butalso,reallyirreducibletoeachother,in asensetobeclarifiedthere.Itwouldhavebeenniceto callit‘two-dimensionalsemantics’,inordertohighlightthe orthogonalityof(1)and(2);but,alas,thenamewasalready taken:see Schroeter (2021).Varioussubject-matter-sensitive accountsofpropositionalcontentareone-component(1C): theyeitherreducetruthconditionstosubjectmatter,or viceversa.However,thereare2Capproachesonthemarket, too,e.g.,thoseby Epstein (1981, 1993); Hawke (2016, 2018); PlebaniandSpolaore (2021);andalsooneofthesemantic proposalsin Yablo (2014)countsas2C.

Thatthetwocomponentsareirreducibleis,Ibelieve,a strongerclaimthanwhatisneededtogetatopic-sensitive logicofintentionalitygoing.Hopefully,subsequentchapters willshowthatwehavegoodtheoreticalreasonsforrepresentingthecomponentsasdistinct,evenifeitherisultimately reducibletotheother.We(myselfandPeterHawke,thecoauthorofchapter 2)trythestrongerstancenonetheless.It popsupafewtimesinthebook,thatrealirreducibilitymay bephilosophicallymoresatisfactorythanusefulpretence.

Anyway,ourown2Csemanticsagreeswithvariousother subject-matter-sensitivesemantics,alsoofthe1Ckind,ona numberoffeaturesofsubjectmatters,whichareintroduced anddiscussedinchapter 2.Theseareimportantforthedevelopmentofatopic-sensitivelogicofintentionality.Inseveral formsofsuchsemantics,logicallyornecessarilyequivalent sentences ϕ and ψ candifferintheirpropositionalcontent whentheyareaboutdifferentthings,thatis,theyhave differenttopics.Thesemanticsare,thus,hyperintensional,

makingdistinctionsmorefine-grainedthanwhatstandard intensional(possibleworlds)semanticsallows.‘Equilateral trianglesareequiangular’and‘EitherPeterpassedtheexam, ornot’differincontenteveniftheyaretrueatthesame possibleworlds(allofthem),fortheyareaboutdifferent things:onlyoneisaboutequilateraltrianglesandhowthey arelike.Evensentenceswhicharenecessaryofthesamekind ofnecessitycansodiffer:‘2+2=4’isnotaboutequilateral triangleseither.

Can’tsuchdistinctionsbemadejustbyresortingtosome structuredaccountofpropositions(Soames 1985; King 1996; Chalmers 2011),whetherRussellianstructuresofdenotations, orstructuresofFregeansenses,orso?Thestructuredpropositionthat2+2=4differsfromtheonethatequilateral trianglesareequiangularinvariousways,e.g.,byincludinga constituent(say,thenumber2),whichisnotincludedinthe other.

Well,inanswertothis,letusstartbyremarkingthat our2Csemanticswillagreewithanumberofothersubjectmatter-sensitivesemantics,alsoofthe1Ckind,intaking varioussententialoperatorsofpropositionallogicas topictransparent:suchoperatorsaddnosubjectmatteroftheir own.WeechotheTractatianWittgenstein’s‘fundamental thought’,that‘the“logicalconstants”donotrepresent’ (4.0312).Inparticular,fornegation:

4.0621That,however,thesigns‘p’and‘∼ p’ can saythesame thingisimportant,foritshowsthatthesign‘∼’corresponds tonothinginreality.Thatnegationoccursinaproposition, isnocharacteristicofitssense(∼∼ p = p).[...]

5.44[...]Andiftherewasanobjectcalled‘∼’,then‘∼∼ p’ wouldhavetosaysomethingotherthan‘p’.Fortheone propositionwouldthentreatof ∼,theotherwouldnot. (Wittgenstein 1921/22)

Thetopicof ¬ϕ isthesameasthatof ϕ.‘Johnisnottall’is exactlyaboutwhat‘Johnistall’isabout,say:John’sheight. Additionally,conjunctionanddisjunctionmergetopics.The topicof ϕ ∧ ψ isthesameasthetopicof ϕ ∨ ψ,namely thefusionofthetopicof ϕ andthatof ψ.‘Johnistalland

handsome’and‘Johnistallorhandsome’arebothaboutthe sametopic,say:theheightandlooksofJohn(Fine 2020,136 makesaforcefulcase).

Iftheseareconstraintsonthetopicsoftherelevant propositions,theyshouldcorrespondtoconstraintsonthe attitudeshavingsuchpropositionsastheircontents:if,in ordertothinkthatJohnistall,youhavetothink,say,about John’sheight,thenthat’sexactlywhatyoumustthinkabout inordertothinkthatJohnisnottall.If,inordertothink thatJohnistallandhandsome,youhavetothink,say,about John’sheightandlooks,thenthat’sexactlywhatyoumust thinkaboutinordertothinkthatJohnistallorhandsome.

Nowthiswon’tautomaticallyworkifweresorttostructuredpropositions.Whatevertheirmerits,oneneedstofix somethingforthemtodeliveraplausibleaccountofsubject matter.ThestructuredpropositionthatJohnisnottall differsfromtheonethatJohnistallbyincluding not asa constituent.Thiswon’tworkforaboutness–apointmadein (Yablo 2014,1):thatpropositionmaybeaboutJohn,John’s height,howJohnislike,butsurelyit’snotabout not.And soitwillbefortheaboutnessofintentionalstateshaving thatpropositionastheircontent:whenyouthinkthatJohn isn’ttall,youarenotthinkingaboutnegation.(Thatdoesn’t makenegationunthinkable,ofcourse:youcanthinkthat negationisaone-placeconnective,forinstance.)Similarly, whenyouthinkthatJohnistallandhandsome,youarenot thinkingabout and,althoughthat,too,isaconstituentofthe structuredproposition.

Thetopic-sensitivesettingsuggestsanumberofclosure andnon-closurepropertiesforpropositionalattitudes,which areexploredstartingfromchapter 3.Whenthetopicof proposition P is x,andonethinksthat P ,onemustbe –stealingacoupleofYablovianmetaphors–‘attentiveto everythingwithin x’;butonecanbe‘oblivioustomatters lyingoutsideof x’evenwhencertainpropositionshaving those(subject)mattersastheirtopicareentailedby P :cf. Yablo (2014),p.39.

Onceonefactorsoutformsoflogicalnon-omniscience dueonlytocertaincognitiveandcomputationallimitations

(difficultiesinparsingthesyntaxofsentences,theboundaries ofpeople’sreasoningandmemorycapacities),claimslike thefollowingseemplausible:onecannotknowthatLisais richandhappywithoutknowingthatshe’srich(Conjunction Elimination);fornotonlyisthelatterknownproposition entailedbytheformer,butalso,whatit’saboutis part of whattheformerisabout.Onecannotimaginethat Jackisshortandthinwithoutimaginingthatheisthin andshort(ConjunctionCommutation)when‘and’stands forBooleanororder-insensitiveconjunction;fornotonly arethetwologicallyequivalent,butalso,theyareabout thesametopic.OnecannotbelievethatMaryisfunny andthatMaryishappywithoutbelievingthatshe’sfunny andhappy(ConjunctionIntroduction);fornotonlyisthe latterpropositionentailedbytheformer,butalso,itstopic isnothingbutthoseoftheformer,takentogether.5 Such closurefeaturesofsomeintentionalstates,mandatedbythe mereologyoftheinvolvedpropositions’topics,havebeen labelled immanentclosure bySteve Yablo (2014, 2017),and Iwilladopttheterminology.

Theideathatthoughtsaretopic-sensitiveand,becauseof this,‘closedundertopicality’ratherthanfullyclosedunder (classical,modal)logicalconsequence,isgainingpopularity. Itcanalsobefound,e.g.,intheworksofauthorslike Yalcin (2016),and Hoek (2022),whofocusonbelief(bothstressthat beliefsaresensitiveto questions;but,aswewillsee,thereare tightconnectionsbetweentopicsandquestions).Thetopicsensitivityofthoughtnaturallydelivers,infact,anumberof invalidities,too:whenyouthinkthatJohnistall,youneedn’t automaticallybethinkingthathe’stallorhandsome,evenif ϕ ∨ ψ isjustonesingleelementaryinferentialstepawayfrom ϕ and even ifyouareadeductivelyunboundedagent.You maynotbethinkingaboutJohn’shandsomenessatall(your mentalstateisn’tautomaticallyAdditive),foranumberof reasonswhichwillbeexploredinsomedetailinthebook.

5 Ifyouhaveissueswiththislast,itmaybeduetothefactthatyouare takingthebeliefattitudeastriggeredbythepassingofsomeintermediate probabilisticordegree-theoreticthreshold,andyouhavedoubtsconnectedto Lottery-orPreface-Paradox-relatedconsiderations.Chapters 3 and 8 willdeal withissuesconcerningthresholds,probabilities,andlotteries.Chapter 4 will saysomethingonthePrefaceParadox.

Also,evenifyouthinkthat ϕ,and ϕ strictlyimplies ψ,that is,itjustcannothappen(thereisnopossibleworldwhere) ϕ holdsbut ψ fails,youmaythinkthat ϕ withoutthinking that ψ,evenifyouaredeductivelyunbounded,becausestrict implicationfailstobetopic-preserving.Thetopicof ψ may be alien toyou:youmaylacktheconceptualresourcesto graspit.Andevenifyouareadeductively and conceptually unboundedagent,youmaynotbeinsuchafavourable epistemicpositionwithrespectto ψ asyouarewithrespectto ϕ,duetothetopicaddressedby ψ.Givencertainempirical information,youareinapositiontoknowthatyouhave hands.There’snowayyoucanbeahandlessbraininavat ifyouhavehands.Butsomeepistemologiststhinkthatthat verysameinformationmaynotputyouinapositiontoknow you’renobraininavat:yourinformation,theymaysay, settlesepistemicissuesabouteverydayexperience;itdoes notaddressthetopicoffar-fetched,scepticalscenarios.

Chapter 3 introducesabasicformalsemanticsforafamily ofTopic-SensitiveIntentionalModals(TSIMs,read‘ZIMMs’): modaloperatorsrepresentingattitudeascriptions,andwhich embedatopic-sensitivityconstraint.TheTSIMoperatorsin focusinit,andinthefollowingthreechapters,aretwo-place, variablystrictmodals(wewillseeexactlywhatthismeans induecourse),oftheform‘X ϕψ’(genericreading:‘Given ϕ,one Xs(or,would X)that ψ’, X expressingtherelevant attitudeascription),withatopicalityconstraintlinking ϕ and ψ.Thesearebothnon-monotonic,thankstotheirvariable strictness,andsuchthattheyfailfullclosureunderlogical consequenceorentailment,thankstotheirtopic-sensitivity.

Variablestrictnessandtopic-sensitivitydifferentiatethe TSIMsexploredinthesechaptersfromthestandardknowledgeandbeliefoperators`alaHintikka.Anotherfeature bringsbacksomesimilaritywiththestandardframework: startingfromthebasicsemanticspresentedinchapter 3,one canaddconstraintsontheaccessibilityrelationsorfunctions usedinthetruthconditionsfortheTSIMs.Suchconstraints validatedifferentlogicalprinciplesandentailmentsunder whichtheoperatorsare,orbecome,closed;andtheyalso suggestdifferentreadingsoftheoperatorsthemselves.That’s similartohow,inastandardmodalsetting,startingfrom

K(thebasicnormalmodallogic),onegetsstrongermodal systemssuchasT,B,S4,S5,byadding(moreorlesscontroversial)constraintsonthevariousaccessibilityrelations; suchconstraintsdelivercertainvalidities,andmakeplausible certaininterpretationsforthecorrespondingoperators.

Three(familiesof)constraintsareexploredinthethree chaptersfollowingchapter 3,givinginterpretationsofthe TSIMsasexpressing,respectively:(i)KnowabilityRelative toInformation(KRI;chapter 4);(ii)imaginationasRealityOrientedMentalSimulation(ROMS;chapter 5),carriedout insuppositionalthought;and(iii)hyperintensionalconditionalbeliefor(static)beliefrevision(withhintsatadynamic expansion;chapter 6).

Inchapter 4,myco-author(PeterHawkeagain)andI arguethattheKRIsetting(‘Kϕψ’:‘Giventotal(empirical) information ϕ,onewouldbeinapositiontoknow ψ’)has alottosayonthebigdebatearoundepistemicclosure,‘one ofthemostsignificantdisputesinepistemologyoverthelast fortyyears’(Kvanvig 2006,256).

Roughly:giventhatoneknows ϕ and(oneknowsthat) ϕ entails ψ,isoneinapositiontoknowthat ψ?Closure deniers(forinstance, Dretske 1970; Nozick 1981; Lawlor 2005; Holliday 2015; Hawke 2016; SharonandSpectre 2017)limit closuretoaddressscepticalworriesanddefendfallibilism(in onetypicalformulation:onecansometimesknowthat ϕ even ifoneisnotinanepistemicpositiontoruleoutallpossible scenariosinwhich ϕ fails).Closuresupporters(forinstance, Williamson 2000; Hawthorne 2004; Roush 2010; Kripke 2011a) oftenstressthategregiousviolationsofspecificclosureinstances,e.g.,ofConjunctionElimination,areunacceptable (howcanonewhoknows ϕ ∧ ψ failto beinaposition toknow that ϕ?).Ingeneral,oneneedstohavesufficientlystrong restrictedclosureprinciplestovindicateobviousideas,such asthatcompetentdeductionfromknownpremises,e.g.,in mathematicalreasoning, must preserveknowability.

PeterandIarguethattopic-sensitivityallowsKRIto invalidatecontroversialformsofclosurewhilevalidatingless controversialones,escapingegregiousviolations.Also,inthe KRIsettingthevariablestrictnessoftherelevantTSIMs

modelsacertainnon-monotonicityofknowledgeacquisition. Unlikethestandardmodalframeworkforepistemiclogic, KRIaccommodatesplausibleapproachestothe dogmatism paradox,duetoKripkeandHarman,wherebyknowingagents seemtobeimmunetorationalpersuasionviainformation bringinginnewevidence.Theparadox,inessence,isthat itappearsrationaltoignorecountervailingevidencetowhat theyknow.Weshowthattheparadoxcanbesplitintotwo sub-paradoxes:oneisdealtwithvianon-monotonicity;the otherishandledbythelimitationsofclosuredeliveredby topic-sensitivity.Inspiteofbeingnon-monotonicandtopicsensitive,KRIalsosatisfiesprinciplescapturingtheideathat knowledgemustbestable,asperthevenerablePlatonicview of epist´eme.

Inchapter 5,Iaddressasortofimaginationinplayin ROMS:thekindofsuppositionalexerciseweengageinall thetime,whenwetrytoguesswhatwillhappenifsuchand-soturnsouttobethecasein‘Whatif’questions (‘WhatwillIdoifIcan’tpaymymortgageanymore?’)or when,counterfactually,wewanttoascertainresponsibilities (‘Wouldhehavemanagedtohitthebrakesintime,ifhe hadnotbeendrinkingbeforedriving?’).InROMSclothing, TSIMs(‘I ϕψ’:‘Supposing ϕ,oneimaginesthat ψ’)are showntomodelinterestingfeaturesofsuchimaginativeand suppositionalthought.

Thestartingpointofthechapterisapuzzle:given thatimaginationisanarchicandarbitrary(inwaysbelief, typically,isnot),howcanithaveepistemicvalue?Howcan itgiveusknowledgeofreality,ifitisanunboundeddeparture fromreality?Thepuzzleisaddressedbydistinguishing voluntaryandinvoluntaryaspectsofROMS.Anumberof plausiblefeaturesofROMS,takenfromresearchincognitive psychologyandthephilosophyofmind,arethenlisted;andit isshownthatourtopic-sensitivesemanticscanmodelthem. Also,thechapterconsiderstheadditionofaconstrainton thesemantics,whoseeffectistovalidateaprincipleof‘equivalenceinimagination’,whichlimitsthehyperintensional anarchyofimaginationandstrengthensitslogic.Equivalence inimaginationisasortofcognitiveequivalence: ϕ and ψ are

equivalentinimaginationforone,whentheyplaythesame roleinone’scognitivelife:whateveroneinfers,concludes, findsplausible,etc.,supposingeither,onedoessupposingthe other,anideaIgotfromLevin Hornischer (2017).

Inchapter 6,TSIMsareshowntohelpwithconditionalbelief and(dispositionsto)beliefrevision(‘Bϕψ’:‘Onebelieves ψ,conditionalon ϕ’;or‘Ifoneweretolearnthat ϕ,one wouldbelievethat ψ wasthecase’).Thestartingpoint is,again,hyperintensionality:itseemsthatwecanbelieve differentthingsconditionalonnecessaryorlogicalequivalents whichdifferintopic.Thethingswebelieve,conditional onthepropositionthatSocratesexists,cangreatlydiffer fromthosewebelieve,conditionalonthepropositionthat Socrates’singleton, {Socrates},exists.Additionally,wedon’t cometotriviallybelieveeverythingjustbecauseweare,on occasion,exposedtoinconsistentinformation.Thisisnot straightforwardlyrepresentedeitherintheAGMframework forbeliefrevision,orinvariousepistemic-doxasticlogics recapturingAGMinamodalsetting.

TheadditiontothebasicsemanticshereconsistsinorderingthepossibleworldsessentiallyasinthemainstreamLewisStalnakersemanticsforconditionallogic–exceptthatthe (pre)orderingdoesn’trepresentobjectivesimilarity,rather subjectiveplausibility,asin Grove (1988):thecloseraworld, themoreplausiblethescenarioitrepresentsforthebelieving agent.Thissettinghasbeenusedtomodeldispositionsto revisebeliefs,orbeliefentrenchment,indoxasticlogicand DynamicEpistemicLogic(DEL): VanDitmarschetal. (2008); VanBenthemandSmets (2015).

BesidesexploringTSIMconditionalbeliefor(static)belief revisionoperators,thechapteralsohintsathowtodevelop thetopic-sensitivesettinginaproperlydynamicfashion viaoperatorsoftheform‘[∗ϕ]ψ’(‘Afterbeliefrevisionby ϕ, ψ holds),interpretedasmodel-transformersasinDEL. Inparticular,oncetopic-sensitivityistakenonboard,we canhaveadynamicsinvolvingthetopicsthemselves:we canmodelhowonecomestograspnewsubjectmatters byexpandingone’sconceptualrepertoire–anideaIhave developedtogetherwithAyb¨uke ¨ Ozg¨un.

Chapter 7 isjointworkwithAyb¨uke.HereweleavetwoplaceTSIMsbehindandfocusonone-placeTSIMsexpressing twosortsofbelief,inordertotackletypicalformsof well-known framingeffects (KahnemanandTversky 1984). These,too,concernagentswhocanhavedifferentattitudes towardslogicallyornecessarilyequivalentpropositions.Framingisknowntohavemomentouspsychologicalandsocial consequences.UnlikeEcons,thefullyconsistentagentsof classicaleconomictheorywhowell-ordertheirpreferencesand maximizeexpectedutility,Humanscanbe‘framed’:nudged intobelievingdifferentthingsdependingonhowequivalent optionsarepresentedtothem(ThalerandSunstein 2008).

Typicalframingeffectsseemtobeamorespecificphenomenonthanthegeneralhyperintensionalityofbelief(revision)modelledinthepreviouschapter:framedbelievers,of thekindstudiedincognitivepsychology,choicetheory,and behaviouraleconomics,canhavedifferentattitudestowards co-intensionalcontentsevenwhenthey(theagents)areon topofalltherelevantsubjectmattersand,inaddition, theycanevenbe,insomesense,awarethatthosecontents areequivalent,althoughinanothersensetheycertainlyare not.Besidesthetopic-sensitivityofbeliefascriptions,this applicationofTSIMtheoryreliesonmodellingthestructural distinction,takenfromcognitivepsychology,betweenbeliefs activatedinworkingmemory(WM)andbeliefsleftinactive inlong-termmemory(LTM).Framedagentscanhavethe beliefthatpatientsshouldgetsurgerywitha90%one-month survivalrateactivatedintheirworkingmemory,without havingtheintensionallyequivalentbeliefthatpatientsshould getsurgerywitha10%first-monthmortalitythere.However, suchagentscanhavealltherelevantinformationaswell astheconcept mortality intheir(declarative)LTM.Calling beliefsactivatedinWM active andbeliefsleftasleepinLTM passive,thischapterprovidesalogicoftopic-sensitiveactive andpassivebeliefforframedagents:abeliefisactivewhen itisavailableinWMtoperformcognitivetaskswithit.It ispassivewhenitisstored,orencoded,intheagent’sLTM knowledgebase,andleftinactivethere.

Uptochapter 7 included,beliefandtheotherattitudes

modelledbytheTSIMsaretakenasall-or-nothingandnonprobabilistic.Inthisrespect,TSIMtheoryisstillinline withstandardepistemiclogic.However,otherapproachesto thelogicofintentionalstatesarequantitative,gradedand, typically,probabilistic(Halpern 2005).Inparticular,beliefis oftenunderstoodintermsof,oratleastlinkedto,degreesof confidencetakenassubjectiveprobabilities,andBayesianism dominatestheliteratureonbeliefrevision.

Thefinalchapterofthebookbeginstoscratchthesurface oftheconnectionsbetweentopicalityandprobabilities.One popularphilosophicalapproachtonon-monotonicindicative conditionals(forinstance, Adams 1975; Edgington 1995; Bennett 2003)understandstheseprobabilistically,too,and instrictconnectiontoconditionalbelief(asstrictasallowed by Lewis (1976)’snotorioustrivialityresults).Theideahas becomemainstreamalsointheso-called‘NewParadigm’in thepsychologyofreasoning(Evansetal. 2003; Evansand Over 2004; OaksfordandChater 2010),whereprobabilistic, non-monotonic,andconditionalreasoningaretightlyrelated.

Nowthetwo-placeTSIMsofchapters3to6areasort ofnon-monotonic,conditional-likeoperator.ThisledAyb¨uke andmetoconsiderhowtopic-sensitivitymayrelateto probabilitiesintheabstractsettingofconditionality.Andso, inchapter 8 weprovideasemanticframeworkthat,leaving possibleworldsbehind,spellsoutacceptabilityconditionsfor atopic-sensitiveindicativeconditionalwhichaddsatopicality componenttoatreatmentintermsofconditionalprobabilities(weusePopperfunctions:conditionalprobabilitiesare primitive,notdefinedviatheRatioFormulaintermsof unconditionalones).

Weremainneutralonthetrickyissueofwhetherindicatives expresspropositionsandcangenerallyhavetruthvalues.We takeasourstartingpointAdams’Thesis(Adams 1966, 1998): theideathattheacceptabilityofasimpleindicative(one withnoindicativesembeddedinitsantecedentorconsequent) equalsthecorrespondingconditionalprobability.TheThesis enjoysconsiderablepopularityinphilosophybut,weargue, it’sfalseandrefutedbyrecentempiricalresults,whichwe summarize.

Inoursetting,asimpleindicative‘

linkedtotheideathat ψ followsfrom ϕ andbackground, unstatedassumptionsconnectedto ϕ (‘BAϕ’). ϕ → ψ is acceptabletotheextentthat(1) p(ψ|ϕ)(theprobabilityof ψ,conditionalon ϕ)ishigh,provided(2) ψ ison-topicwith respectto ϕ and BAϕ.Thisgivesakindofrelevantconditional,unacceptablewhenatopicalityconnectionbetween antecedent(andbackgroundassumptions)andconsequentis missing.Weshowthatthevaliditiesandinvaliditiesinthe probabilisticlogicofsuchaconditionalareboththeoretically desirable,andinlinewithexperimentalresultsonhowpeople reasonwithconditionals.

1.4...AndMoretoCome

Isaidattheoutsetthatthisbookbeginstoexplorean idea.Imeantit.Variousviewsitexperimentswitharenew andrathertentative,variousdiscussionsinitaretosome extentinconclusive,andI’llbesurprisedifproblemsIhaven’t foreseen(itoftenhappenstome!)don’tpopupsoon.I amhappy,however,thattheideaoftopic-sensitivelogicsof thoughtisalreadybeingpickedupbyanumberoflogicians andphilosophers,whohavepaidattentiontopaperson whichthisbookisbasedandhavevariouslycriticizedand/or developedthem.

Ale Giordani (2019)hasaxiomatizedthelogicofimaginationofchapter 5,comingupwithasystemthat’ssound andcompletewithrespecttothesemanticspresentedthere. Additionally,somehavefocusedonbetterrepresentingthe agentivenatureofimaginationasROMSthatchapterdeals with:AleagainandIlariaCanavotto,withsomehelpfrom me(Canavottoetal. 2020),havedevelopedafine-grained approachtovoluntaryimaginationcombiningmyideaswith adynamiclogicbasedonactiontypes,andwithtoolsfrom STITlogics(Segerbergetal. 2020).Theideaofmixing myapproachwithSTIThasalsooccurredtoHeinrich Wansing,whohasworkedonitwithChrisBadura:see BaduraandWansing (2021).Meanwhile,Chrishasalready upgradedtheROMSpropositionalsetting,comingupwith asophisticatedaccountoftopicalityandtopic-inclusionfor

afirst-orderlanguage(Badura 2021b).Pierre Saint-Germier (2020)hasbeenexploringanon-2Capproachwheretopicsensitivetruthmakersemantics`alaFineisemployedtogive ahyperintensionallogicofimaginationasROMS,which maydobetterthanmyattemptfromchapter 5.Ayb¨uke againhasprovidedadynamic,topic-sensitivebeliefrevision operatorandasoundandcompletelogicforit,withsome helpfromme( ¨ Ozg¨unandBerto 2020),aspertheresults mentionedattheendofchapter 6.Sheisalsoworkingwith myStAndrewscolleagueAaron‘KingofMereology’Cotnoir, exploringmereotopologicaldevelopmentsoftheveryidea oftopic-inclusion(I’llsaysomethingonthisattheendof chapter 5).

Overall,topic-sensitivelogicsofintentionalitymakefora nicenewterritory,andIhopemoreandmorepeopleget interestedinexploringit.

1.5ChapterSummary

Thelogicofthought,understoodasthelogicofpropositional or dedicto intentionalmentalstates,suchasknowing, believing,supposing,shouldbetopic-sensitive.What ψsone istothinkasaconsequenceofthinkingthat ϕ shoulddepend onthepropositionsthat ϕ andthat ψ,whichmakeforthe contentsofsuchthoughts.Andthisbookdefendstheidea thatpropositionscanbeseenasindividuated,notjustby thesetsofworldsatwhichtheyaretrue,butalsobywhat theyareabout:theirtopic,orsubjectmatter.Thetopicsensitiveoperatorsusedtoexpressattitudeascriptions,to beexploredinthebook,failfullclosure:givenonesuch operator X,one’s Xingthat ϕ doesnotimplythatone Xs allof ϕ’sentailments.Ontheotherhand,suchoperators arenotlogicallyanarchic.Failureoffullclosureconnectsto theproblemoflogicalomniscience,andwehaveseenthat non-omnisciencehasdistinct,independentsources.Wehave thenbeenthroughasummaryofthecontentsofthecoming chapters,introducingtheirmainideas,andwehavepointed atrecentorin-progressdevelopmentsofsuchideas.

Two-ComponentSemantics

Co-authoredwithPeterHawke

Thelogicofthoughtmustrestonanaccountofpropositions, ifpropositionsarethecontentsof dedicto intentionalstates. Inthischapter,weprovidesuchanaccount.Itsmostdistinctivetraitistheideathatpropositionscanbeusefully representedasfeaturing(atleast)twoconstituents:(1)truth conditionsand(2)subjectmatterortopic.Wealsoarguethat onemayhavereasonsfortakingthetwocomponents(1)and (2)asirreducibletoeachother,inasensetobeclarified. However,oneneednotaccepttheirreducibilityproposed heretoappreciatethelogicspresentedinthefollowing chapters.There,topic-sensitiveintentionalmodaloperators, orTSIMs,getatwo-componentsemanticinterpretationin termsofpossibleworldsandtopics.Onemayfindsucha twofoldsettingtheoreticallyuseful,forinstance,becauseit deliverscertaindesiredlogicalvaliditiesandinvaliditiesfor theoperators,althoughthetwo-componentrepresentation ultimatelyinvolvessomeredundancy.Thecurrentchapter willstillhavetheusefulroleoffamiliarizingitsreaderwith subjectmattersinageneralsetting.

Thissaid,wetrythestrongerstancehere.Onereasonfor doingsoisthatrealirreducibility–thedistinctionbetween (1)and(2)‘carvingatthenaturaljoints’,toadoptthe usualmetaphor–maybemoresatisfactoryphilosophically, althoughsomelogiciansmaynotcareaboutphilosophical satisfaction,takeamoreinstrumentaliststance,andjustlook atwhatthelogicsdeliver.

TopicsofThought:TheLogicofKnowledge,Belief,Imagination. FrancescoBerto,OxfordUniversityPress.©FrancescoBerto2022. DOI:10.1093/oso/9780192857491.003.0002

Westartbypresentingthegeneralideaofatopic-sensitive viewofpropositionalcontent,andintroducethedistinction betweenone-component(1C)andtwo-component(2C)accounts,inSection 2.1.Wedoitviaathesis,whichwename afterYablo,andwedistinguishaFullandaWeakformulation ofit.

InSection 2.2,wediscusshowamereologyoftopicsmay work(Subsection 2.2.1)andwelistanumberofconstraints anytopic-sensitiveaccountofpropositionalcontentshould, wethink,obey.Oneseriesofconstraintsconcernsthetopictransparencyofsomelogicalvocabulary(Subsection 2.2.2). Anotheroneconcernstherebeingtopic-divergingnecessities andco-necessities:sentenceswhichare,respectively,necessary(ofthesamekindofnecessity),ornecessarilyequivalent, butwhichexpressdifferentpropositionsbecausetheyare aboutdifferentthings(Subsection 2.2.3).

InSubsection 2.2.4,wearguethattopic-sensitivity,inspite ofplayingakeyroleinthelogicsofintentionalstatesto bepresentedinthefollowingchapters,maybekeptdistinct fromotherphenomenaconcerningintentionalcontextsand, inparticular,Fregeanpuzzles,whichareoftendealtwith byinvokingrepresentationalguises,ormodesofpresentation thatwouldbeinplayinattitudeascriptions.

InSection 2.3,wespeakof1Csemanticsinageneralsetting. Wecomeupwitha primafacie case,towhich1Ctheorists shouldreact,fortruthconditionsandtopicsbeingirreducible toeachother(Subsection 2.3.1).1Csemanticshasitthat eithertruthconditionsarereducibletosubjectmatter,orvice versa.Wearguethatthefirstdisjunctstandsintensionwith Transparency(Subsection 2.3.2);andthatthesecondmay notaccountfortopic-diverging(co-)necessitiesveryeasily (Subsection 2.3.3).

InSection 2.4,weintroduceaformal2Csemanticswhich deliversverdictsonsame-saying,thatis,onwhichsentences expressthesamepropositiontakenascomposedofatruth setandatopic.Weshowthatsuchsemanticscomplieswith theconstraintspresentedinSection 2.2 inastraightforward way.

InSection 2.5,weexaminetheprospectsfortheFull Yablo’sThesis.Wediscusstwoobjectionstoit:wecall