Twenty-Five Basic Theorems in Situation and World

Twenty-FiveBasicTheoremsinSituationandWorldTheory∗EdwardN.ZaltaCenterfortheStudyofLanguageandInformationStanfordUniversityIn[1981a]and[1981b],BarwiseandPerrysketchedwhattheycalled‘situationsemantics’andarguedthatafull-blowntheorybasedontheirsketchwouldofferabetteranalysisofnaturallanguagethanpossibleworldsemantics.Insteadoftakingobjects,sets,andtotalwaystheworldmightbe(i.e.,worlds)asbasicandreconstructingproperties,relations,andpropositionsasfunctions,BarwiseandPerrytookpartialwaystheworldmightbe(i.e.,situations)asbasicalongwithcertain‘uniformi-ties’acrossthem,suchasobjectsandrelations.Theyrefusedtotaketruth-valuesasthedenotationsofsentences,andrejectedtheideathatthesignificanceofasentenceshiftedinintensionalcontexts.Instead,us-ing‘naked-infinitivereports’astheirguide,theyarguedthatsentencessignifiedsituations,andthatthesesamesituationsweretheobjectsofthepropositionalattitudes.Moreover,theirnewsemanticswasconsis-tentwiththeideathatnecessarilyequivalentproperties,relations,andpropositionscanbedistinct.Alloftheseideascontrastedsharplywiththestandardassumptionsofpossibleworldssemantics,asembodiedbyMontague[1974]andCresswell[1973].Fromitsinception,then,situationsemanticswasthoughttobeincompatiblewithpossibleworldssemantics.Intheirseminalworkof[1983],BarwiseandPerrylefttheimpres-∗ThispaperwaspublishedintheJournalofPhilosophicalLogic12(1993),pp.385-428.TheresearchwasconductedattheCenterfortheStudyofLanguageandInforma-tion(CSLI).IwouldliketothankJohnPerryforgenerouslysupportingmyresearchbothatCSLIandinthePhilosophyDepartmentatStanford.IwouldalsoliketothankBernardLinsky,ChrisMenzel,HarryDeutschandTonyAndersonformanyworthwhileandinterestingsuggestionsforimprovingthepaper.Anearlierversionofthispaper,morenarrowlyfocusedonsituationtheory,appearedasZalta[1991].EdwardN.Zalta2sionthatthisincompatibilitybetweensemanticframeworksindicatedanincompatibilitybetweensituationsandworlds,consideredasmetaphys-icalentities.AndinBarwise[1985],inwhichsomeofAczel’sideasonnonwellfoundednesswereincorporatedintosituationtheory,wefindthesuggestionthat‘reality,allthatis,isnotasituation’(p.191).ButinaninterchangewithStalnaker,Perryofferedapictureinwhichworldscouldbeviewedasjustcertainmaximalsituations(Perry[1986]andStal-naker[1986a]).Eventually,however,in[1989],Barwisedevelopedasetof‘branchpoints’insituationtheory,throughwhichalternativeversionsofthetheorymusttravel.Atonebranchpoint,therearetwoalternatives:onewhichleavesroomonlyfortheactualworld(conceivedasamaximalsituation),theotherwhichleavesroomformultiplepossibleworlds.Thequestionofwhethersituationsandworldscanpeaceablycoex-istinthefoundationsofmetaphysicsiscomplicatedbythefactthatworldtheoristsdisagreeaboutwhatworldsare.Thoughmanyoftheresearchersworkingwithinthepossibleworldsframeworkarecontenttoregardworldsasausefultheoreticaltool,suchanattitudedoesnotsatisfyametaphysician.Ourbesttheoriesquantifyoverworldsandsowebecomeinterestedinthemasmetaphysicalentitiesintheirownright.InLewis[1973]and[1986],Stalnaker[1976]and[1985],Adams[1974],Chisholm[1976],Plantinga[1974],Pollock[1984],andFine[1977],wefindvariousattemptstodevelopatheoryofworlds,oftenbyconstructingthemoutofotherbasicmetaphysicalentities.Interestingly,Chisholm,Plantinga,andPollockdefinedworldsintermsofthenotionofastateofaffairs,anotionwhichhasturnedouttobeoneofthebuildingblocksofsituationtheory.Insituationtheory,statesofaffairsarebasicconstructionsoutofobjectsandrelations,andtheyarethekindofthingthatsituations‘makefactual’.Thisconvergenceofideas,inwhichstatesofaffairsareseenasbasictobothworldandsituationtheory,leadsonetowonderwhetherthereisaunifiedtheorythatcanintegratealloftheseentities.Inthispaper,Iproposetoassimilatestatesofaffairs,situations,andworldsintoasingletheorythatdistinguishes,yetcomprehends,allthreekindsofentity.Thetheoryiscouchedinsomedefinitionsandtheorems,allofwhicharecastinapreciselogicalframework.However,noneofthetheoremsarestipulatedtobetrue;rather,theyallresultasconsequencesofaformal,axiomatictheoryofobjectsandrelationsforwhichthelog-icalframeworkwasoriginallydeveloped.Animportantfeatureofthesubtheoryofsituationsisthevolumeofimportantdefinitionsandtheo-325BasicTheoremsremsofnaivesituationtheorythatitsuccessfullycaptures.Itarticulatesaninterestingpaththroughthemanybranchpointsofsituationtheory.However,themostimportantfeatureofthissubtheoryisthatitresolvestheapparentconflictbetweenworldsandsituations,forworldsareshowntobecertainmaximalsituations.Neithersituationsnorworldsaretakentobeprimitive,nordoesthetheorymakeanessentialappealtopossi-bleworldsemantics.Rather,thenotionsofsituationandworldarebothdefined(worldsandsituationsareidentifiedasobjectsofaspecialsort),andsowenolongerhavetodecidewhichoftheseentitiesismorebasic.Thetheorymayjustifymuchoftherecentworkbothinsituationtheoryandinworldtheorynotjustbyshowingthatthetwotheoriescanbeintegratedsuccessfully,butbyshowingthatmostofthebasicprinciplesofeachtheorycanbederived.Ishouldliketoemphasizethatwhatfollowsconstitutesatheoryandnotamodelofsituationsandworlds.Situationsandworldswillnotbei