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1、LogicallyPossibleWorldsandCounterpartSemanticsforModalLogicMARCUSKRACHTANDOLIVERKUTZAbstract.Thepaperreviewsthetechnicalresultsfrommodallogicaswellastheirphilosophicalsignificance.Itfocusesonpossibleworldssemanticsingeneralandonthenotionofapossibleworld,ofaccessibility,andobject
2、.ContentsIntroduction2Part1.WorldswithoutObjects51.BasicConceptsofModalPropositionalLogic52.TranslationintoClassicalLogic63.OntologyandDualityTheory73.1.LogicalConsequence103.2.SituationsandPossibilities104.PossibleWorldsasanAnalyticTool115.Accessibility135.1.AccessibilityRelat
3、ions135.2.Neighbourhoods145.3.Histories16Part2.TheWorldofObjects176.ModalPredicateLogic176.1.TheClassicalView196.2.FreeLogic206.3.Identity,SubstitutionandLeibniz’Law216.4.Completion.247.CounterpartSemantics.258.IndividualConcepts329.ObjectsinCounterpartFrames3510.DualOntologies
4、,or,TheSemanticalImpactofHaecceitism3911.Metaframes43ReceivedbytheeditorsMay9,2005.Keywordsandphrases.modallogic;counterpartsemantics;logicalpossibility;modalindividual;accessibility;possibleworlds.12MARCUSKRACHTANDOLIVERKUTZ12.EssenceandIdentity4413.OntheStatusoftheModalLangua
5、ge46Sincetobelongandtobelongofnecessityandtobepossibletobelongaredifferent(formanythingsbelong,butneverthelessnotofnecessity,whileothersneitherbe-longofnecessitynorbelongatall,butitispossibleforthemtobelong),itisclearthattherewillalsobedifferentdeductionsofeachandthattheirtermswi
6、llnotbealike:rather,onedeductionwillbefromnecessaryterms,onefromtermswhichbe-long,andonefrompossibleterms.Aristotle:PriorAnalytics,BookI,81Introduction.Modallogichasaremarkablehistoryindeed.Origi-nallyconceivedasthelogicofnecessityandpossibility,itsphilosophicalrootsgobackatlea
7、stasfarasAristotleandtheStoicDiodorusCronus.2WhileDiodorus’s‘MasterArgument’couldbeconsideredanearlyex-ampleofmodalpropositional,morepreciselytemporal,reasoning,3theStagirite’sinvestigationsintomodalsyllogismsprobablyconstitutetheearliestseriousessayoncombiningmodalitywithquant
8、ification.4Interestintomodaldistinctionskeptverymuchali
