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图premiseNarrowingdownsu王博文微博spicionininconsistentp

发布时间:2021-04-05 16:03:57 阅读: 来源:手链厂家

NarrowingDownSuspicion

inInconsistentPremiseSets?

DiderikBatens

CentreforLogicandPhilosophyofScience

UniversiteitGent,Belgium

Diderik.Batens@rug.ac.be

February3,2003

Abstract

Inconsistency-adaptivelogicsisolatetheinconsistenciesthatarederiv-ablefromapremiseset,andrestricttherulesofClassicalLogiconlywhereinconsistenciesareinvolved.Frommanyinconsistentpremisesets,disjunctionsofcontradictionsarederivablenodisjunctofwhichisitselfderivable.Givensuchadisjunction,itisoftenjusti?edtointroducenewpremisesthatstate,withacertaindegreeofcon?dence,thatsomeofthedisjunctsarefalse.Thisisanimportant?rststepontheroadtoconsistency:itnarrowsdownsuspicionininconsistentpremisesetsandhencelocatestherealproblemsamongthepossibleones.InthispaperIpresenttwoapproachesforhandlingsuchnewpremisesinthecontextoftheoriginalpremises.The?rstapproachmayapparentlybecombinedwithallparaconsistentlogics.Thesecondapproachdoesnothavethesamegenerality,butisdecidedlymoreelegant.

Preludium

ImetJerzyPerzanowskiintheearlyseventiesinCracowonanexchangebe-tweenouruniversities.Findingout,uponarrival,thatmylecturewasscheduledinaConferenceontheHistoryofLogic,IapologizedthatIcouldonlytalkonlogic.Iwascomfortedrightaway,“Maybeyourlecturewillbehistorical”,afterwhichtheKrak′owchairmanofSolidarno′s′c—theKrak′owdivisionencompassedNowaHuta—broughtmetoahugeRussian-stylehotelincludingadollarshop.Thisinitiatedalongfriendship,manymeetingsinPoland,Belgiumandcon-ferencesabroad,andlateraresearchcooperation.Logicalontology,modalandpara(in)consistentlogics,andpoliticaldisagreementsservedasareinforcement.OnmynextvisittoCracow,Jerzyhadleftfull-timeforJa′skowski’sTorun,thebirthplaceofMiko??lajKopernik,andhencewaspart-timeinCracow—every

researchforthispaperwassupportedbytheFundforScienti?cResearch–Flanders,bytheResearchFundofGhentUniversity,bytheRoyalFlemishAcademyofBelgiumforScienceandtheArts,andindirectlybytheFlemishMinisterresponsibleforScienceandTechnology(contractBIL01/80).IamindebtedtoLeenDeVreeseforcarefulcommentsonaformerdraft.?The

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premise Narrowing down suspicion in inconsistent premise sets

PoleisactuallymorethanonePole.ThenandduringnextstaysinPolandmylodgingswereofMiddle-Europeancomfortandde?nitelymorecosy.ButJerzyretainedhistypicalsmile,suggestingheknowsbetter.Usuallyhedoes.

Mycontributionwillbeonhandlinginconsistency,GhentstylewithastrongTorun?avour.

1TheProblem

Althoughthescienti?centerpriseisdirectedatobtainingabodyofconsis-tentknowledge,itiswellknownthatinconsistenciesoccurredinseveralcentralepisodesofthedevelopmentofscienti?cdisciplines—see,forexample,,,

,,,.Insomecasesanacceptedtheory—onethatwassuperiortoalternativesinviewofitsproblemsolvingcapacity—turnedouttobeincon-sistent.Inothercasesprogressinadisciplinewasrealizedbyreasoningfromseveralacceptedtheoriesthataremutuallyinconsistent.Instillothercases,progressinadisciplinewasrealizedbyreasoningfromatheoryandasetofdatathataremutuallyinconsistent.

Thereasoningthatoccursinsuchsituationsisexplicatedbyinconsistency-adaptivelogics—see,forexample,,,,,,,,,.Theselogicsisolatetheinvolvedinconsistenciesandinthiswayprovideaninterpre-tationofthepremises(theoriesand/ordata)thatisasconsistentaspossible.Preciselythistypeofinterpretationisneededinordertoreasonfromthein-consistentpremisesandinordertoregainconsistency.

Inconsistency-adaptivelogicsprovideamaximalconsistentinterpretationofthepremises,butdonotthemselvesresolvetheinconsistencies.Ihavearguedonseveraloccasionsthattheeliminationofinconsistenciesisnotataskoflogicbuthastorelyonempiricaldata,ifthetheoryisanempiricalone,oronconceptualanalysis,insumonextra-logicalinformation.AlthoughIdonotwanttochangethisposition,Iadmitthatinconsistency-adaptivelogicsleavetheprocessthatleadstoconsistencyamystery.Theaimofthepresentpaperistoclarifypartofthemystery:ontheroadtoconsistency,logichastoplayarole.Tobemoreprecise,ithastoperformtwodi?erenttasks.First,thelogicalanalysisoftheoldtheoryand,whereappropriate,datashouldindicatewhichspeci?cextra-logicalinformationshouldbesought.Next,oncetheinformationisobtained,logicshouldhandleit,whichincludescombiningitinthesuitablewaywiththeoldtheory.Thepresentpaperconcernsthe?rststepbeyondinterpretingtheinconsistentpremisesetasconsistentlyaspossible.Thiswillrequireabitofexplanation.

Supposethatonederived

(p∧~p)∨(q∧~q)∨(r∧~r)(1)

fromthepremises,butfailedtoderive(p∧~p)∨(q∧~q),(p∧~p)∨(r∧~r),or(q∧~q)∨(r∧~r).Soaccordingtotheavailableinsights,thepremisesrequirethateitherp∧~porq∧~qorr∧~rholdstrue,butdonotspecifywhichofthemdoes.Thiswillhaveconsequencesforinterpretingthepremisesasconsistentlyaspossible.OntheReliabilitystrategy,forexample,p∧~p,q∧~qandr∧~rareallconsideredasunreliable,whichmeansthatnoinferencecanbemadethatpresupposesoneofthemtobefalse.

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premise Narrowing down suspicion in inconsistent premise sets

扩展:suspicion / narrowing / under suspicion

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