1、-讓每一個人相同地提升自我PuttingLogicinitsPlaceFormalConstraintsonRationalBeliefChristensen,David,DepartmentofPhilosophy,UniversityofVermontAbstract:Arerationalbeliefsconstrainedbyformallogic?Thisbookarguesthatifbeliefsareseeninabinaryway(eitheronebelievesapropositionoronedoesnt),thenthestandardconstraintsofded

2、uctivecogency.deductiveconsistencyanddeductiveclosure)areincompatiblewithepistemicrationality.If,however,beliefsareseenasgraded,orcomingindegrees,aprobabilisticconstraint(basedonstandardlogic)isimposedbyidealrationality.Thisconstraint,probabilisticcoherence,explainsboththeappealofthestandarddeductiv

3、econstraintsandthepowerofdeductivearguments.Moreover,itcanbedefendedwithouttakingdegreesofbelief(asmanydecision-theoreticphilosophershave)tobesomehowdefinedorconstitutedbypreferences.Althoughprobabilisticcoherenceishumanlyunattainable,thisdoesnotundermineitsnormativestatusasaconstraintinasuitablyide

4、alizedunderstandingofepistemicrationality.Contents1LOGICANDRATIONALBELIEF12TWOMODELSOFBELIEF123DEDUCTIVECONSTRAINTS:PROBLEMCASES,POSSIBLESOLUTIONS334ARGUMENTSFORDEDUCTIVECOGENCY695Logic,GradedBelief,andPreferences1066LogicandIdealization143PREFACEWhenpeopletalkinformallyaboutbelief,“rational”and“l(fā)og

5、ical”areoftenusedasynonymously.Andeventhosewhothinkcarefullyandpreciselyaboutrationalbeliefoftentakelogictoplayanimportantroleindeterminingwhichbeliefsarerational.Explainingtheimportanceoflogictostudents,philosophersoftensaythingslike,“Rationalbeliefsmustbelogicallyconsistentwithoneanother,”or“Ifyou

6、believpremisesofavalidargument,then,ifyouarerational,youmustbelievetheconclusion.Thisbookaimstoshowthatlogicdoesindeedplayanimportantroleincharacterizingideallyrationalbelief,butthatitsroleisquitedifferentfromwhatitisoftenassumedtobe.Thefirstchaptersetsupparametersforthebooksapproach:itwillfocusonep

7、istemic(ratherthanpragmatic)rationality;itwilllookatconditionsonsimultaneousrationalbeliefs(ratherthanonrationalchangesofbelief);anditwillconcentrateonglobalrationalityconditionsforanagentswholesystemofbeliefs(ratherthanonlocalconditionsfortherationalityofparticularbeliefs).Thesechoicesaredesignedto

8、focus1-讓每一個人相同地提升自我theinquirywhereformallogicismostlikelytobeusefulincharacterizingidealrationality.Thesecondchaptertiesthebookscentralquestiontoachoicebetweentwobasicconceptionsofbelief.Thestandardbinarymodelseesbeliefasanall-or-nothingstate:eitheryoubelieveP,oryoudont.Thegradedmodelseesbeliefascom

9、ingindegrees.Thetwoconceptionsinviteverydifferentformalrationalityconditions.Rationalbinarybeliefsareoftenheldtobesubjecttodeductivecogency,whichrequiresthatanagentsbeliefsformalogicallyconsistentsetwhichincludesallthelogicalconsequencesofwhattheagentbelieves.Gradedbeliefsareoftenheldtobesubjectprob

10、abilistictocoherence:therequirementthattheyobeytheaxiomsofprobabilitytheory.Chapter2arguesthatprobabilitytheoryisbestseennotasanewlogicforgradedbelief,butasawayofapplyingstandarddeductivelogictogradedbelief.Itexploresdifferentwaysofunderstandingtherelationbetweenbinaryandgradedbelief,concludingthatt

11、hewayoneseesthisrelationhasimportantimplicationsforthequestionsofwhetherandhowbeliefsaresubjecttoformalrationalityconstraints.Thethirdandfourthchaptersarguethatideallyrationalbinarybeliefisnotsubjecttodeductivecogency.Chapter3beginswiththe“PrefaceParadox,”-whichposesawellknownchallengetodeductivecog

12、encyrequirements.Thechapterexaminesandrejectsattemptstoavoidtheproblembyunderstandingcogencyrequirementsinweakenedways.Itthendevelopsanextendedversionofaprefacecasewhichshowshowtheintuitivelyirrationalbeliefsrequiredbydeductivecogencywillincertaincasescascadeintomassiveirrationality.Thishighlightsth

13、eproblemsseverityandilluminateswhatsabsurdaboutthebeliefsrequiredbydeductivecogency.ThechapterthenshowsthatsituationswithPrefaceParadoxstructureoccurcommonlyinordinarylife.Finally,itexaminesandrejectsattemptstodefenddeductiveconstraintsbyexplainingawayourtroublesomeintuitionsinprefacecasesandinrelat

14、edcasesvolvingthe“LotteryParadox.”Chapter4takesonadeepersortofresponsetoprefaceandlotterycases.Ithasbeenarguedthatthefundamentalpurposesofbinarybeliefrequiredeductivecogency.Thechapterexaminesandrejectsseveralargumentsofthissort,thestrongestbeingthatifdeductivecogencywerenotrationallyrequired,deduct

15、iveargumentswouldhavenorationalforce.Thechapterdevelopsanddefendsanalternativeexplanationoftheepistemicimportanceofdeductivearguments,rootedinaprobabilisticcoherenceconstraintongradedbelief,andintherelationthatrationalbinarybeliefwouldbeartorationalgradedbeliefonanyplausibleaccount.Thechapterendswit

16、hadiscussionofwhetherbinarybeliefhasanyepistemicimportance;itarguesthatalthoughourbinarywayofendtalkingandthinkingaboutbeliefmaybeveryuseful,itmaynotintheendcaptureanyimportantaspectofrationality.Moreover,furtherdevelopmentofextendedpreface-typecasesshowsthatthesortofbinarybeliefthatwassubjecttodedu

17、ctivecogencycouldnothavetheconnectionstocentralaspectsofourpracticalreasoning,ourassertions,andouremotionsthatseemtogivebeliefitspoint.Thefifthchapterturnstothepositivetaskofdefendingprobabilisticcoherenceasalogicalconstraintongradedbelief.Thetwomainstrandsofargumentforthisviewinthe2-讓每一個人相同地提升自我lit

18、eratureareDutchBookandRepresentationTheoremarguments.Unfortunately,bothofthesesortsofargumentseektodefendconstraintsongradedbeliefbypositingverytightconnectionsbetweengradedbeliefsandpreferences,whicharenotclearlywithintheepistemicdomain.Infact,proponentsoftheseargumentswhohavetendedtobedecision-the

19、oreticallyorientedphilosophersofscience,ratherthanmainstreamepistemologistshavetypicallysoughttodefinebeliefsintermsofpreferences.Thismayseemtochangethesubjectawayfromepistemologyproper,whichIsuspecthelpsexplainwhyprobabilisticapproachestorationalityhavenotfoundmoresupportamongmainstreamepistemologi

20、sts.Thechapterarguesthatdefininggradedbeliefintermsofpreferencesrequiresaninsupportablemetaphysicsofbelief,andthusthattheargumentsastheyhavetypicallybeenofferedfail.Nevertheless,thechaptershowsthattheargumentscanbereworkedinawaythatemploysintuitivelyplausiblenormativeprinciplesconnectingpreferencesw

21、ithbeliefs,eliminatingtheneedforpositingimplausiblemetaphysicalordefinitionalconnections.Thus,probabilisticcoherencecanbedefendedwithoutmakingbeliefsintosomethingtheyarenot.Thefinalchapteraddressestheissueofidealizationinepistemology.Somehavearguedthatprobabilisticcoherenceinparticularimposesanunacc

22、eptablyhighlevelofidealization;otherswouldevenrejectdeductivecogencyasimposingexcessiveidealization.Thechapterexaminesseveralreasonsthathavebeenofferedforrejectingformalmodelsofrationalbeliefonthebasisofexcessiveendidealization.Itdefendstheinterestofidealizedformalmodelsinthinkingaboutrationality,ar

23、guingthatthehumanunattainabilityoflogicalperfectiondoesnotunderminethenormativeforceoflogicalideals.Thisbookhasbenefitedgreatlyfromcorrespondence,informaldiscussion,andcommentsondraftsfrommanyfriendsandcolleagues.IwouldliketothankSinyeeChan,KeithDeRose,JimJoyce,MarkKaplan,HilaryKornblith,ArthurKufli

24、k,DonLoeb,PatrickMaher,BillMann,MarkMoyer,DanaNelkin,DerkPereboom,andJonathanVogel.ImespeciallygratefultoKornblithandPereboom,whoreadeverypartofthemanuscriptatleastonce,andprovidedinvaluablehelpandencouragementthroughout.IdalsoliketothankananonymousreaderforOxfordUniversityPress,andMarkKaplanagain,i

25、nhiscapacityasanot-so-anonymousreaderforOxford,forveryusefulsuggestions.ImgratefultotheACLSandtheUniversityofVermontforsabbaticalsupport,andtoLeslieWeigerforadministrativesupport.Chapter5isbasedontwopaperspublishedearlier:-Book“DutchArgumentsDepragmatized:EpistemicConsistencyforPartialBelievers,Jour

26、nalof”Philosophy93(1996):45079,and“Preference-BasedArgumentsforProbabilism,Philosophy”ofScience68(2001):356Ithankthepublishersforpermissiontoreprintthismaterialhere.MaterialfromChapters3and4waspresentedtotheDartmouthUVMPhilosophyconference,andIdliketothankmycommentator,JimMoor,andtheotherparticipant

27、sintheconferenceforstimulatingdiscussion.Finally,Idliketothankmywife,RuthHorowitz,andmychildren,SophieandSamHorowitz,fortheirlove,theirsupport,andtheirunfailingknackforputtingphilosophicalpursuitsintoproperperspective.Iknowthiswillcomeinhandywhen,aswillinevitablyoccur,errorsarefoundinthisbook.3-讓每一個

28、人相同地提升自我DCend1LOGICANDRATIONALBELIEFDavidChristensenLogicandReasonIfthereisonerespectinwhichhumansdiffermostfundamentallyfromtheotheranimals,perhapsitisoursuperiorabilitytoreasonabout,andunderstand,theworld.Themainproductofourreasoning,andmediumofourunderstanding,is,ofcourse,alsoourchiefrepresentati

29、onoftheworldoursystemofbeliefs.Twodimensionsofevaluationcomeimmediatelytomindinevaluatingapersonsbeliefs.Thefirst,andmostobvious,isaccuracy.Beliefscanrepresenttheworldmoreorlessaccurately,itseems,andthemoreaccuratetheyare,thebetter.Butphilosophershavelongbeeninterestedinadistinctdimensionofevaluatio

30、n.Somebeliefsaremorationalethanothers.Andthoughthedimensionsofaccuracyandrationalitymaywellbelinked,theyareevidentlynotthesame.Afoolmayholdabeliefirrationallyasaresultofaluckyguess,orwishfulthinkingyetthebeliefmighthappentobeaccurate.Conversely,adetectivemightholdabeliefonthebasisofcarefulandexhaust

31、iveexaminationofalltheavailablerelevantevidenceinaparadigmaticallyrationalwayandyettheevidencemighthappentobemisleading,andthebeliefmightturnouttobewayoffthemark.Thepointofevaluatingrationality,aswellasaccuracy,ofbeliefssurelyhastodowithourdesiretoassesstheagentquabeliever.Indoingso,wetrytoabstractf

32、romacertainkindofluck,oraccidentalness.Thefoolisnobetterathinkerforhavingguessedcorrectly.Thedetectiveisnopoorerathinkerforhavingendencounteredmisleadingclues.Rationalbeliefs,itseems,arethosearisingfromgoodthinking,whetherornotthatthinkingwassuccessfulinlatchingontothetruth.Butwhatisitthatmakesthink

33、ing“good”?Astandardanswertothisquestionisthat,atleastinpart,goodthinkingislogicalthinking.ThuslogichasbeenatthecenterofphilosophicalthoughtaboutrationalitysincethetimeoftheancientGreeks.Andthedisciplineoflogicaspracticedtodayincorporatesatitscenterexactlythedivisionbetweengoodthinkingandaccuracyment

34、ionedabove.Thefirstlessoninmostlogiccoursesandinmanygeneralintroductionstophilosophydistinguishessoundnessfromvalidity.Thelatter,whichisoftenthoughtofasthecentralconcernofthelogician,abstractsawayfromissuesofactualtruthandfalsitytoconcentrateonstudyingcorrectandincorrectrelationsbetweenclaimsrelatio

35、nsthatarethoughttobeembodiedingoodandbadthinking,respectively.Ofcourse,theremayturnouttobeadeepconnectionbetweenconsiderationsoftruthandconsiderationswhichmakecertain4-讓每一個人相同地提升自我relationsbetweenclaims“l(fā)ogical.”Butthefirstconcernofthelogicteacheristypicallytoseparatelogicalrelationsfromfactualones.

36、Themotivationsforstudyingthelogicofrationalbeliefareundoubtedlyvarious.Wemightseektoimprovethethinkingofothers,orofourselves,byprovidingrulesthatpeoplecouldself-consciouslyemployinformingorrevisingtheirbeliefs.Wemightseektodiagnoseconfusionincaseswhereourthinkingnaturallyleadsustoparadoxicalresults.

37、Orwemightsimplyseekapurelytheoreticalunderstandingofgoodthinking,foritsownsake.Butregardlessofmotivation,somethinglikethefollowingideaseemstobepresupposedinstudyinglogic:thatthecorrectlogicwillprovideamodelforideallyrationalbelief.ItisthisideathatIwouldliketoexamineand,eventually,defend.Logic,ofcour

38、se,isnotatermthatisusedconsistently,evenwithinacademicphilosophy.TextsonlogicdiscussissuesrangingfromG?delsincompletenesstheoremtowaysofidentifyingadhominemarguments.WhatIhaveinmindisformallogic.Ofcourse,endeventhemeaningofformalisnotclear.Textsoftenreferto,.,entailmentswhosevaliditydependsonlogical

39、formorstructure;butinexplainingwhatcountsasform,thetextstypicallyresorttoexamples.Thus,thefactthatthesentenceSulfurisyellowentailsthesentenceSulfurisyelloworsulphurisgreenmightbecitedasflowingfromthefactthatsentencesoftheform“PorQ”arealwentailedbysentencesoftheformis“aPparadigmatic.”Thisprincipleoff

40、ormallogic.However,theclaimthat(1)entails(3)Sulfurisnotredmightwellnotbeconsideredtoflowfromanyfactaboutlogicalform.Thisissoeventhoughonemightclaimthatsentencesoftheformare“xalwaysisnotredtruewhen”sentencesoftheform“xisyellow”are.AndmostwouldrejecttheclaimthatThisrockismadeofsulfurentailsThisrockism

41、adeoftheelementwithatomicnumber16asamatteroflogic,eventhoughmanywouldholdthatsentencesoftheform“xismadeofsulfur”canonlybetrueatpossibleworldswheresentencesoftheform“xismtheelementwithatomicnumber16”aretrueaswell.Idonotproposeheretosettlethequestionsofwhetherthesecondoftheabove-mentionedentailmentsis

42、alogicalone,orwhythethirdisnot.Provisionally,letustakeformallogicasconcernedwithatleasttheformsorstructurescreatedbythestandardlyacceptedlogicalwordssuchasnot,or,and,ifthen,all,andcorrectlogicofsuchforms(whichisperhapsnotthewholeofformallogic)endprovideamodel(undoubtedlyapartialmodel)forideallyratio

43、nalbelief?5-讓每一個人相同地提升自我Beforebeginningtoanswerthisquestion,itwillbeusefultoclarifywhatsortofrationalityisatissue,inseveralrespects.PragmaticvsEpistemicRationalityAdistinctionisoftenmadebetweentwosensesofrationality,bothofwhichcanbeappliedtobeliefs.Thedistinctionismosteasilyillustratedwithatouched-u

44、pversionofPascalsWager.Supposethat,giventheevidenceavailabletome,itsunlikelythatGodexists.However,supposethattheevidencealsomakesitverylikelythatifGoddoesexistitwillbeoverwhelminglyinmybestintereststotoethetheisticlinenotonlyinmyactions,butinmybeliefs.Itcouldthenberationalforme,inthepragmaticsense,t

45、obelieveinGod:givenwhatIwant,havingthatbeliefcouldbeexpectedtobemostadvantageousrelativetomyButthereisalsoaclearsenseinwhichabeliefadoptedcountertotheevidencewouldnotbearationalone.Itisthissecond,epistemic,senseofrationalitythatIamconcernedwithhere.Thisisnottodenythatthetwoformsofrationalityareconne

46、cted.Onemightsuggestthatepistemicallyrationalbeliefsarethosethatwouldmaximizeonesexpectationofreachingonesparticularlyepistemicgoalorgoals(suchasbelievingtruethingsorfailingtobelievefalsethings).Asitstands,thesuggestionseemsclearlywrong.Afterall,onecanimagineavariantonthePascalexampleinwhichtherewar

47、dsforthecounter-evidentialbeliefwerepurelyepistemic.Consider,forexample,acaseinwhichthree-fingeredaliensofferonevastnewinsightintophysics,endincludingbothnewinformationandcorrectionsofmanycurrentmisconceptions,ontheconditionthatonebelievethatGhengisKhanhadthreefingers(Imassumingthatthealiensoffergiv

48、esonenoevidenceforthisproposition).Inthiscase,itseemscleartomethatifonesomehowcomestobelievethatGhengisKhanwasthree-fingered,thisbeliefisepistemicallyirrationalwhetherornotthealienscanrationallybeexpectedtocomethroughwiththeirpartofthebargain.Buttherearemoresophisticatedwaysofconnectingpragmaticande

49、pistemicrationality,someofwhichwillbediscussedinlaterchapters.Atthispoint,Ijustwanttodistinguishourepistemicnotionfromthepragmaticone.DiachronicvsSynchronicRationalityLogicbooksareoftenwrittenasthoughtheircentraltopicwereinference.Argumentsaresetoutinpremiseconclusionform,anditissuggestedthattheprem

50、isesrepresentanagentspresentbeliefs,andtheconclusionafurtherbeliefthattheagentshould,aftergoingthroughtheargument,adopt.Thissuggeststhatthesortofrationalitybeingaddressedthroughlogicisdiachronicrationality.Diachronicrationalityconstrainsthewaybeliefsarechanged(ormaintained)acrosstime.Theideaseemstob

51、esomethinglike6-讓每一個人相同地提升自我this:logicsrulesofinferencetellyouwhichnewbeliefsyoushouldadopt,onthebasisofyourcurrentbeliefs.ThusModusPonenstellsyouthatifyoubelieveP,andyoualsobelieve),thenifyoudontalreadybelieveQ,youshouldadoptthebeliefthatQ.Itiswell-known,ofcourse,thatthispictureistoosimple.Afterall

52、,ifyoulearnbytheabovelogicalargumentthatyourbeliefsentailQ,youmightwellwanttoreviseyourcurrentbeliefthatP,oryourbeliefthat(),ratherthanadoptthenewbeliefthatQ.Thisisespeciallyclearifyouhappenalreadytobelievenot-Q.ButevenifyourecurrentlyagnosticonQ,ModusPonensitselfprovidesnoreasonforpreferring,.,beco

53、mingaQ-believertoendbecomingaIneachofthesecases,logicgivesyounoguidanceatallregardingwhichoptionforrevisingyourbeliefsispreferable.Thusthe“rulesofinference”givebookscannotbethoughtofinanystraightforwardwayasrulesofdiachronicInfact,despitethewaylogictextsoftenpresentthesubject,itisfarfromclearthatthe

54、basicconcernoflogiciswithchangeofbelief.Avalidargument,asmostoftendefined,isoneinwhichitisimpossibleforthepremisestobetruewhiletheconclusionisfalse.Inotherwords,thenotionofvalidargumentflowsfromadeepernotion,anotioninvolvingthepossibilityofsentencessimultaneouslyhavingcertaintruth-values.Factsaboutt

55、hepossibletruth-valuedistributionsamongthemembersofacertainsetofsentencesarenotdiachronicfactsaboutthosesentences.Ofcourse,thefactsaboutpossibletruth-valuedistributionshaveimplicationsforinferencesconstructedfromthosesentences.thatcertaininferencesaretruth-preserving.Buttheseimplicationsdonotreallyg

56、obeyondthefundamentalfactsaboutsimultaneoustruth-valuedistributions.Theviewoflogicasconcernedmostbasicallywithsimultaneoustruth-valuedistributionssuggestssimplerwaysofapplyinglogictothetheoryofrationalbelief.Wesawabovethatlogicdidnothelptherationalagentchoosebetween,ontheonehand,adoptingtheendbelief

57、thatQand,ontheotherhand,droppingthebeliefthatPorthebeliefthat().Butlogicdidsuggestsomeconstraintsonouragentsbeliefs.Infact,theapparentneedforsomerevisionorotherstemmedfromtheideathattherewassomethingwrongwithcertainsetsofsimultaneousbeliefs.Mostplausibly,itmaybeclaimedthatlogicprecludestheoptionofra

58、tionallybelievingallofP,(),andnot-Qatthesametime.AndonemightalsoseelogicasprecludingtheoptionofrationallyremainingagnosticonQwhilebelievingbothPand().Generalizingthesetwosuggestionsyieldsthetwomostprominentproposalsforusinglogictoconstrainrationalbelief:therequirementthatarationalagentsbeliefsbelogi

59、callyconsistent,andtherequirementthattherationalagentsbeliefsbeclosedunderdeduction.thattheagentbelieveeverythinglogicallyimpliedbyherbeliefs).Bothoftheseproposalsare,ofcourse,forsynchronicconstraintsonrationality.ThusIwouldliketoconcentrateonthequestionofwhetherlogiccanprovidesynchronicconstraintso

60、nideallyrationalbeliefs.Thismayseemmisguided,ifwewantrationalbeliefstobethosethatareinsomesensetheproductsofgoodthinking.“Goodthinking”seemstobeanactivity,andanotionofrationalitythattriedtocapturewhatgoodthinkingwasmightseemtobeanessentially7-讓每一個人相同地提升自我diachronicnotion,involvingtheevaluationofhoww