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1、Corcoran,J.1998.Information-theoreticlogic,inTruthinPerspectiveeditedbyC.Martínez,U.Rivas,L.Villegas-Forero,AshgatePublishingLimited,Aldershot,England(1998)113-135.6Information-theoreticlogicJohnCorcoranInmemoryofAlfredTarski1901-1983andAlonzoChurch1903-1995onthefortiethannivers
2、aryoftheirclassicworks:Logic,Semantics,MetamathematicsandIntroductiontoMathematicalLogic.6.1.IntroductionInformation-theoreticapproaches[114]toformallogicanalysethe"commonintuitive"conceptofprepositionalimplication(orargumentalvalidity)intermsofinformationcontentofpropositionsan
3、dsetsofpropositions:onegivenpropositionimpliesasecondiftheformercontainsalloftheinformationcontainedbythelatter;anargumentisvalidiftheconclusioncontainsnoinformationbeyondthatofthepremise-set.Thispaperlocatesinformation-theoreticapproacheshistorically,philosophicallyandpragmatic
4、ally.Advantagesanddisadvantagesareidentifiedbyexaminingsuchapproachesinthemselvesandbycontrastingthemwithstandardtransformation-theoreticapproaches.Transformation-theoreticapproachesanalysevalidity(andthusimplication)intermsoftransformationsthatmaponeargumentontoanother:agivenar
5、gumentisvalidifnotransformationcarriesitontoanargumentwithalltruepremisesandfalseconclusion.Model-theoretic,set-theoretic,andsubstitution-theoreticapproaches,whichdominatecurrentliterature,canbeconstruedastransformation-theoretic,ascantheso-calledpossible-worldsapproaches.Ontica
6、ndepistemicpresuppositionsofbothtypesofapproachesareconsidered.Attentionisgiventothequestionofwhetherourhistoricallycumulativeexperienceapplyinglogicisbetterexplainedfromapurelyinformation-theoreticperspectiveorfromapurelytransformation-theoreticperspectiveorwhetherapparentconfl
7、ictsbetweenthetwotypesofapproachesneedtobereconciledinordertoforgeanewtypeofapproachthatrecognizestheirbasiccomplementarity.6.2.PreliminariesTheinformation-theoreticviewpointdominatedlogicintheperiodduringwhichtheseedsofmathematicallogicwerebeingsownbyBoole,DeMorgan,Jevons,Venna
8、ndothers.Infact,thewritingsofthelogicianswhosuc