Deduction-Vs.-Induction

FormalVersusInformalLogicDeductiveVersusInductiveFormsofReasoningTwobasiccategoriesofhumanreasoning•Deduction:reasoningfromgeneralpremises,whichareknownorpresumedtobeknown,tomorespecific,certainconclusions.•Induction:reasoningfromspecificcasestomoregeneral,butuncertain,conclusions.•Bothdeductiveandinductiveargumentsoccurfrequentlyandnaturally…bothformsofreasoningcanbeequallycompellingandpersuasive,andneitherformispreferredovertheother(Hollihan&Baske,1994).DeductionVs.InductionDeduction:•commonlyassociatedwith“formallogic.”•involvesreasoningfromknownpremises,orpremisespresumedtobetrue,toacertainconclusion.•theconclusionsreachedarecertain,inevitable,inescapable.Induction•commonlyknownas“informallogic,”or“everydayargument”•involvesdrawinguncertaininferences,basedonprobabalisticreasoning.•theconclusionsreachedareprobable,reasonable,plausible,believable.DeductiveVersusInductiveReasoningDeduction•Itistheformorstructureofadeductiveargumentthatdeterminesitsvalidity•thefundamentalpropertyofavalid,deductiveargumentisthatifthepremisesaretrue,thentheconclusionnecessarilyfollows.•Theconclusionissaidtobe“entailed”in,orcontainedin,thepremises.–example:useofDNAtestingtoestablishpaternityInduction•Bycontrast,theformorstructureofaninductiveargumenthaslittletodowithitsperceivedbelievabilityorcredibility,apartfrommakingtheargumentseemmoreclearormorewell-organized.•Thereceiver(ora3rdparty)determinestheworthofaninductiveargumentInductiveordeductivereasoning?•AsampleoffiftymotoristswhowerestoppedbytheCHPatasobrietycheckpointonaSaturdayatmidnightrevealedthatoneinfourdriverswereeitheruninsured,intoxicated,orboth.Thus,ifyougetinvolvedinanaccidentonthefreewaythereisa25%chancetheothermotoristwillbedrunkoruninsured.•TheLawoftheSeatreatystatesthatanyvesselbeyonda12milelimitisininternationalwaters.Thetreatyalsostatesthatanyvesselininternationalwaterscannotbelegallystoppedorboarded.Therefore,whentheU.S.CoastGuardinterceptsboatscomingfromCubaorHaitimorethan12milesfromtheU.S.coast,itisviolatingtheLawoftheSea.SampleDeductiveandInductiveArgumentsExampleofDeduction•majorpremise:Alltortoisesarevegetarians•minorpremise:Bessieisatortoise•conclusion:Therefore,BessieisavegetarianExampleofInduction•Bosstoemployee:“Biffhasatattooofananchoronhisarm.HeprobablyservedintheNavy.”Bessietortoisesvegetariananimalssample“Venndiagram”ofadeductiveargumentAlltortoisesfallinthecircleofanimalsthatarevegetariansBessiefallsintothecircleofanimalsthataretortoisesThus,BessiemustbeavegetarianOthertypesofdeductivearguments•Supposeeveryplaceintheworldthatpeopleliveisrepresentedbythebluespaceinsidetherectangle.Supposethelongpinkovalrepresentsallthewoodenhousesintheworld.And,supposethegreencirclerepresentsCanada.Themostlogicalconclusiononecandrawfromthefigureis:A.allwoodenhousesarefoundinCanadaB.EveryonelivesinawoodenhouseC.SomeCanadiansliveinwoodenhousesD.NoonelivesinCanadaOthertypesofdeductivearguments•Supposethefollowingstatementsarealltrue:–PersonLisshorterthanpersonX–PersonYisshorterthanpersonL–PersonMisshorterthanpersonY•Whatadditionalpieceofinformationwouldberequiredtoconcludethat“PersonYisshorterthanPersonJ”?A.PersonListallerthanJB.PersonXistallerthanJC.PersonJistallerthanLD.PersonJistallerthanME.PersonMistallerthanYSolution:AnswerCMYLXSo,ifJistallerthanL,YmustbeshorterthanJOthertypesofdeductiveargumentsAmotherwantstoorderonelargepizza,withexactly5toppingsforherthreepickychildren.Shecanchoosefrom7toppings;cheese,mushrooms,olives,ham,sausage,onions,andpineapple.–Fifisaystherehastobepineapple–Monasaystherecannotbeanyolives–Rexsaysthatifthereisgoingtobesausage,thentherehastobehamtoo.Whichcombinationoftoppingsshouldsheselectifsheistosatisfyallthreechildren’scombineddemands?A.pineapple,onions,cheese,mushrooms,sausageB.cheese,sausage,ham,olives,pineappleC.cheese,mushrooms,ham,onions,pineappleD.sausage,mushrooms,onions,cheese,andham.thefivetoppingsolutioncheesemushroomolivehamsausageonionpineappleFifiYesMonaNoRexthenhamifsausageNote:thestatement“ifsausage,thenham”doesn’timply“Ifhamthensausage.”Theobversedoesn’tnecessarilyfollow.DeductionVersusInduction---continued•Deductivereasoningiseither“valid”or“invalid.”Adeductiveargumentcan’tbe“sortof”valid.•Ifthereasoningemployedinanargumentisvalidandtheargument’spremisesaretrue,thentheargumentissaidtobesound.validreasoning+truepremises=soundargument•Inductivereasoningenjoysawiderangeofprobability;itcanbeplausible,possible,reasonable,credible,etc.•theinferencesdrawnmaybeplacedonacontinuumrangingfromcogentatoneendtofallaciousattheother.fallaciouscogentDeductionVersusInduction--stillmore•Deductivereasoningiscommonlyfoundinthenaturalsciencesor“hard”sciences,lesssoineverydayarguments•Occasionally,everydayargumentsdoinvolvedeductivereasoning:Example:“Twoormorepersonsarerequiredtodriveinthediamondlane.Youdon’thavetwoormorepersons.Thereforeyoumaynotdriveinthediamondlane”•Inductivereasoningisfoundinthecourtroom,theboardroom,theclassroom,andthroughoutthemedia•Most,butnotalleverydayargumentsarebasedoninduction–Examples:The“reasonableperson