What Is a Sound Argument? - Think, But How?

For example, the statements, “It is raining,” and, “The street is wet,” can be combined by the logical operator 'and' to make a compound ... Skiptocontent Haveyoueverwantedtodisagreewithsomeone’sargument,butyoucouldn’tfindanyflawinit?It’spossibleyouwerefacingasoundargument.  Anargumentisaseriesofstatementsthattrytoproveapoint.Thestatementthatthearguertriestoproveiscalledtheconclusion.Thestatementsthattrytoprovetheconclusionarecalledpremises.  Here’sasampleargument: Premise1:Ifitisraining,thenthestreetiswet.Premise2:Itisraining. Conclusion:Therefore,thestreetiswet. Aboveisanexampleofaseriesofstatementsthatcountsasanargumentsinceithasapremiseandconclusion.That’sallittakesforsomethingtobeanargument:itneedstohaveapremiseandaconclusion.  Asoundargumentprovesthearguer’spointbyprovidingdecisiveevidenceforthetruthoftheirconclusion.  Asoundargumenthastwofeatures:  Theargumenthasavalidform,and Allthepremisesaretrue. I’mgoingtotalkaboutthesepointsinorder.Tounderstandthevalidform,weneedtounderstandthelogicalformofanargumentandthelogicalformofastatement. WhatIsanArgument’sLogicalForm? Whenwesayanargumentisvalid,wearetalkingaboutanargument’slogicalform.Iwroteaboutvalidargumentsandlogicalformsinthispiecehereindetail. Logicalformsarelikemathformulas.Eachcomprisesvariablesandoperators.Forexample,themathformula“x+x=2x”comprisesavariable‘x’andanoperator‘+’.Ifweweretopluginthevalue1forx,thenwewouldget“1+1=2.”Logicalformsaresimilar.Thedifferenceisthatinsteadofmathematicaloperators,logicalformsuselogicaloperators,andinsteadofvariablesthatarefilledinwithnumbers,thevariablesoflogicalformsarefilledinwithstatements.  Howdoyougetattheformofanargument?Anargumentisaseriesofstatements,sotogetattheformofanargument,youneedtogetattheformofthestatementsthatcomposeit.  TheLogicalFormofaStatement Hereareacoupleofexamplesofstatements:“Itisraining.”;“Thestreetiswet.” Statementscanbecombinedusinglogicaloperatorssuchasthefollowing: NotBoth…and…Either…or…If…then……ifandonlyif… Whenwecombinetwoormorestatementsusinglogicaloperators,theresultisacompoundstatement.  Forexample,thestatements,“Itisraining,”and,“Thestreetiswet,”canbecombinedbythelogicaloperator‘and’tomakeacompoundstatementasfollows:“Itisraining,andthestreetiswet.”Ortheycanbecombinedusing‘if…then…’asfollows:“Ifitisraining,thenthestreetiswet.” Herearemoreexamplesofstatementsformedwithlogicaloperators:“Itisnotraining,”“Jamesistall,orAdamisfast,”“Eitheryoucangostraight,oryoucanmakearight,”“Shawncanwintheraceifandonlyifheentersit.”  Nowthatweunderstandthelogicalformofastatement,let’stalkaboutthelogicalformofanargument.Anargumentiscomposedofstatements.Thepremisesandtheconclusionofanargumentareallstatements.Soifyouwanttoknowthelogicalformofanargument,youstartbyidentifyingthelogicalformofthestatementscomposingit. Here’sanexampleofanargument:  Premise1:Allmammalsareanimals.Premise2:Alldogsaremammals.Conclusion:Therefore,alldogsareanimals. Here’stheformoftheargument: AllMareA AllDareM Therefore,allDareA  Logicianshaveanameforthisformofargument.Itisavaliddeductiveargumentcalledacategoricalsyllogism.  Now,anargument’sformisvalidifandonlyifthetruthoftheargument’spremisesguaranteesthetruthofitsconclusion.Ifweplugintruepremises,inotherwords,avalidformguaranteesatrueconclusion.  Avalidformissimilartoanaccuratemathformula.Forexample,inmathematics,ifyouwanttogettheareaofacircle,youwillfirstgettheformulatocalculatetheareaofacircle.Inthiscase,theformulawillbe“A=π(r)^2.”Atthispoint,allyouneedtodoisplugintheradiusrofthecircleintheformulatogetanaccurateresult.Ifyougettheaccurateradius,thenyouareguaranteedanaccuratearea. Thecategoricalsyllogismisavalidformbecauseifthetwopremisesaretruethentheconclusionhastobetrue.Inotherwords,ifpremises1and2aretrue,thentheconclusion(Alldogsareanimals)hastobetrue–it’simpossibleforittobefalse. Nowthatwe’vetalkedaboutformsofstatementsandarguments,let’stalkaboutwhatitmeansforanargumenttobeasoundargument.  Whatmakesavalidargumentintoasoundargument? Nowthatweunderstandwhatavalidargumentis,itiseasiertounderstandasoundargument.Anargumentissoundifandonlyifitisavalidargumentandallthepremisesaretrue.Examplesofsoundargumentsincludecategoricalsyllogismswhosepremisesarealltrue. Inordertodeterminewhetheranargumentissound,youneedtoaskthefollowingtwoquestions. 1.Doesthisargumenthaveavalidform? 2.Areallthepremisestrue? Oncetheanswertoboth1and2isyes,thenyouknowit’sasoundargument.  Thefollowingargumentisanotherexampleofcategoricalsyllogism:  Premise1:Allmenaremortal. Premise2:Socratesisaman.Conclusion:Therefore,Socratesismortal. Let’slookattheaboveexamplewithtwoquestionsinmindtodeterminewhetherthisargumentissound. Doesthisargumenthasavalidform?Yes.Theaboveformiscalledacategoricalsyllogism,anditisavalidform.Logicianshavecompiledalistoftime-testedvalidargumentformssuchasModusponens,Modustollens,andDisjunctivesyllogism.Categoricalsyllogismisoneofthemostpopularforms,anditisavalidformbecauseifthetwopremisesaretruethentheconclusionhastobetrue. Areallthepremisestrue?Yes.Bothofthepremisesabovearetrue.Premisesarestatements.Statementscanbeeithertrueorfalse.Astatementistruewhentheworldmatchesthestatement.IfIweretosay,“2plus2is4,”thenthisstatementistruesinceitmatcheshowtheworldis.IfIweretosay,“2plus2is5,”thenthisstatementisfalsesinceitdoesn’tmatchhowtheworldis. Ifyoucan’tdeterminewhetherthepremisesaretrueorfalse,youcanchoosetowithholdjudgment.Withholdingjudgmentmeansyoudon’tmakeadecisiontoacceptorrejectaclaim.Forexample,supposeyoudon’thavedecisiveevidencefororagainstthisclaim:“Thereislifeoutsideoftheearth.”Youdon’thavetomakeadecisionaboutwhetherornottheclaimistrue.Youcanwithholdyourjudgmenttillyougetmoreevidencefororagainsttheclaim.  Iftheanswertoquestions1and2isyes,thenyouknowthattheaboveargumentissound.Youknowthattheargumentactuallyprovesitspoint.Itactuallyprovesthattheconclusionistrue. However,iftheanswertoquestion1isyes,andyou’rewithholdingjudgmentaboutquestion2,thenatleastyouknowthattheargumentisavalidargumentevenifyoudon’tknowwhethertheargumentissound. SummaryandConclusionofSoundArgument Anargumentisaseriesofstatementsthattrytoproveapoint.Thestatementthatthearguertriestoproveiscalledtheconclusion.Thestatementsthattrytoprovetheconclusionarecalledpremises.Argumentsarenottrueorfalse.Statementsaretrueorfalse.Whenwesayanargumentisvalid,wearetalkingabouttheformofanargument.Anargumentisvalidifandonlyifthetruthofthepremisesguaranteesthetruthoftheconclusion.Validityisafeatureofdeductiveargumentsnotinductivearguments.Logicianshavetestsforlogicalconsequenceandmethodsforconstructingvaliddeductivearguments.  Anargumentissoundifandonlyifitisavalidargumentandallthepremisesaretrue.Unsoundargumentseitherdon’thaveavalidformortheyhaveatleastonefalsepremise.Ifthepremisesofanargumentarefalse,thentheargumentdoesn’tproveanything.Anargumentwithevenasinglefalsepremisedoesn’tproveanything.Knowinghowtoidentifysoundargumentsisessentialtodevelopingcriticalthinkingskills.Notallinvalidformsarefallacies.Inductiveargumentsareinvalidarguments,buttheyaren’tfallacies.Ifinductiveargumentshavetruepremises,theystillgiveussomereasontothinktheirconclusionsaretrue.Theyjustdon’tprovetheirconclusions.Aninductiveargumentwithtruepremisescanstillhaveafalseconclusion;it’sjustthattheconclusionisprobablytrue.Aninductiveargumentwithtruepremisesissometimescalledacogentargument.  Tweet Postnavigation ←PreviousPost LeaveaCommentCancelReplyYouremailaddresswillnotbepublished.Requiredfieldsaremarked*Typehere..Name* Email* Website Savemyname,email,andwebsiteinthisbrowserforthenexttimeIcomment. 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