Validity and Soundness | Internet Encyclopedia of Philosophy

It is important to stress that the premises of an argument do not have actually to be true in order for the argument to be valid. An argument is valid if the ... ValidityandSoundness Adeductiveargumentissaidtobevalidifandonlyifittakesaformthatmakesitimpossibleforthepremisestobetrueandtheconclusionneverthelesstobefalse.Otherwise,adeductiveargumentissaidtobeinvalid. Adeductiveargumentissoundifandonlyifitisbothvalid,andallofitspremisesareactuallytrue.Otherwise,adeductiveargumentisunsound. Accordingtothedefinitionofadeductiveargument(seetheDeductionandInduction),theauthorofadeductiveargumentalwaysintendsthatthepremisesprovidethesortofjustificationfortheconclusionwherebyifthepremisesaretrue,theconclusionisguaranteedtobetrueaswell.Looselyspeaking,iftheauthor’sprocessofreasoningisagoodone,ifthepremisesactuallydoprovidethissortofjustificationfortheconclusion,thentheargumentisvalid. Ineffect,anargumentisvalidifthetruthofthepremiseslogicallyguaranteesthetruthoftheconclusion.Thefollowingargumentisvalid,becauseitisimpossibleforthepremisestobetrueandtheconclusionneverthelesstobefalse: ElizabethownseitheraHondaoraSaturn. ElizabethdoesnotownaHonda. Therefore,ElizabethownsaSaturn. Itisimportanttostressthatthepremisesofanargumentdonothaveactuallytobetrueinorderfortheargumenttobevalid.Anargumentisvalidifthepremisesandconclusionarerelatedtoeachotherintherightwaysothatifthepremisesweretrue,thentheconclusionwouldhavetobetrueaswell.Wecanrecognizeintheabovecasethatevenifoneofthepremisesisactuallyfalse,thatiftheyhadbeentruetheconclusionwouldhavebeentrueaswell.Consider,thenanargumentsuchasthefollowing: Alltoastersareitemsmadeofgold. Allitemsmadeofgoldaretime-traveldevices. Therefore,alltoastersaretime-traveldevices. Obviously,thepremisesinthisargumentarenottrue.Itmaybehardtoimaginethesepremisesbeingtrue,butitisnothardtoseethatiftheyweretrue,theirtruthwouldlogicallyguaranteetheconclusion’struth. Itiseasytoseethatthepreviousexampleisnotanexampleofacompletelygoodargument.Avalidargumentmaystillhaveafalseconclusion.Whenweconstructourarguments,wemustaimtoconstructonethatisnotonlyvalid,butsound.Asoundargumentisonethatisnotonlyvalid,butbeginswithpremisesthatareactuallytrue.Theexamplegivenabouttoastersisvalid,butnotsound.However,thefollowingargumentisbothvalidandsound: Insomestates,nofelonsareeligiblevoters,thatis,eligibletovote. Inthosestates,someprofessionalathletesarefelons. Therefore,insomestates,someprofessionalathletesarenoteligiblevoters. Here,notonlydothepremisesprovidetherightsortofsupportfortheconclusion,butthepremisesareactuallytrue.Therefore,soistheconclusion.Althoughitisnotpartofthedefinitionofasoundargument,becausesoundargumentsbothstartoutwithtruepremisesandhaveaformthatguaranteesthattheconclusionmustbetrueifthepremisesare,soundargumentsalwaysendwithtrueconclusions. Itshouldbenotedthatbothinvalid,aswellasvalidbutunsound,argumentscanneverthelesshavetrueconclusions.Onecannotrejecttheconclusionofanargumentsimplybydiscoveringagivenargumentforthatconclusiontobeflawed. Whetherornotthepremisesofanargumentaretruedependsontheirspecificcontent.However,accordingtothedominantunderstandingamonglogicians,thevalidityorinvalidityofanargumentisdeterminedentirelybyitslogicalform.Thelogicalformofanargumentisthatwhichremainsofitwhenoneabstractsawayfromthespecificcontentofthepremisesandtheconclusion,thatis,wordsnamingthings,theirpropertiesandrelations,leavingonlythoseelementsthatarecommontodiscourseandreasoningaboutanysubjectmatter,thatis,wordssuchas“all,”“and,”“not,”“some,”andsoforth.Onecanrepresentthelogicalformofanargumentbyreplacingthespecificcontentwordswithlettersusedasplace-holdersorvariables. Forexample,considerthesetwoarguments: Alltigersaremammals. Nomammalsarecreatureswithscales. Therefore,notigersarecreatureswithscales. Allspidermonkeysareelephants. Noelephantsareanimals. Therefore,nospidermonkeysareanimals. Theseargumentssharethesameform: AllAareB; NoBareC; Therefore,NoAareC. Allargumentswiththisformarevalid.Becausetheyhavethisform,theexamplesabovearevalid.However,thefirstexampleissoundwhilethesecondisunsound,becauseitspremisesarefalse.Nowconsider: Allbasketballsareround. TheEarthisround. Therefore,theEarthisabasketball. AllpopesresideattheVatican. JohnPaulIIresidesattheVatican. Therefore,JohnPaulIIisapope. Theseargumentsalsohavethesameform: AllA’sareF; XisF; Therefore,XisanA. Argumentswiththisformareinvalid.Thisiseasytoseewiththefirstexample.Thesecondexamplemayseemlikeagoodargumentbecausethepremisesandtheconclusionarealltrue,butnotethattheconclusion’struthisn’tguaranteedbythepremises’truth.Itcouldhavebeenpossibleforthepremisestobetrueandtheconclusionfalse.Thisargumentisinvalid,andallinvalidargumentsareunsound. Whileitisacceptedbymostcontemporarylogiciansthatlogicalvalidityandinvalidityisdeterminedentirelybyform,thereissomedissent.Consider,forexample,thefollowingarguments: Mytableiscircular.Therefore,itisnotsquareshaped. Juanisabachelor.Therefore,heisnotmarried. Thesearguments,atleastonthesurface,havetheform: xisF; Therefore,xisnotG. Argumentsofthisformarenotvalidasarule.However,itseemsclearintheseparticularcasesthatitis,insomestrongsense,impossibleforthepremisestobetruewhiletheconclusionisfalse.However,manylogicianswouldrespondtothesecomplicationsinvariousways.Somemightinsist–althoughthisiscontroverisal–thattheseargumentsactuallycontainimplicitpremisessuchas“Nothingisbothcircularandsquareshaped”or“Allbachelorsareunmarried,”which,whilethemselvesnecessarytruths,neverthelessplayaroleintheformofthesearguments.Itmightalsobesuggested,especiallywiththefirstargument,thatwhile(evenwithouttheadditionalpremise)thereisanecessaryconnectionbetweenthepremiseandtheconclusion,thesortofnecessityinvolvedissomethingotherthan“logical”necessity,andhencethatthisargument(inthesimpleform)shouldnotberegardedaslogicallyvalid.Lastly,especiallywithregardtothesecondexample,itmightbesuggestedthatbecause“bachelor”isdefinedas“adultunmarriedmale”,thatthetruelogicalformoftheargumentisthefollowinguniversallyvalidform: xisFandnotGandH; Therefore,xisnotG. Thelogicalformofastatementisnotalwaysaseasytodiscernasonemightexpect.Forexample,statementsthatseemtohavethesamesurfacegrammarcanneverthelessdifferinlogicalform.Takeforexamplethetwostatements: (1)Tonyisaferocioustiger. (2)Clintonisalameduck. Despitetheirapparentsimilarity,only(1)hastheform“xisaAthatisF.”FromitonecanvalidlyinferthatTonyisatiger.Onecannotvalidlyinferfrom(2)thatClintonisaduck.Indeed,oneandthesamesentencecanbeusedindifferentwaysindifferentcontexts.Considerthestatement: (3)TheKingandQueenarevisitingdignitaries. Itisnotclearwhatthelogicalformofthisstatementis.EithertherearedignitariesthattheKingandQueenarevisiting,inwhichcasethesentence(3)hasthesamelogicalformas“TheKingandQueenareplayingviolins,”ortheKingandQueenarethemselvesthedignitarieswhoarevisitingfromsomewhereelse,inwhichcasethesentencehasthesamelogicalformas“TheKingandQueenaresnivelingcowards.”Dependingonwhichlogicalformthestatementhas,inferencesmaybevalidorinvalid.Consider: TheKingandQueenarevisitingdignitaries.Visitingdignitariesisalwaysboring.Therefore,theKingandQueenaredoingsomethingboring. Onlyifthestatementisgiventhefirstreadingcanthisargumentbeconsideredtobevalid. Becauseofthedifficultyinidentifyingthelogicalformofanargument,andthepotentialdeviationoflogicalformfromgrammaticalforminordinarylanguage,contemporarylogicianstypicallymakeuseofartificiallogicallanguagesinwhichlogicalformandgrammaticalformcoincide.Intheseartificiallanguages,certainsymbols,similartothoseusedinmathematics,areusedtorepresentthoseelementsofformanalogoustoordinaryEnglishwordssuchas“all”,“not”,“or”,“and”,andsoforth.Theuseofanartificiallyconstructedlanguagemakesiteasiertospecifyasetofrulesthatdeterminewhetherornotagivenargumentisvalidorinvalid.Hence,thestudyofwhichdeductiveargumentformsarevalidandwhichareinvalidisoftencalled“formallogic”or“symboliclogic.” Inshort,adeductiveargumentmustbeevaluatedintwoways.First,onemustaskifthepremisesprovidesupportfortheconclusionbyexamingtheformoftheargument.Iftheydo,thentheargumentisvalid.Then,onemustaskwhetherthepremisesaretrueorfalseinactuality.Onlyifanargumentpassesboththesetestsisitsound.However,ifanargumentdoesnotpassthesetests,itsconclusionmaystillbetrue,despitethatnosupportforitstruthisgivenbytheargument. Note:thereareother,related,usesofthesewordsthatarefoundwithinmoreadvancedmathematicallogic.Inthatcontext,aformula(onitsown)writteninalogicallanguageissaidtobevalidifitcomesoutastrue(or“satisfied”)underalladmissibleorstandardassignmentsofmeaningtothatformulawithintheintendedsemanticsforthelogicallanguage.Moreover,anaxiomaticlogicalcalculus(initsentirety)issaidtobesoundifandonlyifalltheoremsderivablefromtheaxiomsofthelogicalcalculusaresemanticallyvalidinthesensejustdescribed. Foramoresophisticatedlookatthenatureoflogicalvalidity,seethearticleson“LogicalConsequence”inthisencyclopedia.Thearticleson“Argument”and“DeductiveandInductiveArguments”inthisencyclopediamayalsobehelpful. AuthorInformation Theauthorofthisarticleisanonymous.TheIEPisactivelyseekinganauthorwhowillwriteareplacementarticle. Anencyclopediaofphilosophyarticleswrittenbyprofessionalphilosophers. StayConnected &nbsp&nbsp &nbsp&nbsp &nbsp&nbsp BrowsebyTopicBrowsebyTopic SelectCategory HistoryofPhilosophy    17thCenturyEuropean    18thCenturyEuropean    19thCenturyEuropean    AncientPhilosophy    HistoryMisc.    HistoryofAnalytic    MedievalPhilosophy    Philosophers    RenaissancePhilosophy Metaphysics&Epistemology    Epistemology    Metaphysics    Mind&CognitiveScience    PhilosophyofLanguage    PhilosophyofReligion    Uncategorized PhilosophicalTraditions    AmericanPhilosophy    ChinesePhilosophy    ContinentalPhilosophy    FeministPhilosophy    IndianPhilosophy    IslamicPhilosophy    TraditionMisc. Science,Logic,&Mathematics    Logic    PhilosophyofMathematics    PhilosophyofScience ValueTheory    Aesthetics    Bioethics    Ethics    PhilosophyofLaw    PoliticalPhilosophy    ValueMisc.