Validity and Soundness – A Brief Introduction to Philosophy

A deductive argument is an argument whose conclusion is supposed to follow from its premises with absolute certainty, thus leaving no possibility that the ... Skiptocontent IncreaseFontSize 1.7Soundness Agoodargumentisnotonlyvalid,butalsosound.Soundnessisdefinedintermsofvalidity,sosincewehavealreadydefinedvalidity,wecannowrelyonittodefinesoundness.Asoundargumentisavalidargumentthathasalltruepremises.Thatmeansthattheconclusionofasoundargumentwillalwaysbetrue.Why?Becauseifanargumentisvalid,thepremisestransmittruthtotheconclusionontheassumptionofthetruthofthepremises.Butifthepremisesareactuallytrue,astheyareinasoundargument,thensinceallsoundargumentsarevalid,weknowthattheconclusionofasoundargumentistrue.ComparethelasttwoObamaexamplesfromtheprevioussection.Whilethefirstargumentwassound,thesecondargumentwasnotsound,althoughitwasvalid.Therelationshipbetweensoundnessandvalidityiseasytospecify:allsoundargumentsarevalidarguments,butnotallvalidargumentsaresoundarguments. Althoughsoundnessiswhatanyargumentshouldaimfor,wewillnotbetalkingmuchaboutsoundnessinthisbook.Thereasonforthisisthattheonlydifferencebetweenavalidargumentandasoundargumentisthatasoundargumenthasalltruepremises.Buthowdowedeterminewhetherthepremisesofanargumentareactuallytrue?Well,therearelotsofwaystodothat,includingusingGoogletolookupananswer,studyingtherelevantsubjectsinschool,consultingexpertsontherelevanttopics,andsoon.Butnoneoftheseactivitieshaveanythingtodowithlogic,perse.Therelevantdisciplinestoconsultifyouwanttoknowwhetheraparticularstatementistrueisalmostneverlogic!Forexample,logichasnothingtosayregardingwhetherornotprotozoaareanimalsorwhethertherearepredatorsthataren’tintheanimalkingdom.Inordertolearnwhetherthosestatementsaretrue,we’dhavetoconsultbiology,notlogic.Sincethisisalogictextbook,however,itisbesttoleavethequestionofwhatisempiricallytrueorfalsetotherelevantdisciplinesthatstudythosetopics.Andthatiswhytheissueofsoundness,whilecrucialforanygoodargument,isoutsidethepurviewoflogic. 1.8Deductivevs.Inductivearguments Theconceptsofvalidityandsoundnessthatwehaveintroducedapplyonlytotheclassofwhatarecalled“deductivearguments”.Adeductiveargumentisanargumentwhoseconclusionissupposedtofollowfromitspremiseswithabsolutecertainty,thusleavingnopossibilitythattheconclusiondoesn’tfollowfromthepremises.Foradeductiveargumenttofailtodothisisforittofailasadeductiveargument.Incontrast,aninductiveargumentisanargumentwhoseconclusionissupposedtofollowfromitspremiseswithahighlevelofprobability,whichmeansthatalthoughitispossiblethattheconclusiondoesn’tfollowfromitspremises,itisunlikelythatthisisthecase.Hereisanexampleofaninductiveargument: Tweetsisahealthy,normallyfunctioningbirdandsincemosthealthy,normallyfunctioningbirdsfly,Tweetsprobablyflies. Noticethattheconclusion,Tweetsprobablyflies,containstheword“probably.”Thisisaclearindicatorthattheargumentissupposedtobeinductive,notdeductive.Hereistheargumentinstandardform: Tweetsisahealthy,normallyfunctioningbird Mosthealthy,normallyfunctioningbirdsfly Therefore,Tweetsprobablyflies Giventheinformationprovidedbythepremises,theconclusiondoesseemtobewellsupported.Thatis,thepremisesdogiveusastrongreasonforacceptingtheconclusion.Thisistrueeventhoughwecanimagineascenarioinwhichthepremisesaretrueandyettheconclusionisfalse.Forexample,supposethatweaddedthefollowingpremise: Tweetsis6fttallandcanrun30mph. Werewetoaddthatpremise,theconclusionwouldnolongerbesupportedbythepremises,sinceanybirdthatis6fttallandcanrun30mph,isnotakindofbirdthatcanfly.ThatinformationleadsustobelievethatTweetsisanostrichoremu,whicharenotkindsofbirdsthatcanfly.Asthisexampleshows,inductiveargumentsaredefeasibleargumentssincebyaddingfurtherinformationorpremisestotheargument,wecanoverturn(defeat)theverdictthattheconclusioniswell-supportedbythepremises.Inductiveargumentswhosepremisesgiveusastrong,evenifdefeasible,reasonforacceptingtheconclusionarecalled,unsurprisingly,stronginductivearguments.Incontrast,aninductiveargumentthatdoesnotprovideastrongreasonforacceptingtheconclusionarecalledweakinductivearguments. Whereasstronginductiveargumentsaredefeasible,validdeductiveargumentsaren’t.Supposethatinsteadofsayingthatmostbirdsfly,premise2saidthatallbirdsfly. Tweetsisahealthy,normallyfunctionbird. Allhealthy,normallyfunctioningbirdscanfly. Therefore,Tweetscanfly. Thisisavalidargumentandsinceitisavalidargument,therearenofurtherpremisesthatwecouldaddthatcouldoverturntheargument’svalidity.(True,premise2isfalse,butaswe’veseenthatisirrelevanttodeterminingwhetheranargumentisvalid.)EvenifweweretoaddthepremisethatTweetsis6fttallandcanrun30mph,itdoesn’toverturnthevalidityoftheargument.Assoonasweusetheuniversalgeneralization,“allhealthy,normallyfunctionbirdscanfly,”thenwhenweassumethatpremiseistrueandaddthatTweetsisahealthy,normallyfunctioningbird,ithastofollowfromthosepremisesthatTweetscanfly.ThisistrueevenifweaddthatTweetsis6fttallbecausethenwhatwehavetoimagine(inapplyingourinformaltestofvalidity)isaworldinwhichallbirds,includingthosethatare6fttallandcanrun30mph,canfly. Althoughinductiveargumentsareanimportantclassofargumentthatarecommonlyusedeverydayinmanycontexts,logictextstendnottospendasmuchtimewiththemsincewehavenoagreeduponstandardofevaluatingthem.Incontrast,thereisanagreeduponstandardofevaluationofdeductivearguments.Wehavealreadyseenwhatthatis;itistheconceptofvalidity.Inchapter2wewilllearnsomeprecise,formalmethodsofevaluatingdeductivearguments.Therearenosuchagreeduponformalmethodsofevaluationforinductivearguments.Thisisanareaofongoingresearchinphilosophy.Inchapter3wewillrevisitinductiveargumentsandconsidersomewaystoevaluateinductivearguments. 1.9Argumentswithmissingpremises Quiteoften,anargumentwillnotexplicitlystateapremisethatwecanseeisneededinorderfortheargumenttobevalid.Insuchacase,wecansupplythepremise(s)neededinordersomaketheargumentvalid.Makingmissingpremisesexplicitisacentralpartofreconstructingargumentsinstandardform.Wehavealreadydealtinpartwiththisinthesectiononparaphrasing,butnowthatwehaveintroducedtheconceptofvalidity,wehaveausefultoolforknowingwhentosupplymissingpremisesinourreconstructionofanargument.Insomecases,themissingpremisewillbefairlyobvious,asinthefollowing: Garyisaconvictedsex-offender,soGaryisnotallowedtoworkwithchildren. Thepremiseandconclusionofthisargumentarestraightforward: Garyisaconvictedsex-offender Therefore,Garyisnotallowedtoworkwithchildren(from1) However,asstated,theargumentisinvalid.(Beforereadingon,seeifyoucanprovideacounterexampleforthisargument.Thatis,comeupwithanimaginaryscenarioinwhichthepremiseistrueandyettheconclusionisfalse.)Hereisjustonecounterexample(therecouldbemany):Garyisaconvictedsex-offenderbutthecountryinwhichhelivesdoesnotrestrictconvictedsex-offendersfromworkingwithchildren.Idon’tknowwhetherthereareanysuchcountries,althoughIsuspectthereare(anditdoesn’tmatterforthepurposeofvaliditywhetherthereareoraren’t).Inanycase,itseemsclearthatthisargumentisrelyinguponapremisethatisn’texplicitlystated.Wecanandshouldstatethatpremiseexplicitlyinourreconstructionofthestandardformargument.Butwhatistheargument’smissingpremise?Theobviousoneisthatnosex-offendersareallowedtoworkwithchildren,butwecouldalsouseamorecarefullystatementlikethisone: WhereGarylives,noconvictedsex-offendersareallowedtoworkwithchildren. Itshouldbeobviouswhythisisamore“careful”statement.Itismorecarefulbecauseitisnotsouniversalinscope,whichmeansthatitiseasierforthestatementtobemadetrue.Byrelativizingthestatementthatsex-offendersarenotallowedtoworkwithchildrentotheplacewhereGarylives,weleaveopenthepossibilitythatotherplacesintheworlddon’thavethissamerestriction.Soevenifthereareotherplacesintheworldwhereconvictedsex-offendersareallowedtoworkwithchildren,ourstatementscouldstillbetruesinceinthisplace(theplacewhereGarylives)theyaren’t.(Formoreonstrongandweakstatements,seesection1.10).Sohereistheargumentinstandardform: Garyisaconvictedsex-offender. WhereGarylives,noconvictedsex-offendersareallowedtoworkwithchildren. Therefore,Garyisnotallowedtoworkwithchildren.(from1-2) Thisargumentisnowvalid:thereisnowayfortheconclusiontobefalse,assumingthetruthofthepremises.Thiswasafairlysimpleexamplewherethemissingpremiseneededtomaketheargumentvalidwasrelativelyeasytosee.Aswecanseefromthisexample,amissingpremiseisapremisethattheargumentneedsinordertobeasstrongaspossible.Typically,thismeanssupplyingthestatement(s)thatareneededtomaketheargumentvalid.Butinadditiontomakingtheargumentvalid,wewanttomaketheargumentplausible.Thisiscalled“theprincipleofcharity.”Theprincipleofcharitystatesthatwhenreconstructinganargument,youshouldtrytomakethatargument(whetherinductiveordeductive)asstrongaspossible.Whenitcomestosupplyingmissingpremises,thismeanssupplyingthemostplausiblepremisesneededinordertomaketheargumenteithervalid(fordeductivearguments)orinductivelystrong(forinductivearguments). Althoughinthelastexamplefiguringoutthemissingpremisewasrelativelyeasytodo,itisnotalwayssoeasy.Hereisanargumentwhosemissingpremisesarenotaseasytodetermine: Sincechildrenwhoareraisedbygaycouplesoftenhavepsychologicalandemotionalproblems,thestateshoulddiscouragegaycouplesfromraisingchildren. Theconclusionofthisargument,thatthestateshouldnotallowgaymarriage,isapparentlysupportedbyasinglepremise,whichshouldberecognizablefromtheoccurrenceofthepremiseindicator,“since.”Thus,ourinitialreconstructionofthestandardformargumentlookslikethis: Childrenwhoareraisedbygaycouplesoftenhavepsychologicalandemotionalproblems. Therefore,thestateshoulddiscouragegaycouplesfromraisingchildren. However,asitstands,thisargumentisinvalidbecauseitdependsoncertainmissingpremises.Theconclusionofthisargumentisanormativestatement—astatementaboutwhethersomethingoughttobetrue,relativetosomestandardofevaluation.Normativestatementscanbecontrastedwithdescriptivestatements,whicharesimplyfactualclaimsaboutwhatistrue.Forexample,“Russiadoesnotallowgaycouplestoraisechildren”isadescriptivestatement.Thatis,itissimplyaclaimaboutwhatisinfactthecaseinRussiatoday.Incontrast,“Russiashouldnotallowgaycouplestoraisechildren”isanormativestatementsinceitisnotaclaimaboutwhatistrue,butwhatoughttobetrue,relativetosomestandardofevaluation(forexample,amoralorlegalstandard).Animportantideawithinphilosophy,whichisoftentracedbacktotheScottishphilosopherDavidHume(1711-1776),isthatstatementsaboutwhatoughttobethecase(i.e.,normativestatements)canneverbederivedfromstatementsaboutwhatisthecase(i.e.,descriptivestatements).Thisisknownwithinphilosophyastheis-oughtgap.Theproblemwiththeaboveargumentisthatitattemptstoinferanormativestatementfromapurelydescriptivestatement,violatingtheis-oughtgap.Wecanseetheproblembyconstructingacounterexample.Supposethatinsocietyxitistruethatchildrenraisedbygaycoupleshavepsychologicalproblems.However,supposethatinthatsocietypeopledonotacceptthatthestateshoulddowhatitcantodecreaseharmtochildren.Inthiscase,theconclusion,thatthestateshoulddiscouragegaycouplesfromraisingchildren,doesnotfollow.Thus,wecanseethattheargumentdependsonamissingorassumedpremisethatisnotexplicitlystated.Thatmissingpremisemustbeanormativestatement,inorderthatwecaninfertheconclusion,whichisalsoanormativestatement.Thereisanimportantgenerallessonhere:Manytimesanargumentwithanormativeconclusionwilldependonanormativepremisewhichisnotexplicitlystated.Themissingnormativepremiseofthisparticularargumentseemstobesomethinglikethis: Thestateshouldalwaysdowhatitcantodecreaseharmtochildren. Noticethatthisisanormativestatement,whichisindicatedbytheuseoftheword“should.”Therearemanyotherwordsthatcanbeusedtocapturenormativestatementssuchas:good,bad,andought.Thus,wecanreconstructtheargument,fillinginthemissingnormativepremiselikethis: Childrenwhoareraisedbygaycouplesoftenhavepsychologicalandemotionalproblems. Thestateshouldalwaysdowhatitcantodecreaseharmtochildren. Therefore,thestateshoulddiscouragegaycouplesfromraisingchildren.(from1-2) However,althoughtheargumentisnowinbettershape,itisstillinvalidbecauseitisstillpossibleforthepremisestobetrueandyettheconclusionfalse.Inordertoshowthis,wejusthavetoimagineascenarioinwhichboththepremisesaretrueandyettheconclusionisfalse.Hereisonecounterexampletotheargument(therearemany).Supposethatwhileitistruethatchildrenofgaycouplesoftenhavepsychologicalandemotionalproblems,therateofpsychologicalproblemsinchildrenraisedbygaycouplesisactuallylowerthaninchildrenraisedbyheterosexualcouples.Inthiscase,evenifitweretruethatthestateshouldalwaysdowhatitcantodecreaseharmtochildren,itdoesnotfollowthatthestateshoulddiscouragegaycouplesfromraisingchildren.Infact,inthescenarioI’vedescribed,justtheoppositewouldseemtofollow:thestateshoulddiscourageheterosexualcouplesfromraisingchildren. Butevenifwesupposethattherateofpsychologicalproblemsinchildrenofgaycouplesishigherthaninchildrenofheterosexualcouples,theconclusionstilldoesn’tseemtofollow.Forexample,itcouldbethatthereasonthatchildrenofgaycoupleshavehigherratesofpsychologicalproblemsisthatinasocietythatisnotyetacceptingofgaycouples,childrenofgaycoupleswillfacemoreteasing,bullyingandgenerallackofacceptancethanchildrenofheterosexualcouples.Ifthisweretrue,thentheharmtothesechildrenisn’tsomuchduetothefactthattheirparentsaregayasitistothefactthattheircommunitydoesnotacceptthem.Inthatcase,thestateshouldnotnecessarilydiscouragegaycouplesfromraisingchildren.Hereisananalogy:Atonepointinourcountry’shistory(ifnotstilltoday)itisplausiblethatthechildrenofblackAmericanssufferedmorepsychologicallyandemotionallythanthechildrenofwhiteAmericans.ButforthegovernmenttodiscourageblackAmericansfromraisingchildrenwouldhavebeenunjust,sinceitislikelythatiftherewasahigherincidenceofpsychologicalandemotionalproblemsinblackAmericans,thenitwasduetounjustandunequalconditions,nottotheblackparents,perse.So,toreturntoourexample,thestateshouldonlydiscouragegaycouplesfromraisingchildreniftheyknowthatthehigherincidenceofpsychologicalproblemsinchildrenofgaycouplesisn’ttheresultofanykindofinjustice,butisduetothesimplefactthattheparentsaregay. Thus,onewayofmakingtheargument(atleastcloserto)validwouldbetoaddthefollowingtwomissingpremises: A.Therateofpsychologicalproblemsinchildrenofgaycouplesishigherthaninchildrenofheterosexualcouples. B.Thehigherincidenceofpsychologicalproblemsinchildrenofgaycouplesisnotduetoanykindofinjusticeinsociety,buttothefactthattheparentsaregay. Sothereconstructedstandardformargumentwouldlooklikethis: Childrenwhoareraisedbygaycouplesoftenhavepsychologicalandemotionalproblems. Therateofpsychologicalproblemsinchildrenofgaycouplesishigherthaninchildrenofheterosexualcouples. Thehigherincidenceofpsychologicalproblemsinchildrenofgaycouplesisnotduetoanykindofinjusticeinsociety,buttothefactthattheparentsaregay. Thestateshouldalwaysdowhatitcantodecreaseharmtochildren. Therefore,thestateshoulddiscouragegaycouplesfromraisingchildren.(from1-4) Inthisargument,premises2-4arethemissingorassumedpremises.Theiradditionmakestheargumentmuchstronger,butmakingthemexplicitenablesustoclearlyseewhatassumptionstheargumentreliesoninorderfortheargumenttobevalid.Thisisusefulsincewecannowclearlyseewhichpremisesoftheargumentwemaychallengeasfalse.Arguably,premise4isfalse,sincethestateshouldn’talwaysdowhatitcantodecreaseharmtochildren.Rather,itshouldonlydosoaslongassuchanactiondidn’tviolateotherrightsthatthestatehastoprotectorcreatelargerharmselsewhere. Theimportantlessonfromthisexampleisthatsupplyingthemissingpremisesofanargumentisnotalwaysasimplematter.Intheexampleabove,Ihaveusedtheprincipleofcharitytosupplymissingpremises.Masteringthisskillistrulyanart(ratherthanascience)sincethereisneverjustonecorrectwayofdoingit(cf.section1.5)andbecauseitrequiresalotofskilledpractice. Exercise6:Supplythemissingpremiseorpremisesneededinordertomakethefollowingargumentsvalid.Trytomakethepremisesasplausibleaspossiblewhilemakingtheargumentvalid(whichistoapplytheprincipleofcharity). Edrideshorses.Therefore,Edisacowboy. Tomwasdrivingoverthespeedlimit.Therefore,Tomwasdoingsomethingwrong. Ifitisrainingthenthegroundiswet.Therefore,thegroundmustbewet. AllelvesdrinkGuinness,whichiswhyOlafdrinksGuinness. Markdidn’tinvitemetohomecoming.Instead,heinvitedhisfriendAlexia.SohemustlikeAlexiamorethanme. ThewatchmustbebrokenbecauseeverytimeIhavelookedatit,thehandshavebeeninthesameplace. OlafdranktoomuchGuinnessandfelloutofhissecondstoryapartmentwindow.Therefore,drinkingtoomuchGuinnesscausedOlaftoinjurehimself. Markjumpedintotheair.Therefore,Marklandedbackontheground. In2009intheUnitedStates,thenetworthofthemedianwhitehouseholdwas$113,149ayear,whereasthenetworthofthemedianblackhouseholdwas$5,677.Therefore,asof2009,theUnitedStateswasstillaracistnation. Thetemperatureofthewateris212degreesFahrenheit.Therefore,thewaterisboiling. Capitalpunishmentsometimestakesinnocentlives,suchasthelivesofindividualswhowerelaterfoundtobenotguilty.Therefore,weshouldnotallowcapitalpunishment. AllowingimmigrantstomigratetotheU.S.willtakeworkingclassjobsawayfromworkingclassfolks.Therefore,weshouldnotallowimmigrantstomigratetotheU.S. Prostitutionisafaireconomicexchangebetweentwoconsentingadults.Therefore,prostitutionshouldbeallowed. Collegesaremoreinterestedinmakingmoneyoffoftheirfootballathletesthanineducatingthem.Therefore,collegefootballoughttobebanned. EdwardreceivedanFincollegeAlgebra.Therefore,Edwardshouldhavestudiedmore. Previous/nextnavigation Previous:WhatisanArgument? Next:Attribution Backtotop License ABriefIntroductiontoPhilosophybySouthernAlbertaInstitutionofTechnology(SAIT)islicensedunderaCreativeCommonsAttribution-NonCommercial-ShareAlike4.0InternationalLicense,exceptwhereotherwisenoted. ShareThisBook ShareonTwitter