[A03] Validity - PHILOSOPHY@HKU

A valid argument is one where the truth of the premises guarantees the truth of the conclusion, but validity does not guarantee that the premises are in fact ... 思方網•criticalthinkingweb ( ∀ ∴ ⊧ ≠ ↔ ⊥ ∃ )   Home(current) Tutorials CriticalthinkingMeaninganalysisArgumentanalysisBasiclogicVenndiagramsSententiallogicPredicatelogicScientificmethodologyBasicstatisticsValuesStrategicreasoningFallaciesandbiasesCreativity Sitemap Resources About Search [A03]Validity Module:Argumentanalysis A00.Introduction A01.Whatisanargument?A02.ThestandardformatA03.ValidityA04.SoundnessA05.ValidpatternsA06.ValidityandrelevanceA07.HiddenAssumptionsA08.InductiveReasoningA09.GoodArgumentsA10.ArgumentmappingA11.AnalogicalArgumentsA12.MorevalidpatternsA13.Arguingwithotherpeople Quoteofthepage Agreatmanypeoplethinktheyarethinkingwhentheyaremerelyrearrangingtheirprejudices. -WilliamJames Helpuspromotecriticalthinking! Popularpages Whatiscriticalthinking? Whatislogic? Hardestlogicpuzzleever Freeminiguide Whatisanargument? Knightsandknavespuzzles Logicpuzzles Whatisagoodargument? Improvingcriticalthinking Analogicalarguments §1.Definitionofvalidity Onedesirablefeatureofargumentsisthattheconclusionshouldfollowfromthepremises.Butwhatdoesitmean?Considerthesetwoarguments: Argument#1: Barbieisover90yearsold.SoBarbieisover20yearsold. Argument#2:Barbieisover20yearsold.SoBarbieisover90yearsold. Intuitively,theconclusionofthefirstargumentfollowsfromthepremise,whereastheconclusionofthesecondargumentdoesnotfollowfromitspremise.Buthowshouldweexplainthedifferencebetweenthetwoargumentsmoreprecisely?Hereisathought:Inthefirstargument,ifthepremiseisindeedtrue,thentheconclusioncannotbefalse.Ontheotherhand,evenifthepremiseinthesecondargumentistrue,thereisnoguaranteethattheconclusionmustalsobetrue.Forexample,Barbiecouldbe30yearsold. Soweshallmakeuseofthisideatodefinethenotionofadeductivelyvalidargument,orvalidargument,asfollows: Anargumentisvalidifandonlyifthereisnologicallypossiblesituationwhereallthepremisesaretrueandtheconclusionisfalseatthesametime. Theideaofvalidityprovidesamorepreciseexplicationofwhatitisforaconclusiontofollowfromthepremises.Applyingthisdefinition,wecanseethatthefirstargumentaboveisvalid,sincethereisnopossiblesituationwhereBarbiecanbeover90butnotover20.Thesecondargumentisnotvalidbecausethereareplentyofpossiblesituationswherethepremiseistruebuttheconclusionisfalse.ConsiderasituationwhereBarbieis25,oronewheresheis85.Thefactthatthesesituationsarepossibleisenoughtoshowthattheargumentisnotvalid,orinvalid. §2.Validityandtruth Whatifwehaveanargumentwithmorethanonepremise?Hereisanexample: Allpigscanfly.Anythingthatcanflycanswim.Soallpigscanswim. Althoughthetwopremisesofthisargumentarefalse,thisisactuallyavalidargument.Toevaluateitsvalidity,askyourselfwhetheritispossibletocomeupwithasituationwhereallthepremisesaretrueandtheconclusionisfalse.(Wearenotaskingwhetherthereisasituationwherethepremisesandtheconclusionarealltrue.)Ofcourse,theansweris'no'.Ifpigscanindeedfly,andifanythingthatcanflycanalsoswim,thenitmustbethecasethatallpigscanswim. Sothisexampletellsussomething: Thepremisesandtheconclusionofavalidargumentcanallbefalse. Hopefullyyouwillnowrealizethatvalidityisnotabouttheactualtruthorfalsityofthepremisesortheconclusion.Validityisaboutthelogicalconnectionbetweenthepremisesandtheconclusion.Avalidargumentisonewherethetruthofthepremisesguaranteesthetruthoftheconclusion,butvaliditydoesnotguaranteethatthepremisesareinfacttrue.Allthatvaliditytellsusisthatifthepremisesaretrue,theconclusionmustalsobetrue. §3.Showingthatanargumentisinvalid Nowconsiderthisargument: AdamlovesBeth.BethlovesCathy.SoAdamlovesCathy. Thisargumentisnotvalid,foritispossiblethatthepremisesaretrueandyettheconclusionisfalse.PerhapsAdamlovesBethbutdoesnotwantBethtoloveanyoneelse.SoAdamactuallyhatesCathy.Themerepossibilityofsuchasituationisenoughtoshowthattheargumentisnotvalid.Letuscallthesesituationsinvalidatingcounterexamplestotheargument.Basically,wearedefiningavalidargumentasanargumentwithnopossibleinvalidatingcounterexamples.Tosharpenyourskillsinevaluatingarguments,itisthereforeimportantthatyouareabletodiscoverandconstructsuchexamples. Noticethatacounterexampleneednotberealinthesenseofbeinganactualsituation.ItmightturnoutthatinfactthatAdam,BethandCathyaremembersofthesamefamilyandtheyloveeachother.Buttheaboveargumentisstillinvalidsincethecounterexampleconstructedisapossiblesituation,evenifitisnotactuallyreal.Allthatisrequiredofacounterexampleisthatthesituationisacoherentoneinwhichallthepremisesoftheargumentaretrueandtheconclusionisfalse.Soweshouldrememberthis: Anargumentcanbeinvalideveniftheconclusionandthepremisesareallactuallytrue. Togiveyouanotherexample,hereisanotherinvalidargumentwithatruepremiseandatrueconclusion:"ParisisthecapitalofFrance.SoRomeisthecapitalofItaly.".ItisnotvalidbecauseitispossibleforItalytochangeitscapital(saytoMilan),whileParisremainsthecapitalofFrance. Anotherpointtorememberisthatitispossibleforavalidargumenttohaveatrueconclusionevenwhenallitspremisesarefalse.Hereisanexample: Allpigsarepurpleincolour.Anythingthatispurpleisananimal.Soallpigsareanimals. Beforeproceedinganyfurther,pleasemakesureyouunderstandwhytheseclaimsaretrueandcangiveexamplesofsuchcases. Thepremisesandtheconclusionofaninvalidargumentcanallbetrue. Avalidargumentshouldnotbedefinedasanargumentwithtruepremisesandatrueconclusion. Thepremisesandtheconclusionofavalidargumentcanallbefalse. Avalidargumentwithfalsepremisescanstillhaveatrueconclusion. §4.Areminder Theconceptofvalidityprovidesamorepreciseexplicationofwhatitisforaconclusiontofollowfromthepremises.Sincethisisoneofthemostimportantconceptsinthiscourse,youshouldmakesureyoufullyunderstandthedefinition.Ingivingourdefinitionwearemakingadistinctionbetweentruthandvalidity.Inordinaryusage"valid"isoftenusedinterchangeablywith"true"(similarlywith"false"and"notvalid").Butherevalidityisrestrictedtoonlyargumentsandnotstatements,andtruthisapropertyofstatementsbutnotarguments. Soneversaythingslike"thisstatementisvalid"or"thatargumentistrue"! Aretheseargumentsvalid? Someoneissick. Someoneisunhappy. Sosomeoneisunhappyandsick. answer Ifhelovesmethenhegivesmeflowers. Hegivesmeflowers. Sohelovesme. answer Beckhamisfamous. Beckhamisafootballplayer. Therefore,Beckhamisafamousfootballplayer. answer Ifitrains,thestreetswillbewet. Ifthestreetsarewet,accidentswillhappen. Therefore,accidentswillhappenifitrains. answer JohnwasinBritainwhenMarydiedinHongKong. SoMarycouldnothavebeenkilledbyJohn. answer IfthereislifeonPlutothenPlutocontainswater. ButthereisnolifeonPluto. ThereforePlutodoesnotcontainwater. answer Therewereonlytworabbitsintheroomlastweek. Norabbithaslefttheroomsincethen. Thereforethereareonlytworabbitsintheroomnow. answer Allwhaleshavewings. Mobydoesnothavewings. SoMobyisnotawhale. answer Aretheseargumentsvalid? Johnshothimselfinthehead.SoJohnisdead. answer Johnshothimselfinthehead.SoJohnshothimselfinthehead. answer Valid.Thisisacircularargumentsincetheconclusionisalsoapremise.Butitisnonethelessvalidsinceitisimpossibleforthepremisestobetruewhiletheconclusionisfalse. Allmanagementconsultantsarebald.Peterisbald.SoPeterisamanagementconsultant. answer Iftimetravelispossible,wewouldnowhavelotsoftime-travelvisitorsfromthefuture.Butwehavenosuchvisitors.Sotimetravelisnotpossible. answer JeniseitherinSanDiegoorinTokyo.SincesheisnotinTokyo,sheisinSanDiego. answer Somepeoplearenice.Somepeoplearerich.Sosomepeoplearerichandnice. answer IfIdrinkthenIwillbehappy.IfIamhappythenIwilldance.SoifIdrinkthenIwilldance. answer Everyredfishisafish. answer Theservicesofmobilephonecompaniesaregettingworseastherehasbeenanincreasingnumberofcomplaintsagainstmobilephonecompaniesbyconsumers. answer Allcapitalistsexploittheweakandthepoor.Propertydevelopersexploittheweakandthepoor.Sopropertydevelopersarecapitalists. answer previoustutorialnexttutorial homepage•top•contact•sitemap ©2004-2022JoeLau&JonathanChan