[A04] Soundness - PHILOSOPHY@HKU

So given that a sound argument is valid and has true premises, its conclusion must also be true. So if you have determined that an argument is indeed sound, ... 思方網•criticalthinkingweb ( ∀ ∴ ⊧ ≠ ↔ ⊥ ∃ )   Home(current) Tutorials CriticalthinkingMeaninganalysisArgumentanalysisBasiclogicVenndiagramsSententiallogicPredicatelogicScientificmethodologyBasicstatisticsValuesStrategicreasoningFallaciesandbiasesCreativity Sitemap Resources About Search [A04]Soundness Module:Argumentanalysis A00.Introduction A01.Whatisanargument?A02.ThestandardformatA03.ValidityA04.SoundnessA05.ValidpatternsA06.ValidityandrelevanceA07.HiddenAssumptionsA08.InductiveReasoningA09.GoodArgumentsA10.ArgumentmappingA11.AnalogicalArgumentsA12.MorevalidpatternsA13.Arguingwithotherpeople Quoteofthepage Alltrulywisethoughtshavebeenthoughtalreadythousandsoftimes;buttomakethemtrulyours,wemustthinkthemoveragainhonestly,tilltheytakerootinourpersonalexperience. -JohannWolfgangvonGoethe Helpuspromotecriticalthinking! Popularpages Whatiscriticalthinking? Whatislogic? Hardestlogicpuzzleever Freeminiguide Whatisanargument? Knightsandknavespuzzles Logicpuzzles Whatisagoodargument? Improvingcriticalthinking Analogicalarguments Itshouldbeobviousbynowthatvalidityisaboutthelogicalconnectionbetweenthepremisesandtheconclusion.Whenwearetoldthatanargumentisvalid,thisisnotenoughtotellusanythingabouttheactualtruthorfalsityofthepremisesortheconclusion.Allweknowisthatthereisalogicalconnectionbetweenthem,thatthepremisesentailtheconclusion. Soevenifwearegivenavalidargument,westillneedtobecarefulbeforeacceptingtheconclusion,sinceavalidargumentmightcontainafalseconclusion.Whatweneedtocheckfurtherisofcoursewhetherthepremisesaretrue.Ifanargumentisvalid,andallthepremisesaretrue,thenitiscalledasoundargument.Ofcourse,itfollowsfromsuchadefinitionthatasoundargumentmustalsohaveatrueconclusion.Inavalidargument,ifthepremisesaretrue,thentheconclusioncannotbefalse,sincebydefinitionitisimpossibleforavalidargumenttohavetruepremisesandafalseconclusioninthesamesituation.Sogiventhatasoundargumentisvalidandhastruepremises,itsconclusionmustalsobetrue.Soifyouhavedeterminedthatanargumentisindeedsound,youcancertainlyaccepttheconclusion. Anargumentthatisnotsoundisanunsoundargument.Ifanargumentisunsound,itmightbethatitisinvalid,ormaybeithasatleastonefalsepremise,orboth. Isitpossibletohaveargumentsofthefollowingkinds?Ifso,provideanexample.Ifnot,explainwhy.Itisparticularlyimportanttonotethehighlightedcases.   Trueconclusiontruepremises Trueconclusionfalsepremises Falseconclusiontruepremises Falseconclusionfalsepremises Valid&sound answeransweransweranswer Valid&unsound answeransweranswer answer Invalid&sound answeransweransweranswer Invalid&unsound answer answer answer answer Arethefollowingstatementstrueorfalse?Why? Allinvalidargumentsareunsound. answer Alltruestatementsarevalid. answer Toshowthatanargumentisunsound,wemustatleastshowthatsomeofitspremisesareactuallyfalse. answer Aninvalidargumentmusthaveafalseconclusion. answer Ifallthepremisesofavalidargumentarefalse,thentheconclusionmustalsobefalse. answer Ifallthepremisesandtheconclusionofanargumentaretrue,thentheargumentisvalid. answer Allsoundargumentsaretrue. answer Anyvalidargumentwithatrueconclusionissound. answer Herearesomecommonquestionsfromstudentsaboutvalidityandsoundnessandtheiranswers.Seeifyouknowhowtoanswerthemyourself. Anargumentisvalid,ifwhenallthepremisesaretruetheconclusionistrue. Whatifthepremisesareinconsistent?Whatifitisimpossibleforallthepremisestobetrueatthesametime? Istheargumentstillvalid? answer Yes.Anargumentwithinconsistentpremisesisvalid,regardlessofwhattheconclusionis.Ifanargumenthasinconsistentpremises,thenitisimpossibleforallthepremisestobetrueatthesametime;henceitisimpossibleforallthepremisestobetruewhiletheconclusionisfalse. Iftheconclusionofanargumentistautological,doesthatmeansthattheargumentisvalid? answer Yes.Anargumentwithatautologicalconclusionisvalid,regardlessofwhatthepremisesare.Iftheconclusionisatautology,thenthereisnopossiblesituationwheretheconclusionisfalse.Hencethereisnopossiblesituationwherethepremisesaretruewhiletheconclusionisfalse. Ifeveryargumentwithatautologicalconclusionisvalid,thenshouldn'tthisargumentbevalidratherthaninvalid? (Premise)Allcowsaremammals. (Conclusion)Therefore,thesunislargerthanthemoon. Isn’ttheconclusionatautology? answer Thisargumentisinvalidsincethereisapossiblesituationwhereallcowsaremammals,butthesunnottobelargerthanthemoon.Theconclusionistrue,buttheconclusionisnotatautology;itislogicallypossibleforthesuntobesmallerthanthemoon. "Itisraining.Therefore1+1=2." Whyisthisavalidargumentasthepremiseandtheconclusionaretalkingaboutcompletelydifferentthings? answer Anargumentisvalidifthereisnopossiblesituationwherethepremisesaretrueandtheconclusionisfalse.Sinceitisnecessarilytruethat1+1=2,thereisnopossiblesituationwheretheconclusionisfalse.Sothereisnotpossiblesituationwherethepremisesaretrueandtheconclusionisfalse.Thus,theargumentisvalid. Youmightthinkthatthisisstrange,andindeeditis.Somephilosophersandlogicianshavearguedthatweneedabetterdefinitionofvalidity.Butitturnsoutthatthisisnotaneasytask,andotherdefinitionshavetheirproblemstoo.Herewewillsticktothesimplerdefinition. Iknowthatallsoundargumentsmusthavetrueconclusionsbecausesuchargumentsarebydefinitionvalid withalltruepremises.Ontheotherhand,ifanargumentisvalidandhasatrueconclusion, doesitfollowthatitissound? answer No.Avalidargumentmayhaveatrueconclusionevenifnotallitspremisesaretrue.Forinstance: (Premise)Allcatsareflyingcreatures. (Premise)Allflyingcreaturesaremammals. (Conclusion)Therefore,allcatsaremammals. "Allargumentsareeithervalidorunsound."Isthisstatementtrue? answer Yes.Allargumentsareeithervalidorinvalid.Allinvalidargumentsareunsound.Soallargumentsareeithervalidorunsound. previoustutorialnexttutorial homepage•top•contact•sitemap ©2004-2022JoeLau&JonathanChan