Phil 106: Critical Thinking - SIUE

Soundness. A. Good Deductive Form + Good Content = Soundness. B. Definition: An argument is sound =df It is valid and has all true premises. Phil 106:CriticalThinking LARKIN Southern IllinoisUniversityEdwardsville     Deductive Concepts   I.                     Deduction vs.Induction A.      DeductiveForm:Thepremisesareintendedtoprovideconclusivereasons orproofoftheconclusion.   B.       InductiveForm:Thepremisesareintendedtoprovidecompellingbutnot conclusivereasonsfortheconclusion.     II.                   Validity A.      Good DeductiveForm=Validity   B.       Definitions (thesedefinitionsarejusttwodifferentwaysofsayingthesamething) 1.        An argumentisvalid=dfIfallthepremisesaretrue,thenthe conclusionmustbetrue.   2.       Anargumentisvalid=dfItisimpossibleforall thepremisestobetruebuttheconclusionfalse.   C.       Validity (inthetechnicalsensejustdefined)appliesonlytoarguments,neverto individualclaims.   D.      Validity iscompletelydeterminedbyanargument’sstructure,notitscontent. Ifsomeargumentisvalid,thenevery argumentwiththesamestructureisalsovalid.     III.                 Soundness A.      Good DeductiveForm+GoodContent=Soundness   B.       Definition: Anargumentissound=dfItisvalid andhasalltruepremises.   C.       If anargumenthasoneormorefalsepremisesoritisnotvalid,thenthe argumentisnotsound.   D.      Like validity,soundness(inthetechnicalsensejustdefined)appliesonlyto arguments,nevertoindividualstatements/claims.     IV.                 True/False Questions 1.        A validargumentmusthaveatrueconclusion   FALSE: Avalid argumentmusthaveatrueconclusiononlyifallofthepremisesaretrue. Soitispossibleforavalidargumentto haveafalseconclusionaslongasatleastonepremiseisfalse.   2.        A soundargumentmusthaveatrueconclusion.   TRUE: Ifan argumentissound,thenitisvalidandhasalltruepremises. Sinceitisvalid,theargumentissuchthat ifallthepremisesaretrue,thentheconclusionmustbetrue. Asoundargumentreallydoeshavealltrue premisessoitdoesactuallyfollowthatitsconclusionmustbetrue.   3.        If avalidargumenthasafalseconclusion,thenatleastonepremisemustbe false.   TRUE: Avalid argumentcannothavealltruepremisesandafalseconclusion. Soifavalidargumentdoeshaveafalse conclusion,itcannothavealltruepremises.  Thusatleastonepremisemustbefalse.   4.        If aninvalidargumenthasalltruepremises,thentheconclusionmustbefalse.   FALSE: Itis possibleforaninvalidargumenttohavealltruepremisesandatrue conclusion.      Ex:          P1: Alldogsare mammals.                                                            P2: Allterriersaremammals.                                                            C: Allterriersaredogs.   Thisargumentreallydoeshavealltruepremisesand atrueconclusion,butstillitisinvalid—becauseitispossibleforan argumentwiththisstructuretohavetruepremisesandafalseconclusion:                                            Ex:         P1: Alldogsaremammals.                                                            P2: Allcatsaremammals.                                                            C: Allcatsaredogs.   5.        If anargumenthasalltruepremisesandatrueconclusion,thenitisvalid.   FALSE: Itis possibleforanargumenttohavealltruepremisesandatrueconclusionbut stillbeinvalid. Seeabove(#4).   6.        If anargumenthasalltruepremisesandafalseconclusion,thenitisinvalid.   TRUE: Avalid argumentcannotpossiblyhavealltruepremisesandafalseconclusion. Ifsomeargumentreallydoeshavealltrue premisesandafalseconclusion,thenitisobviouslypossibleforsuchan argumenttohavetruepremisesandafalseconclusion. Sotheargumentisinvalid.