5 - Categorical syllogism

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1、1SyllogismAsyllogismisatwo-premisedeductiveargument.Or,acategoricalsyllogismisanargumentinwhichboththepremisesandtheconclusionarecategoricalpropositions.2Thereare3propositions.Thereare3terms.Eachtermisusedtwice.Noneofthetermisusedtwiceinthesameproposition.3

2、Allsoldiersarepatriots.Notraitorsarepatriots.Therefore,notraitorsaresoldiers.4MajortermMajortermisthepredicateoftheconclusion.Soldiers5MinortermMinortermisthesubjectoftheconclusion.Traitors6MiddletermMiddletermisthelinkbetweenthetwopremises.Itdoesnotoccurin

3、theconclusion.Patriots7MajorandminorpremisesThemajorpremiseisthepremisethatcontainsthemajorterm:“Allsoldiersarepatriots”.Theminorpremiseisthepremisethatcontainstheminorterm:“Notraitorsarepatriots”.8StandardformThemajorpremiseislistedfirst,theminorpremisesec

4、ond,andtheconclusionlast.MajorpremiseMinorpremiseConclusion9MoodThemoodistheorderofthetypeofpropositionsinacategoricalsyllogism.Inthepreviousexample,themoodisAEE.Aisthetypeofthemajorpremise,Eforminorpremise,thefinalEfortheconclusion.10FigureThefigureofacate

5、goricalpropositionisdeterminedbythelocationofthetwooccurrencesofthemiddleterminthepremises.Therefore,thereare4possiblefigures.11Figure1Figure2Figure3Figure4MPSMSPPMSMSPMPMSSPPMMSSP12Positionsofthe4SetsofMiddleTermsRemembertheW-shapedfigure13Sincetherearefou

6、rkindsofcategoricalpropositionsandthreecategoricalpropositionsineachsyllogism,wecanhave64(4x4x4)possiblemoods.Andsincewehave4possiblefigures,thereareatotalof256differentforms(mood-figure)ofcategoricalsyllogism.14Ifyoucanwriteouttheformofaparticularcategoric

7、alsyllogism,thenyoucancheckwhetheritisunconditionallyvalidornot.Ifwefurtherrequirecertaintermsinthesyllogismtorefertoactuallyexistingthings,thenweareconcernedwithconditionalvalidity.15UnconditionallyValidFigure1Figure2Figure3Figure4AAAEAEIAIAEEEAEAEEAIIIAIA

8、IIEIOOAOEIOEIOAOOEIO16Don’tworrythatyouhavetorememberalltheforms.Youaresimplyrequiredtounderstandtheunderlyingprinciple.Justbyknowingthemood-figureofasyllogism,wecancheckwhetherthesyllogismisunconditio