a concise introduction to logic_2005

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1、TraditionalSquareofOppositionContraryAETTContradictorySubalternationdictorySubalternationContraFFIOSubcontraryLogicallyEquivalentStatementFormsConversionGivenstatementConverseE:NoSareP.NoPareS.I:SomeSareP.SomePareS.ObversionGivenstatementObverseA:AllSareP.NoSarenon-P.E:NoSareP.AllSarenon-P

2、.I:SomeSareP.SomeSarenotnon-P.O:SomeSarenotP.SomeSarenon-P.ContrapositionGivenstatementContrapositiveA:AllSareP.Allnon-Parenon-S.O:SomeSarenotP.Somenon-Parenotnon-S.ValidSyllogisticFormsUnconditionallyValidFormsFigure1Figure2Figure3Figure4AAAEAEIAIAEEEAEAEEAIIIAIAIIEIOOAOEIOEIOAOOEIOCondit

3、ionallyValidFormsRequiredFigure1Figure2Figure3Figure4conditionAAIAEOAEOSexistEAOEAOAAIEAOMexistEAOAAIPexistRulesforCategoricalSyllogismsRule1:Themiddletermmustbedistributedatleastonce.Fallacy:UndistributedmiddleRule2:Ifatermisdistributedintheconclusion,thenitmustbedistributedinthepremise.F

4、allacy:Illicitmajor;illicitminorRule3:Twonegativepremisesarenotallowed.Fallacy:ExclusivepremisesRule4:Anegativepremiserequiresanegativeconclusion,andanegativeconclusionrequiresanegativepremise.Fallacy:Drawinganaffirmativeconclusionfromanegativepremise;drawinganegativeconclusionfromaffirmativ

5、epremisesRule5:Ifbothpremisesareuniversal,theconclusioncannotbeparticular.Fallacy:ExistentialfallacyNOTE:IfonlyRule5isbroken,thesyllogismisvalidfromtheAristotelianstandpointifthecriticaltermdenotesactuallyexistingthings.TruthTablesforthePropositionalOperatorspq~pp•qpvqp⊃qp≡qTTFTTTTTFFFTFFF

6、TTFTTFFFTFFTTRulesfortheProbabilityCalculus1.P(AornotA)=12.P(AandnotA)=03.P(AandB)=P(A)
P(B)(whenAandBareindependent)4.P(AandB)=P(A)
P(BgivenA)5.P(AorB)=P(A)+P(B)(whenAandBaremutuallyexclusive)6.P(AorB)=P(A)+P(B)–P(AandB)7.P(A)=1–P(notA)www.wadsworth.comwww.wadsworth.comistheWorldWideWebsi

7、teforWadsworthandisyourdirectsourcetodozensofonlineresources.Atwww.wadsworth.comyoucanfindoutaboutsup-plements,demonstrationsoftware,andstudentresources.Youcanalsosendemailtomanyofourauthorsandpreviewnewpublicationsandexcitingnewtechnologies.www.wadsworth.comC