Cambridge Logic Tutorials 2013-3-21

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1、TutorialsTutorialOne:ConsistencyandValidityTutorialTwo:PropositionalCalculus:LanguageTutorialThree:PropositionalCalculus:TableauxTutorialFour:PredicateCalculus:LanguageTutorialFive:PredicateCalculus:TableauxTutorialSix:PredicateCalculuswithIdentityTutorialSeven:DesignatorsTutorialEight:Relations 1:C

2、onsistencyandValidity ThesubjectmatterofLogicTheLogicwearedealingwithisconcernedwiththesortsofthingswhichcanbetrueorfalse,suchasbeliefsand declarativesentences. Truthandfalsehoodare truth-values. Logicisnot,however,concernedmuchwiththe actual truth-valuesofbeliefsandsentences,butratherwithsuchquesti

3、onsas:             Issuchandsuchasetofbeliefsorsentencesconsistent?             Issuchandsuchanargumentvalid? Consistency/InconsistencyAsetofbeliefsisconsistentjustifitwouldbepossibleforthemalltobetruetogether:thatis,iftheyareeitherinfactalltrueorcouldallhavebeentrue. Asetofbeliefsisinconsistentjust

4、ifitwouldbeimpossibleforthemalltobetrue. Asinglebeliefcanalsobesaidtobeconsistent(ifitispossibleforittobetrue)orinconsistent(ifitisnotpossible).Aninconsistentbeliefissaidtobe self-contradictory,ora contradiction. Asinglebeliefwhichcouldnotbefalseissaidtoexpressa necessarytruth. Asinglebeliefwhichisn

5、otinconsistentanddoesnot  expressanecessarytruthissaidtobe contingent. Note:wearedealingwithaveryweaksortofpossibility,oraverystrongsortofimpossibility.Forthepurposethesedefinitions,itispossibleforahumanbeingtorunamileinunderaminute(humansmighthavebeenstronger;thelawsofnaturemighthavebeendifferent)b

6、utitisnotpossiblefor2and2tomake5;itisnotpossibleforapersontobebothabachelorandmarried;itisnotpossibleforittobebothrainingandnotraininginthesameplaceatthesametime.Asetofsentencesisconsistentjustifitwouldbepossibleforthesentences asbeingused alltobetrue. Asetofsentencesisinconsistentjustifitwouldbeimp

7、ossibleforthesentences asbeingused alltobetrue. Asinglesentencemayalsobeinconsistent;inwhichcaseitissaidtobe self-contradictory,ora contradiction. Asinglesentencewhichcouldnotbefalseissaidtobea necess