Colin Howson - 1997 - Logic with Trees - An Introduction to Symbolic Logic

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1、LogicwithtreesLogicwithtreesisanewandoriginalintroductiontomodernformallogic.Unlikemosttextsonthesubject,itincludesdiscussionsofmorephilosophicalissuessuchastruth,conditionalsandmodallogic.Preferringexplanationandargumenttointimidatinglyrigorousdevelopment,ColinH

2、owsonpresentstheformalmaterialinaclearandinformalstylethatbothbeginnersandthosewithsomeknowledgeofformalmethodswillappreciate.Examplesandexercisesguidereadersthroughthebook,andanswerstoselectedexercisesattheendallowthemtomonitortheirownprogress.LogicwithTreesgive

3、sstudents•acompleteandclearaccountofthetruthtreesystemforfirst-orderlogic•anunderstandingoftheimportanceoflogicandofitsrelevancetootherdisciplines•theskillstograspsophisticatedformalreasoningtechniquesthatarenecessarytoexplorecomplexmetalogic•andtheabilitytoconte

4、stclaimsthat‘ordinary’reasoningiswellrepresentedbyformalfirst-orderlogicHowson’scarefullyplannedtextbookcoversbothtruth-functionalandfullfirst-orderlogic,usingthetruthtreeorsemantictableauapproach;hegivescompletenessandsoundnessproofsforbothtruth-functionalandfir

5、st-ordertrees,andmakesextensiveuseofinduction.Inaddition,hediscussesalternativedeductivesystems,transfinitenumbersandcategoricity,theLöwnheim-SkolemtheoremsandthecelebratedtheoremsofGödelandChurch.ThebookconcludeswithanaccountofKripke’sattempttosolvetheLiarParado

6、xandadiscussionoftheweaknessesofthetruth-functionalaccountofconditionals.LogicwithTreeswillbeparticularlyusefulforthosewhofeelwaryofformalmethods,sinceitshowshowsimpleevenquitesophisticatedformalreasoningcanbe.Itwillbeofinteresttostudentsofphilosophyatundergradua

7、televelandbeyond,aswellastostudentsofmathematicsandcomputerscience.ColinHowsonisReaderinLogicattheLondonSchoolofEconomicsandPoliticalScience.TheLondonSchoolofEconomicsandPoliticalScience/RoutledgeBookspublishedunderthejointimprintofLSE/Routledgeareworksofhighacad

8、emicmeritapprovedbythePublicationsCommitteeoftheLondonSchoolofEconomicsandPoliticalScience.Thesepublicationsaredrawnfromthewiderangeofacademicstudiesinthesocia