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1、AppendixIReferenceAnswersUnit1MathematicsPartIESTReadingReading1SectionAPre-readingTaskWarm-upQuestions:Workinpairsanddiscussthefollowingquestions.1.WhoisBertrandRussell?BertrandArthurWilliamRussell(b.1872–d.1970)wasaBritishphilosopher,logician,essayistandsocialcriticbestknownforhisworkinmathemati
2、callogicandanalyticphilosophy.Hismostinfluentialcontributionsincludehisdefenseoflogicism(theviewthatmathematicsisinsomeimportantsensereducibletologic),hisrefiningofthepredicatecalculusintroducedbyGottlobFrege(whichstillformsthebasisofmostcontemporarylogic),hisdefenseofneutralmonism(theviewthatthew
3、orldconsistsofjustonetypeofsubstancethatisneitherexclusivelymentalnorexclusivelyphysical),andhistheoriesofdefinitedescriptionsandlogicalatomism.Russellisgenerallyrecognizedasoneofthefoundersofmodernanalyticphilosophy,andisregularlycreditedwithbeingoneofthemostimportantlogiciansofthetwentiethcentur
4、y.2.WhatisRussell’sParadox?Russelldiscoveredtheparadoxthatbearshisnamein1901,whileworkingonhisPrinciplesofMathematics(1903).Theparadoxarisesinconnectionwiththesetofallsetsthatarenotmembersofthemselves.Suchaset,ifitexists,willbeamemberofitselfifandonlyifitisnotamemberofitself.Theparadoxissignifican
5、tsince,usingclassicallogic,allsentencesareentailedbyacontradiction.Russell'sdiscoverythuspromptedalargeamountofworkinlogic,settheory,andthephilosophyandfoundationsofmathematics.3.WhateffectdidRussell’sParadoxhaveonGottlobFregg’ssystem?AtfirstFregeobservedthattheconsequencesofRussell’sparadoxarenot
6、immediatelyclear.Forexample,“Isitalwayspermissibletospeakoftheextensionofaconcept,ofaclass?Andifnot,howdowerecognizetheexceptionalcases?Canwealwaysinferfromtheextensionofoneconcept’scoincidingwiththatofasecond,thateveryobjectwhichfallsunderthefirstconceptalsofallsunderthesecond? Becauseofthesekind
7、sofworries,Fregeeventuallyfeltforcedtoabandonmanyofhisviews.4.WhatisRussell’sresponsetotheparadox?Russell'sownresponsetotheparadoxcamewiththedevelopmentofhistheoryoftypesin1903.ItwascleartoRussellthatsomerestrict
