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1、Unit1MathematicsPartIESTReadingReading1(http://www.scientificamerican.com/article.cfm?id=what-is-russells-paradoxSectionAPre-readingTaskWarm-upQuestions:Workinpairsanddiscussthefollowingquestions.1.WhoisBertrandRussell?BertrandArthurWilliamRussell(b.1872–d.1970)wasaBritishphilosopher,logici
2、an,essayistandsocialcriticbestknownforhisworkinmathematicallogicandanalyticphilosophy.Hismostinfluentialcontributionsincludehisdefenseoflogicism(theviewthatmathematicsisinsomeimportantsensereducibletologic),hisrefiningofthepredicatecalculusintroducedbyGottlobFrege(whichstillformsthebasisofm
3、ostcontemporarylogic),hisdefenseofneutralmonism(theviewthattheworldconsistsofjustonetypeofsubstancethatisneitherexclusivelymentalnorexclusivelyphysical),andhistheoriesofdefinitedescriptionsandlogicalatomism.Russellisgenerallyrecognizedasoneofthefoundersofmodernanalyticphilosophy,andisregula
4、rlycreditedwithbeingoneofthemostimportantlogiciansofthetwentiethcentury.2.WhatisRussell’sParadox?Russelldiscoveredtheparadoxthatbearshisnamein1901,whileworkingonhisPrinciplesofMathematics(1903).Theparadoxarisesinconnectionwiththesetofallsetsthatarenotmembersofthemselves.Suchaset,ifitexists,
5、willbeamemberofitselfifandonlyifitisnotamemberofitself.Theparadoxissignificantsince,usingclassicallogic,allsentencesareentailedbyacontradiction.Russell'sdiscoverythuspromptedalargeamountofworkinlogic,settheory,andthephilosophyandfoundationsofmathematics.3.WhateffectdidRussell’sParadoxhaveon
6、GottlobFregg’ssystem?AtfirstFregeobservedthattheconsequencesofRussell’sparadoxarenotimmediatelyclear.Forexample,“Isitalwayspermissibletospeakoftheextensionofaconcept,ofaclass?Andifnot,howdowerecognizetheexceptionalcases?Canwealwaysinferfromtheextensionofoneconcept’scoincidingwiththatofaseco
7、nd,thateveryobjectwhichfallsunderthefirstconceptalsofallsunderthesecond? Becauseofthesekindsofworries,Fregeeventuallyfeltforcedtoabandonmanyofhisviews.4.WhatisRussell’sresponsetotheparadox?Russell'sownresponsetotheparadoxcamewiththedevelopmentofhistheory
