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1、Unit1MathematicsPartIESTReadingReading1Warm-upQuestions:Workinpairsanddiscussthefollowingquestions.1.WhoisBertrandRussell?BertrandArthurWilliamRussell(b.1872–d.1970)wasaBritishphilosopher,logician,essayistandsocialcriticbestknownforhisworkinmathematicallog
2、icandanalyticphilosophy.Hismostinfluentialcontributionsincludehisdefenseoflogicism(theviewthatmathematicsisinsomeimportantsensereducibletologic),hisrefiningofthepredicatecalculusintroducedbyGottlobFrege(whichstillformsthebasisofmostcontemporarylogic),hisde
3、fenseofneutralmonism(theviewthattheworldconsistsofjustonetypeofsubstancethatisneitherexclusivelymentalnorexclusivelyphysical),andhistheoriesofdefinitedescriptionsandlogicalatomism.Russellisgenerallyrecognizedasoneofthefoundersofmodernanalyticphilosophy,and
4、isregularlycreditedwithbeingoneofthemostimportantlogiciansofthetwentiethcentury.2.WhatisRussell’sParadox?Russelldiscoveredtheparadoxthatbearshisnamein1901,whileworkingonhisPrinciplesofMathematics(1903).Theparadoxarisesinconnectionwiththesetofallsetsthatare
5、notmembersofthemselves.Suchaset,ifitexists,willbeamemberofitselfifandonlyifitisnotamemberofitself.Theparadoxissignificantsince,usingclassicallogic,allsentencesareentailedbyacontradiction.Russell'sdiscoverythuspromptedalargeamountofworkinlogic,settheory,and
6、thephilosophyandfoundationsofmathematics.3.WhateffectdidRussell’sParadoxhaveonGottlobFregg’ssystem?AtfirstFregeobservedthattheconsequencesofRussell’sparadoxarenotimmediatelyclear.Forexample,“Isitalwayspermissibletospeakoftheextensionofaconcept,ofaclass?And
7、ifnot,howdowerecognizetheexceptionalcases?Canwealwaysinferfromtheextensionofoneconcept’scoincidingwiththatofasecond,thateveryobjectwhichfallsunderthefirstconceptalsofallsunderthesecond?Becauseofthesekindsofworries,Fregeeventuallyfeltforcedtoabandonmanyofhi
8、sviews.4.WhatisRussell’sresponsetotheparadox?Russell'sownresponsetotheparadoxcamewiththedevelopmentofhistheoryoftypesin1903.ItwascleartoRussellthatsomerestrictionsneededtobeplacedupontheoriginalcomprehension(
