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《(奎因) W.V. Quine - 1938 - 'On the Theory of Types'》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、THEJona~nr,OFSTYBOLICLOOICVolume3.Number4,December1838ONTHETHEORYOFTYPES'Inthispaperthetheoryoflogicaltypeswillbeexamined,andcertainde-parturesfromitwillbesuggested.Thoughthepurposeofthepaperisnotprimarilyexpository,anapproachhasbeenpossiblewhichpresuppo
2、sesnofamiliaritywithspecialliterature.Mattersatvariancewithsuchanapproachhavebeenconfinedtoappendicesandfootnotes.Intheearlypagesthelogicalparadoxeswillbeconsidered--aninfiniteseriesofthem,ofwhichRussell'sparadoxisthefirst.ThenRussell'ssimpletheoryoftype
3、swillbeformulated,inadaptationtoaminimalsetoflogicalprimitives:inclusionandabstraction.Twoaspectsofthetheorywillbedistinguished:anontologicaldoctrineandaformalrestrictio?z.Itwillbefoundthatbyrepudiatingtheformerwecanavoidcertainunnaturaleffectsofthetypet
4、heory-notablythereduplicationoflogicalconstantsfromtypetotype,andtheapparentdependenceoffinitearithmeticuponanaxiomofinfinity.Buttheformalrestrictionitselfhasunnaturaleffects,whichsurvive,eveninanaggravatedform,afterthetypeontologyhasbeendropped.Aliberal
5、izationoftheformalrestrictionwillbeproposedwhichremovesthemoreirksomeoftheseanomalies.1.Basicformalconcepts.Usewillbemadeofthefollowinglogicalnotionsandnotations.Membership:"(zq)"meansthatzisamemberoftheclassy.(Inthisandtheensuingnotations,parentheseswil
6、lbesuppressedwhenthereisnoriskofambiguity.)Inclusion:"(zCy)"meansthattheclasszisincludedintheclassy;i.e.,thateverymemberofzisamemberofy.Identity:"(x=y)"meansthatzandyarethesameobject.Conditional,Biconditional,Conjunction,Denial:"(.-3--)","(...=---)",[[(.
7、..,---)",and([N..."meanrespectively"If...then---","...ifandonlyif---","...and---",and"Itisnotthecasethat...",wheretheblanksarefilledbyanystatements.Abstraction:"5..."denotestheclasswhosemembersarejusttheobjectszsatisfyingthecondition"...".(Theblankisfill
8、edbyanystatement,ordinarilyonecontaining"z".)Universalquantiwion:"(z)..."meansthatthecondition"..."issatisfiedbyallvaluesof"z".Universalclass:vistheclasstowhicheverythingbelongs.Nullclass:Aistheclasstowhichnothingbelopgs.U
