Algebra of Logic

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1、TheProjectGutenbergEBookofTheAlgebraofLogic,byLouisCouturatThiseBookisfortheuseofanyoneanywhereatnocostandwithalmostnorestrictionswhatsoever.Youmaycopyit,giveitawayorre-useitunderthetermsoftheProjectGutenbergLicenseincludedwiththiseBookoronlineatwww.gutenberg.netTitle:TheAlgebraofL

2、ogicAuthor:LouisCouturatReleaseDate:January26,2004[EBook#10836]Language:EnglishCharactersetencoding:TeX***STARTOFTHISPROJECTGUTENBERGEBOOKTHEALGEBRAOFLOGIC***ProducedbyDavidStarner,ArnoPeters,SusanSkinnerandtheOnlineDistributedProofreadingTeam.1THEALGEBRAOFLOGICBYLOUISCOUTURATAUTHO

3、RIZEDENGLISHTRANSLATIONBYLYDIAGILLINGHAMROBINSON,B.A.WithaPrefacebyPHILIPE.B.JOURDAIN.M.A.(Cantab.)PrefaceMathematicalLogicisanecessarypreliminarytologicalMathematics.Math-ematicalLogicisthenamegivenbyPeanotowhatisalsoknown(afterVenn)asSymbolicLogic;andSymbolicLogicis,inessenti

4、als,theLogicofAristotle,givennewlifeandpowerbybeingdressedupinthewonderfulalmostmagicalarmourandaccoutrementsofAlgebra.Inlessthanseventyyears,logic,touseanexpressionofDeMorgan's,hassothrivenuponsym-bolsand,inconsequence,sogrownandalteredthattheancientlogicianswouldnotrecognizeit,

5、andmanyold-fashionedlogicianswillnotrecognizeit.Themetaphorisnotquitecorrect:Logichasneithergrownnoraltered,butwenowseemoreofitandmoreintoit.Theprimarysignicanceofasymboliccalculusseemstolieintheecon-omyofmentaleortwhichitbringsabout,andtothisisduethecharacteristicpowerandrapidde

6、velopmentofmathematicalknowledge.Attemptstotreattheoperationsofformallogicinananalogouswayhadbeenmadenotinfre-quentlybysomeofthemorephilosophicalmathematicians,suchasLeibnizandLambert;buttheirlaborsremainedlittleknown,anditwasBooleandDeMorgan,aboutthemiddleofthenineteenthcentury,to

7、whomamathematicalthoughofcoursenon-quantitativewayofregardinglogicwasdue.Bythis,notonlywasthetraditionalorAristoteliandoctrineoflogicreformedandcompleted,butoutofithasdeveloped,incourseoftime,aninstrumentwhichdealsinasuremannerwiththetaskofinvestigatingthefun-damentalconceptsofma

8、thematicsataskwhichphilos