Hopeless paper

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1、TheBulletinofSymbolicLogicVolume4,Number1,March1998ANEDITORRECALLSSOMEHOPELESSPAPERSWILFRIDHODGES§1.Introduction.Idedicatethisessaytothetwo-dozen-oddpeoplewhoserefutationsofCantor’sdiagonalargument(Imeantheoneprovingthatthesetofrealnumbersandthesetofnaturalnumbershavedifferentcardin

2、alities)havecometomeeitherasrefereeoraseditorinthelasttwentyyearsorso.Sadlythesesubmissionswereallquiteunpublishable;IsentthembackwithwhatIhopewerehelpfulcomments.Afewyearsagoitoccurredtometowonderwhysomanypeopledevotesomuchenergytorefutingthisharmlesslittleargument—whathaditdoneto

3、makethemangrywithit?SoIstartedtokeepnotesofthesepapers,inthehopethatsomepatternwouldemerge.Thesepagesreporttheresults.Theymightbeusefulforeditorsfacedwithsimilarproblempapers,orevenfortheauthorsofthepapersthemselves.Butthemainmessagetoreachmeisthatthereareseveralpointsofbasicelemen

4、tarylogicthatweusuallyteachandexplainverybadly,ornotatall.In1995anengineernamedWilliamDilworth,whohadpublishedarefu-tationofCantor’sargumentintheTransactionsoftheWisconsinAcademyofSciences,ArtsandLetters,suedforlibelamathematiciannamedUn-derwoodDudleywhohadcalledhimacrank([9]pp.44f

5、,354).Thecasewasdismissed.FormyselfIammorescaredofthecopyrightlawthanthelawoflibel.AftertakinglegaladviceIdecidednottoquoteanyoftheauthorsdirectly.Thealternativewastowritesomeletterssayingineffect:‘I’msorrywecouldn’tpublishyourpaperasacontributiontologic.CanIpleasepublishpartsofitas

6、examplesofgarbage?’Notmuchislost,becausealmostallofthepaperswerewrittenbymanifestamateurswhohadgreatdifficultyexplainingwhattheymeant,andIfreelyadmitthatmuchofwhatfollowsismyownattempttodiscernsomethoughtsbehindthestreamsofwords.Thisisinnosenseascientificanalysisofexperimentaldata.§2.

7、Cantor’sproof.Theauthorsofthesepapers—henceforthletmecallthemjusttheauthors—seemtohavereadCantor’sargumentinavarietyofplaces.InmyrecordsonlyoneauthorrefersdirectlytoCantor’sownargument[7].OnequotesRussell’s‘Principlesofmathematics’[20]laterReceivedOctobeer6,1997;revisedOctober15,19

8、97.c1998,AssociationforSy