cassirer (about helmholtz) concept of group and theory of perception外语英文电子书外语英文电子书

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1、¡.PHILOSOPHYANDPHENOMENOLOGICALRESEARCHAQuarlerlyJmanalVOLUMEV,No.1SEPTE:>mER,1944THECO~CEPTOFGROUPANDTHETHEORYOFPERCEPTIO~*Thefil'stattempttoapplycertainmathematicalspeculationsconcerningtheconoeptolgrouptopsychologicalproblemsofperceptionwasmadebyHelmholtzinhisessayU(berdieTatsachen,

2、diederGeometrieZIIGrwu1eliegen(1868).Túbesure,HelmholtzVasnotabletoscethenewproblemwhichhehadraisedwithcompleteprecisiQllandtorealizeitsfullimp9rtance.For,whenHelmboltzwrotehisessay,theconceptofgroupwasnotyetrecognizedasthatuniversalinstrumentoímathematicalthoughtvhichitlaterturnedou

3、ttobe.ItsapplicationVasconfinedtocertainproblemsofcombinatoricsandalgebra.Atthebeginningofthenineteenthcentury,Cauchyhadintl'oducedtheconceptoígroupintothesedomains.InGaIoís'theoryofalgebraicequationstheéoncepthadprovedeminentlyfruitful.ItVas,however,notbeforethesecondhalfofthecentur

4、ythatthosestudieswereinauguratedthroughVhichthetheoryofgroupswastobeestablishedasaspecialdiscipline.VerysoonthetheoryfOW1dapplica•tionsinthemostvariedbranchesofmathematicsasanorganizingandclari•íyingprincipie.l!tsestablishmentiscloselyconnectedwithag,eneraIl'e•oJ'ientationofgeometrica

5、lthought.Theneworientation,broughtaboutbythediscoveryoíthenon-Euclideangeometries,succeededináfull}rsatisfactoryway,whenSophusLieandFelixKleinassigncdtotheconceptofgroup.acentralpositioninthesystemoígeometricalthought.Helm•holtzcouIdnotavailhimselfoíal!theseadvances.Hethereforefailstog

6、iveanexplicitdefinitionandanalyticalc!arificationoftheconceptofgraup.Nonethelesshisessaycontainsagreatmanypromisingconcretestartiug-pointsandproblems.Fo!'sorneerl'Orsofan.alyticaltreatmentwhichVeredisc10sedandc01Tectedlater,thereaderismorethancompen•satedbythebreadthoíHelmholtz'genera

7、lepistimologicalhorizonandthevig.orofsynthesiswhichenableshimtobringtogethel'problemspertainingtúhighlydifferentfieldsofstudy.*ThisartielewaspublíshedinF¡'enchintheJournaldePsyc/wlogie,1938,pp.368--414.TheEnglishversionwassuggestedbySQmeof111)'Americanfriends.TheJournaldePsychologiec