资源描述：
《on the foundations of mathematical economics》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、ONTHEFOUNDATIONSOFMATHEMATICALECONOMICSJ.BarkleyRosser,Jr.JamesMadisonUniversityrosserjb@jmu.eduhttp://cob.jmu.edu/rosserjbFebruary,2010Abstract:KumaraswamyVelaVelupillai[74]presentsaconstructivistperspectiveonthefoundationsofmathematicaleconomics,praisingthevi
2、ewsofFeynmanindevelopingpathintegralsandDiracindevelopingthedeltafunction.HeseestheirapproachasconsistentwiththeBishopconstructivemathematicsandconsidersitsviewontheBolzano-Weierstrass,Hahn-Banach,andintermediatevaluetheorems,andthentheimplicationsoftheseargume
3、ntsforsuch“crownjewels”ofmathematicaleconomicsastheexistenceofgeneralequilibriumandthesecondwelfaretheorem.HealsorelatestheseideastotheweakeningofcertainassumptionstoallowformoregeneralresultsasshownbyRosser[51]inhisextensionofGödel’sincompletenesstheoreminhiso
4、peningsection.Thispaperconsiderstheseargumentsinreverseorder,movingfromthemattersofeconomicsapplicationstothebroaderissueofconstructivistmathematics,concludingbyconsideringtheviewsofRosseronthesematters,drawingbothonhiswritingsandonpersonalconversationswithhim.
5、Acknowledgements:IthankK.VelaVelupillaimostparticularlyforhiseffortstopushmetoconsiderthesemattersinthemostseriousmanner,aswellasmylatefather,J.BarkleyRosser[Sr.]andalsohisfriend,thelateStephenC.Kleene,fortheirpersonalremarksonthesematterstomeoveralongperiodoft
6、ime.IalsowishtothankEricBach,KenBinmore,HerbGintis,JeromeKeisler,RogerKoppl,DavidLevy,andAdrianMathiasforusefulcomments.Theusualcaveatholds.IalsowishtodedicatethistoK.VelaVelupillaiwhoinspireditwithhisinsistencethatIfinallydealwiththeworkandthoughtofmyfather,J.
7、BarkleyRosser[Sr.],aswellasShu-HengChen,whosupportedhiminthisinsistence.Ithankbothofthemforthis.I.Introduction“Beautyistruth,truthbeauty.”---JohnKeats,OdeonaGrecianUrn,1819.“Forme,andIsupposeformostmathematicians,thereisanotherreality,whichIshallcall‘mathematic
8、alreality’;andthereisnoagreementaboutthenatureofmathematicalrealityamongeithermathematiciansorphilosophers.Someholdthatitis‘mental’andthatinsomesenseweconstructit,othersthat
