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An Interview with Kenneth J. Arrow Author(S): J An Interview with Kenneth J. Arrow Author(s): J. S. Kelly and Kenneth J. Arrow Source: Social Choice and Welfare, Vol. 4, No. 1 (1987), pp. 43-62 Published by: Springer Stable URL: http://www.jstor.org/stable/41105852 . Accessed: 27/09/2013 14:15 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Springer is collaborating with JSTOR to digitize, preserve and extend access to Social Choice and Welfare. http://www.jstor.org This content downloaded from 150.135.135.70 on Fri, 27 Sep 2013 14:15:11 PM All use subject to JSTOR Terms and Conditions " Soc Choice Welfare 4 : 43-62 Z (1987) Social# Choice ^Welfare © Springer-Verlag 1987 An Interviewwith Kenneth J. Arrow J. S. Kelly Departmentof Economics,Syracuse University, Maxwell Hall, Syracuse,NY 13210, USA The followingis an editedtranscript of an interviewconducted on March 4, 1986 withProfessor Arrow while he was visitingSyracuse University to deliverthe Frank W. Abrams LectureSeries to be publishedas The UncertainFuture and Present Action by Syracuse UniversityPress. This interviewwas to elaborate on his description,presented in Volume 1 of his CollectedPapers (Harvard University Press,1983), of the originsof his work in collectivechoice theory. JK. You startedoff the story in the collectedpapers withremarks about studying relationallogic whileyou werein Townsend- Harris High School in New York City. KA. Not in highschool in the senseof in myhigh school courses,but duringthis periodI was an omnivorousreader and gotinto all sortsof things. One of themwas Bertrand Russell's Introductionto MathematicalPhilosophy and it made a tremendousimpression on me.It was theidea oflogic that was inthere. I don't really recall,for example, if there was a formaldefinition of a relationas a set of ordered pairs, but I learned the ideas of mathematicallogic and its applications to mathematicsin Russell'sbook. It seemsto me thatI also read one or two otherlogic books around that time. JK. Later,when you wentto CityCollege of New Yorkas a mathematicsmajor, you encounteredmore mathematical logic. KA . Yes, butagain thelogic study was on myown, there were no coursesin it.I don't reallyremember exactly what I read. I rememberonce takingout the Principia Mathematicabut of course it's not thesort of thingone reallyreads from.I was lookingup some theoremsin it and thingslike that. I reallyam not preparedto tell you whatI read,but at somepoint things like the idea ofdefining rational numbers by orderedpairs and equivalenceclasses by orderedpairs was somethingI got to This content downloaded from 150.135.135.70 on Fri, 27 Sep 2013 14:15:11 PM All use subject to JSTOR Terms and Conditions 44 J. S. Kelly know. I was fascinatedby thisand used to aggravatemy professors by writingout proofsin very strictly logical form, avoiding words as muchas possibleand thingsof that kind. JK. You did takea formalcourse with Tar ski in thePhilosophy Department ; how did you happento take thatcourse? KA. Yes. Well,I knewthat Alfred Tarski was a greatand famouslogician and there he was in mylast termin school and obviouslyI was going to take a course with AlfredTarski. It turnedout he had two courses.One was a kind of introductory courseand I feltI knewmore than that. The othercourse he gave was in thecalculus of relations.To say it was in the calculus of relationsmeant that he gave an axiomatictreatment of relations,although he motivatedit of course by motivating the axioms. You neverhad xRy; you onlyhad R and S and T. You see, he never mentionedindividuals in the formaltheory. He had an axiomatic theorylike an axiomatictreatment of set theory. Relations have somespecial aspects, in particular the idea of relativeproduct, RS. If thereis a z such thatxRz and zSy, thenxRSy. The relativesquare, R2=RR is especiallyinteresting; if the relative square is includedin R you have transitivity. So it was a fascinatingthing, although it was reallyvery elementary; really very easy. The concepts were not verysubtle compared withthe deep thingshe was workingon like the truthprinciple. JK. At thispoint you wereinvolved in translatingsome of Tarskfs work. KA. He wrotea textbookcalled Introductionto Logic [1] whichis one ofthe modern treatments,modern as of 1940. It had been publishedin German,may even have beenorginally published in Polish. I didn'ttranslate it. What happened was he had a translatorand I read theproofs. I wasjust finishingcollege and he asked me to read theproofs for him. He didn'tknow any English,you see. This was the interesting thing.He came to thiscountry in September,1939 forsome kind of congressor conferenceand was trappedhere by the outbreakof the war. He knew Polish, he knewGerman, but he didn'tknow any Englishso he spentthe Fall termlearning some Englishso he could teachus in theSpring. At firstwe couldn't understanda word he was sayingbut afterabout a week or so we began to catch on and we realizedit wasn't his rate of progress it was ourrate of progress that was relevant.His stresseswere all wrong. He was aware of this and thereforefelt he couldn't proofreadin English.It's ratherinteresting as a coincidencethat the translator was a Germanphilosopher named Olaf Helmerand Helmercomes back into mystory eightyears later. It's interesting. Tarski,although his Englishwas weak,had a verygood sense oflanguage and he kepton askingme "Is thatreally good English?"Not in thesense of being grammaticallycorrect, but, well forexample, Helmet was veryfond of usingthe word "tantamount"and Tarski got the feelingthat somehowit's not a word used veryoften. Actually his instinctsfor language were extremelygood. I suppose that was connected with his general work on formalizationsand metalanguages.Anyway, I was just a proofreader. This content downloaded from 150.135.135.70 on Fri, 27 Sep 2013 14:15:11 PM All use subject to JSTOR Terms and Conditions An Interviewwith Kenneth J. Arrow 45 JK. You writethat as a graduatestudent at Columbiayou spenttime as an exercise translatingconsumer theory in the logic of relationsand orderings.What got you startedon thatand whatdid you get out of it? KA.I wentto Columbiabecause . .wellthere were several problems. One was that wewere extremely poor and the question of going anywhere depended on resources. Columbiahad thegreat advantage, of course,that I could liveat home,which wasn'ttrue anywhere else. I didn'tget any financial support for my first year, none at all. Butanother of the things I had learned on myown at collegewas mathematical statisticsand I reallyhad become fascinated with it. There was a coursein statistics [atCCNY] ; theteacher, a man by the name of Robinson, had no realknowledge of itI wouldsay, basically - 1won't even say he had a goodreading list - buthe did list one book,J. F. Kenney[2] ifI remembercorrectly, which happened to havean excellentbibliography. It was not one of those cookbooks in statistics but actually didhave some attempts at mathematics.Kenney had references to R. A. Fisherand gaveyou enough to getyou interested. So I startedreading Fisher and oneof the firstthings was tryingto workout his derivationof the distributionof the correlationcoefficient under the null hypothesis,which was an integrationin ^-dimensionalspace. In Fisherit was done by intuition. I mean it's rigorous if you're sufficientlysophisticated ; to meit was gibberish. But I knewenough multivariate calculusto be able to translateit into rigorousform, at least a formthat I understood,and then I couldsee that he really was right. But I couldn'tsee it the way he wroteit. ThenI supposebecause of mylogical background what was really importantwas readingthe Neyman-Pearson papers which were then new and writtenin ratherobscure places, but they were available in the[CCNY] library. FromFisher alone, I thinkI would have been hopelessly confused about the logic of statisticaltests, although Fisher was greaton derivingdistributions. So, I knewI wantedto studymathematical statistics, which however was not a field,not a Departmentat Columbia.It was spreadout in otherDepartments. I knewthat Hotelling was one of themajor figures, but he was in theEconomics Department.I rather naively thought I would study mathematics and thenwould takethe statistics from Hotelling. I had no interestin Economics. I wasin the Mathematics Department, taking courses like Functions of a Real Variable,but I was goingto takecourses from Hotelling. In thefirst term he happenedto givea coursein MathematicalEconomics. So outof curiosity I took thisand gotcompletely transformed. The courseto an extentrevolved around Hotelling's own papers.But, as it happens,they were kind of central. He gavea rigorousderivation of supplyand demand.There was one paperon thetheory of the firm, one on thetheory of the consumer[3, 4]. And he gavea rigorousderivation of demandfunctions in the consumertheory paper and derived the Slutsky equations. I thinkhe knewabout Slutsky'swork, though I'm not sure he actually referred to Slutsky.So, anyway,this wasone of the best papers around at thetime. It's now a stapleof our literature but thenreally was novel.One of thethings, he was a very,very strong ordinalist, emphasizedthat
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