Clicca qui per scaricare

Boole, Ramsey and the Keynes-Townshend exchanges on subjective probability
Autori/Curatori: Rogério Arthmar, Michael Emmett Brady 
Anno di pubblicazione:  2018 Fascicolo: Lingua: Inglese 
Numero pagine:  20 P. 55-74 Dimensione file:  235 KB
DOI:  10.3280/SPE2018-002003
Il DOI è il codice a barre della proprietà intellettuale: per saperne di più:  clicca qui   qui 

Contrary to what is accepted in many quarters, John M. Keynes actually rejected Frank Ramsey’s subjective theory of probability, in general. He did accept, though, Ramsey’s betting quotient approach, but only in the special case where the weight of the evidence w equaled 1, so that all the probabilities were linear, additive, single number answers. In general, however, Keynes’s probabilities were indeterminate, that is, interval valued with the characteristic of being non-additive and nonlinear because the weight of evidence w was generally less than 1. The Boolean roots of Keynes’s approach to probability and his often-neglected exchanges with Hugh Townshend in 1937-38 provide strong evidence that Keynes never changed his mind on the subjective approach to probability. It is shown that, for Ramsey, the degree of belief is the confidence a decision maker has in the betting odds while, for Keynes, it is the degree of ‘rational’ or logical belief based on George Boole’s logic of propositions.

Keywords: Probability, risk, uncertainty, decision-making, weight of evidence
Jel Code: B13, B16, B31

  1. Arthmar R. and Brady M. E. (2016). The Keynes-Knight and the de Finetti-Savage’s approaches to probability: an economic interpretation. History of Economic Ideas, 24(1): 105-124.
  2. Basili M., Zappia C. (2009). Keynes’s ‘non-numerical’ probabilities and non-additive measures. The Journal of Economic Psychology, 30: 419-30.
  3. Bateman B. (2003). The end of Keynes and philosophy? In Runde J. and S. Mizuhara (eds.). (2003): 71-84.
  4. Bateman B. (1996). Keynes’s Uncertain Revolution, Ann Arbor, University of Michigan Press.
  5. Bateman B. (1992a). More on Keynes and probability: Response. Correspondence. Journal of Economic Perspectives, 6(4): 205-208.
  6. Bateman B. (1992b). What we do with our heroes? [Is probability theory relevant for uncertainty? A Post Keynesian perspective]. Correspondence. Journal of Economic Perspectives, 6(1): 201-10.
  7. Bentham J. (1788). The Principles of Morals and Legislation, New York, Prometheus Books.
  8. Binmore K. (2009). Rational Decisions (The Gorman Lectures in Economics), Princeton, Princeton University Press, 4th ed.
  9. Binmore K., L. Stewart and A. Voorhoeve (2012). How much ambiguity aversion? Finding indifferences between Ellsberg’s risky and ambiguous bets. Journal of Risk and Uncertainty, 45(3): 215-38.
  10. Boole G. (1854). An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probability, New York, Dover Publications.
  11. Brady M. E. (2016). Reviewing the Reviewers of Keynes’s A Treatise on Probability, Philadelphia, Xlibris Press.
  12. Brady M. E. and R. Arthmar (2012). Keynes, Boole and the interval approach to probability. History of Economic Ideas, 20(3): 65-84.
  13. Brady M. E. (1993). J. M. Keynes’s theoretical approach to decision making under condition of risk and uncertainty. The British Journal for the Philosophy of Science, 44(2): 357-76.
  14. Bridel P. (1987). Cambridge Monetary Thought, New York, St. Martin’s Press.
  15. Dardi M. and M. Gallegati (1992). Marshall on speculation. History of Political Economy, 24(3): 571-94.
  16. Davis J. B. (2003). The relationship between Keynes’s early and later philosophical thinking. In Runde J. and S. Mizuhara (eds.): 97-107.
  17. Fitzgibbons A. (2003). Keynes’s epistemology. In Runde J. and S. Mizuhara (eds.): 64-76.
  18. Friedman M. and L.J. Savage (1948). The utility analysis of choices involving risk. Journal of Political Economy, LVI(4): 279-304.
  19. Gillies D. (2003). Probability and uncertainty in Keynes’s The General Theory. In Runde J. and S. Mizuhara (eds.): 108-26.
  20. Hacking I. (2006). The Emergence of Probability, Cambridge, Cambridge University Press.
  21. Hailperin T. (1986). Boole’s Logic and Probability: Critical Exposition from the Standpoint of Contemporary Algebra, Logic and Probability Theory. Studies in Logic and the Philosophy of Mathematics, London, North Holland. Keynes J. M. (1921). A Treatise on Probability, London, Macmillan.
  22. Keynes J. M. (1972 [1931]). Frank Ramsey as a philosopher. In Moggridge D. E. (ed.) CWK X: 335-46.
  23. Keynes J. M. (1964 [1936]). The General Theory of Employment, Interest and Money, Harbinger, Harcourt, Brace, and World.
  24. Keynes J. M. (1979 [1937]). Letter to Townshend. In Moggridge, D. E. (ed.) (1979). CWK, XXIX: 258-9.
  25. Keynes J. M. (1979 [1938]). Letter to Townshend. In Moggridge, D. E. (ed.) (1979). CWK, XXIX: 293-4.
  26. Kyburg Jr. H. E. and H. E. Smokler (eds.) (1980). Studies in Subjective Probability, New York, Kreiger, 2nd ed.
  27. Moggridge D. E. (ed.) (1971-1989). The Collected Writings of John Maynard Keynes (CWK), London, Macmillan, Cambridge University Press for the Royal Economic Society.
  28. Pigou A. C. (1912). Wealth and Welfare, London, Macmillan.
  29. Ramsey F. P. (1989 [1922]). Mr Keynes on probability. British Journal for the Philosophy of Science, 40(2): 219-22.
  30. Ramsey Frank P. (1980 [1926]). Truth and Probability. In Kyburg Jr. H. E. and H. E. Smokler, (eds.): 23-52.
  31. Runde J. (1994). Keynes after Ramsey: In defense of A Treatise on Probability. Studies in the History of the Philosophy of Science, 25(1): 97-121.
  32. Runde J. and S. Mizuhara (eds.) (2003). Keynes’s Philosophy: Probability, Uncertainty and Convention, London, Routledge.
  33. Shackle G. L. S. (1938). Expectations, Investment and Income, Oxford, Oxford University Press.
  34. Skidelsky R. (1994). John Maynard Keynes. The Economist as Savior 1920-1937. Volume Two, New York, Penguin.
  35. Townshend H. (1979 [1937]). Letter to Keynes, in Moggridge D. E. (ed.). CWK, XXIX: 236-7.
  36. Townshend H. (1979 [1938]). Letter to Keynes. In Moggridge D. E. (ed.). CWK, XXIX: 240-5.
  37. Townshend H. (1979 [1938]). Letter to Keynes. In Moggridge D. E. (ed.). CWK, XXIX: 257-8.
  38. Zappia C. (2015). Keynes on probability and decision: Evidence from the correspondence with Hugh Townshend. History of Economic Ideas, 23(2): 145-64.

  1. Michael Emmett Brady, An Analysis of Keynes’s Straightforward, Easy to Follow, Alleged 'Infamous' Footnote 2 on pp. 55-56 of the General Theory - Is It Really that Difficult and Abominable? in SSRN Electronic Journal /2010 pp. , DOI: 10.2139/ssrn.1681236
  2. Michael Emmett Brady, Given Keynes's Definitions of Logical Probability and Evidential Weight, It Is Impossible for Keynes’s Approach to Measurement to Be an Ordinal Theory; His 'Non Numerical' Probabilities Must Be Based on Inexact and Imprecise Measurement Using Approximation Involving Boolean Upper and Lower Probability Bounds and Bounded Outcomes in SSRN Electronic Journal /2019 pp. , DOI: 10.2139/ssrn.3335681
  3. Michael Emmett Brady, A Very Short Note Covering the Five Easy Steps Needed to Show that Keynes’s Analysis in Footnote Two on Page 55 of the General Theory is Correct with a Minor Exception that Was Correctly Analyzed by Keynes in Footnote One on p. 283 of the General Theory in Chapter 20 in SSRN Electronic Journal /2010 pp. , DOI: 10.2139/ssrn.1732251
  4. Jochen Hartwig, Keynes’s Aggregate Supply Function: Everything You Always Wanted to Know About Z in SSRN Electronic Journal /2011 pp. , DOI: 10.2139/ssrn.1855728
  5. Michael Emmett Brady, Correcting Skidelsky's Fairy Tales About J M Keynes's Mathematical Capabilities and Exposition in the a Treatise on Probability, General Theory and After in SSRN Electronic Journal /2016 pp. , DOI: 10.2139/ssrn.2890758
  6. Michael Emmett Brady, How Keynes's Mathematical Analysis in Chapters 20 and 21 of the General Theory of His Elasticity Ew, Which Could Take on Any Values between ew =0 (Rigid, Given, Fixed, Constant, or Inflexible Money Wages) and ew =1 (Flexible Money Wages) Completely Destroys F. Modigliani's 1944 Econometrica Conclusion that Keynes's General Theory Category of Involuntary Unemployment Required Rigid Money Wages in SSRN Electronic Journal /2018 pp. , DOI: 10.2139/ssrn.3166762
  7. Michael Emmett Brady, A Refutation of the Paul Davidson and Post Keynesian Claim that Paul Samuelson Was Never a Keynesian in SSRN Electronic Journal /2016 pp. , DOI: 10.2139/ssrn.2875039
  8. Michael Emmett Brady, The Role of Ignorance About Keynes’s Inexact, Approximation Approach to Measurement in the A Treatise on Probability in the Keynes-Tinbergen Exchanges of 1938–1940 in SSRN Electronic Journal /2019 pp. , DOI: 10.2139/ssrn.3353637
  9. Michael Emmett Brady, The Mathematically Erroneous, Error Filled Post Keynesian 'D-Z' Model: Blaming J M Keynes for 60 Years of Post Keynesian Errors and Mistakes in SSRN Electronic Journal /2013 pp. , DOI: 10.2139/ssrn.2318947
  10. Michael Emmett Brady, Correcting Modigliani's 1944 'Liquidity Preference and the Theory of Interest and Money': This Article Dealt with Hicks's Interpretation of Keynes, but not with Keynes's General Theory Model in SSRN Electronic Journal /2017 pp. , DOI: 10.2139/ssrn.2995316
  11. Michael Emmett Brady, On L. Klein’s Erroneous Assessments of J M Keynes’s Views on Probability, Mathematics, and Statistics: Reviewing His 1951 Review of Harrod’s the Life of John Maynard Keynes in SSRN Electronic Journal /2018 pp. , DOI: 10.2139/ssrn.3253471
  12. Michael Emmett Brady, An Assessment of Nobel Laureate Robert Shiller’s Assessment of J M Keynes’s a Treatise on Probability and Its Connection to the General Theory: Correct in General, but Incorrect on Specifics in SSRN Electronic Journal /2019 pp. , DOI: 10.2139/ssrn.3331008
  13. Michael Emmett Brady, On Keynes’s Two Simplifications of His Aggregate Supply Curve Analysis in Chapter 21 of the General Theory: O. Lange (1938) Overlooked Chapter 20 and the Two Simplifications on Pages 295–296 of the General Theory in Chapter 21 in SSRN Electronic Journal /2018 pp. , DOI: 10.2139/ssrn.3257209
  14. Michael Emmett Brady, Keynes’s Method in the A Treatise on Probability and the General Theory Is Inexact Measurement Involving Approximation, Imprecise Probability, and Indeterminate Probability Using Boolean Interval Valued Probability: There Is no Explicit Theory of Ordinal Measurement Developed, Used or Deployed Anywhere in Either the A Treatise on Probability or the General Theory in SSRN Electronic Journal /2019 pp. , DOI: 10.2139/ssrn.3340343

Rogério Arthmar, Michael Emmett Brady, in "HISTORY OF ECONOMIC THOUGHT AND POLICY" 2/2018, pp. 55-74, DOI:10.3280/SPE2018-002003


FrancoAngeli è membro della Publishers International Linking Association associazione indipendente e no profit per facilitare l'accesso degli studiosi ai contenuti digitali nelle pubblicazioni professionali e scientifiche