ON THE REPEATED ERRORS MADE ABOUT KEYNES’S LOGICAL RELATION, V, THE EVIDENTIAL WEIGHT OF THE ARGUMENT, FOR OVER 90 YEARS: FROM BAYLIS (1935) TO BREKEL (2025)

Author: Michael Emmett Brady

ABSTRACT

The major error, committed by all academicians writing on Keynes’s evidential weight of the argument, V, in  Chapter VI of his A Treatise on Probability, is the failure to recognize that Probability and Evidential Weight at that point in the treatise are completely independent of each other.They can never be analyzed together until both logical relations have been defined as variables specified in degrees, which are measured by an index defined on the unit interval,[0,1]. This means that both probability and evidential weight are defined in terms of degrees.

Keynes’s definition of logical probability is P(a/h) =α (Keynes,1921, p.119), where P denotes the logical relation between propositions a and h. α is a partial degree of rational belief, which is defined on the unit interval [0,1] as 0 ≤α≤1.

Nowhere in chapter VI of Keynes’s A Treatise on Probability (1921) does Keynes define that V is measured or is defined in degrees. The only type of analysis offered by Keynes in chapter VI is qualitative comparisons involving the logical strength of different arguments based on the relevant evidence.

Only in chapter XXVI does Keynes measure V using an index defined on [0,1], which Keynes called w, the degree of the completeness of the evidence.

Keywords:  Decision Weights, Imprecise Probability, Evidential Weight, V, Confidence, Incommensurability, Conventional Coefficient of Weight and Risk, C, W, The Degree of The Completeness of the Evidence

REFERENCES

  • Arthmar, Rogério & Brady, Michael Emmett. (2016). The Keynes-Knight and the deFinetti-Savage’s Approaches to Probability: An Economic Interpretation. History of Economic Ideas, Vol. XXIV, no.1, pp.105-124.
  • Arthmar, Rogério & Brady, Michael Emmett. (2017). Reply to Feduzi, Runde,and Zappia. History of Economic Ideas, Vol.XXV, no.1, pp.55-74.
  • Basili, M. and Zappia, C. (2009). Keynes’s ‘non-numerical’ probabilities and non- additive measures, Journal of Economic Psychology, vol. 30, 419–30.
  • Bateman, B. (1987). Keynes’s changing conception of probability. Economics and Philosophy,3, (March), pp.97-119.
  • Bateman, B. (1989).” Human Logic” and Keynes’s Economics: A Comment. Eastern Economic Journal,15, no.1(Jan.-Mar.), pp.63-67
  • Bateman,B. (1990). Keynes, Induction, and econometrics. History of Political economy,22, no.2, pp.359-380.
  • Bateman, B. (1992). Response from Bradley Bateman. Journal of Economic Perspectives, Volume 6, Number 4, (Fall), pp. 206–209.
  • Bateman, B. (2016). Review of Frank Ramsey (1903-1930): A Sister’s Memoir. History of Political Economy., p.181-183.
  • Bateman, B. (2021). Pragmatism and Probability: Re-examining Keynes’s thinking on probability. Journal of the History of Economic Thought, Volume 43, Issue 4, (December), pp. 619 – 632.
  • Baylis, C.A. (1935). The Nature of Evidential Weight. The Journal of Philosophy, Vol.32 no.11(May), pp281-286.
  • Blackburn S. (2021). Review of Misak’s Frank P. Ramsey. Mind, Vol.130, no.520, (October), pp.1367-1375.
  • Boole, George. (1854). An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probability. New York: Dover Publications, [1958].
  • Borel, Emile. 1924.A propos d’un traité de probabilités.Revue Philosophique de laFrance et de l’Étranger, T. 98 (JUILLET A DÉCEMBRE,1924), pp. 321-336.
  • Brady, Michael Emmett. (1987). J.M. Keynes’ ‘Theory of Evidential Weight’: It’s Relation to Information Processing Theory and Application in the General Theory, Synthese, Vol. 71, No. 1, April, pp. 37-59.
  • Brady, Michael E. (1989). Dynamics of Choice Behavior: The Logical Relation between Linear Objective Probability and Nonlinear Subjective Probability.  Psychological Reports.  Vol. 64, February, pp. 91-97 (with H.B. Lee).
  • Brady, Michael E. (1989).  Is There an Ellsberg-Fellner Paradox?  A Note on its Resolution.  Psychological Reports.  64, June, pp.1087-1090 (with H.B. Lee).
  • Brady, Michael E. (1989).  Is There an Allais Paradox?  A Note on its Resolution.  Psychological Reports, 64, June, pp. 1223-1230 (with H.B. Lee).
  • Brady, Michael E. (1991).  Theoretical Comparison of the Decision Theories of J.M. Keynes, Kahneman-Tversky and Einhorn-Hogarth.  Psychological Reports, 69, August. 243-251 (with H.B. Lee).  Reprinted in John Cunningham Wood, editor.  1994. Critical Assessments (second series).  Vol. VIII.  Essay 140, pp. 269-277.  Routledge, England.
  • Brady, Michael Emmett. (1993). J.M. Keynes’ Theoretical Approach to Decision Making Under Conditions of Risk and Uncertainty.  British Journal for the Philosophy of Science.  Vol. 43, June, pp. 357-376.
  • Brady, Michael E. (1994).  J.M. Keynes’ Decision Theory: A Technical Note.  Psychological Reports. Vol. 74, April, pp. 465-466.
  • Brady, Michael E. (1994). A Note on the Extension of J.M. Keynes’ Decision Theory.  Psychological Reports. Vol. 75, August ,1994, pp.112-114.
  • Brady, Michael Emmett (1994). On the Application of Keynes’ Approach to Decision Making, International Studies in the Philosophy of Science.  Vol. 8, No. 2, August, pp.99-112.
  • Brady, Michael Emmett. (2002). J.M. Keynes’ Decision Theory and Preference Reversals, International Journal of Applied Economics and Econometrics, 10, No. 2, pp.301-308. Reprinted in Growth of Economics in the Twentieth Century: Theories and Practices, 2009, K Puttaswamaiah, ed., Isle Publishing Company, USA.
  • Brady, Michael Emmett. (2002). Further Applications of J.M. Keynes’ Approach to Decision-Making under Risk and Uncertainty, International Journal of Applied Economics and Econometrics, 10, No. 3, pp. 422-430. Reprinted in Growth of Economics in the Twentieth Century: Theories and Practices, 2009, K Puttaswamaiah, ed., Isle Publishing Company, USA.
  • Brady, Michael Emmett. (2004a). J. M. Keynes’ Theory of Decision Making, Induction, and Analogy. The Role of Interval Valued Probability in His Approach. Xlibris Corporation: Pennsylvania; Philadelphia.
  • Brady, Michael Emmett. (2004b). Essays on John Maynard Keynes and …. Xlibris Corporation. Pennsylvania; Philadelphia.
  • Brady, Michael Emmett. (2011). How to use Keynes’s conventional coefficient of risk and weight c, to clear up misunderstandings about Keynes’s view on the use of his principle of indifference versus the use of Laplace’s principle of non-sufficient reason, Int. J. App. Econ & Econometrics, Vol. 19, no. 3, (July/September), pp.21-32.
  • Brady, Michael Emmett. (2012). Boole, Keynes, and the Interval approach to Probability, History of Economic Ideas, Vol. 20, no.3, (December), pp.1-20.
  • Brady, Michael Emmett. (2012a).  J M Keynes on base rates, weight of evidence, worth of evidence, reference classes, and the Tversky-Kahneman blue-green taxicab problem, Int. J. App. Econ & Econometrics, Vol.20, no.1, pp.170-187.
  • Brady, Michael Emmett. (2012b). Keynes, mathematics and probability: a reappraisal, J. App. Econ & Econometrics, no.2, (April/June), pp.324-357.
  • Brady, Michael Emmett. (2021). On the correction of all thirty-five errors contained in Ramsey’s 1922 and 1926 reviews of Keynes’s Treatise. Journal of Management Information and Decision Sciences, Vol.24, special issue, no.6,2021, pp.1-19.
  • Brady, Michael Emmett. (2022). Keynes never assumed at any time in his life “…that all statements or propositions stand in logical relation to each other”. Advances in Politics and Economics, Vol.4.no.3, pp.20-30.
  • Brady, Michael Emmett. (2023). Using Keynes’s Non-Probabilistic Coefficient of Evidential Weight, [2w/(1+w)], to Analyze Knightian Uninsurable Uncertainties, Scenario Analysis and Entrepreneurship Studies. Journal of Insurance and Financial Management, Vol.7, no.4, pp.54-65.
  • Brady, Michael Emmett. (2023a). I J GOOD’S CLAIM, THAT KEYNES’S EVIDENTIAL WEIGHT OF THE ARGUMENT, V, A LOGICAL RELATION, IS A NUMBER, IS FALSE. Theoretical and Practical Research in the Economic Fields, Vol.14, no.1(Summer), pp.5-15.
  • Brady, Michael Emmett. (2023b). Corrigendum for Runde’s “Keynesian Uncertainty and The Weight of Arguments ” in Economics and Philosophy, 1990. Available at ResearchGate and Academia.
  • Brady, Michael Emmett. (2023c). On Baylis’s erroneous work on Keynes’s weight in 1935 in The Journal of Philosophy. Available at ResearchGate or Academia.
  • Brady, Michael Emmett. (2024). Opinion about the Liquidity Preference Theory discussions concerning weight and risk in the Townshend-Keynes letters of November-December ,1938. Theoretical and Practical Research in the Economic Fields, Vol.15, no.1, (June), pp.45-53.
  • Brady, Michael Emmett. (2024). A Study of Post Keynesian Attempts at hiding Townshend’s main question to Keynes in his Nov.,1938 letter and Keynes’s answer. Theoretical and Practical Research in the Economic Fields, Vol.15, no.2, (December), pp.864-870.
  • Braithwaite, R.B. (1931). Book review of Harold Jeffrey’s Probability. Mind. Volume XL, no.160(October), pp.492-501.
  • Braithwaite, R. (1973). Editorial Foreword to A Treatise on Probability, Vol.8, CWJMK edition. London, Macmillan, pp. xiv-xxii).
  • Brekel, J. (2022).  A Very Confusing Problem: Interpreting Keynesian Weight. Master of Arts Thesis, Department of Philosophy, Colorado State University, Colorado, (Fall), pp.1-83.
  • Brekel, J. (2025). A new look at Keynesian weight of evidence. Erkenntnis (September).
  • Broad, C. D.1922.Review of A Treatise on Probability. Mind ,31:72–85.
  • Bures, C. (1938). The Concept of Probability. A Critical Survey of Recent Contributions. Philosophy of Science.  Vol. 5, No. 1 (January), pp. 1-20.
  • Carabelli, A. (1988). On Keynes’s Method. Palgrave Macmillan; London.
  • Carabelli, A. (2003). Keynes: economics as a branch of probable logic. In Runde and Mizuhara(eds.),2003, the philosophy of Keynes’s economics, London, Routledge, pp.216-226.
  • Cohen, L.J. (1986). Twelve questions about Keynes’s concept of weight. The British Journal for the Philosophy of Science, Vol.37, no.3(September), pp.263-278.
  • Davis, John B. (1994). Review of Maynard Keynes, D. Moggridge. Economics & Philosophy, Vol.10 (no.2), pp.359-364.
  • Davis, John B. (2021). Keynes’s Treatise on Probability 100 Years Later: Small vs. large worlds and closed vs. open systems. Working Paper series 2022-02. College of Business Administration, Marquette University, pp.1-19. See also History of Economic Ideas,2021, Vol.29, no.3, (November).
  • Dequech, D. (1997). A Brief Note on Keynes, Unknown Probabilities, and Uncertainty in a Strong Sense. History of Economic Ideas, Vol.5, no.2, pp.101-110.
  • Edgeworth, F. Y. (1922). The philosophy of chance, Mind, 31(23), 157-185.
  • Edgeworth, F. Y. (1922). Review of A Treatise on Probability. By John Maynard Keynes.JRSS,85,107-113.
  • Gerrard,Bill. (1992). From A Treatise on Probability to The General Theory: continuity or change in Keynes’s thought?’. In The Philosophy and Economics of JM Keynes. Aldershot: Edward Elgar. 1992:80-95
  • Gerrard, Bill. (2003). Keynesian uncertainty: what do we know? In Runde and Mizuhara, (eds.). The Philosophy of Keynes’s Economics.London; Routledge
  • Gerrard, B. (2023). Ramsey and Keynes Revisited. Cambridge Journal of Economics, , 47, (jan.), pp. 195–213.
  • Gillies, Donald. (1972). Review: The Subjective Theory of Probability. The British Journal for the Philosophy of Science.Vol.23, no.2, (May), pp.138-157.
  • Gillies, Donald. (2000). Philosophical Theories of Probability. London; Routledge.
  • Gillies, Donald. (2021). Difficulties in the Logical Interpretation of Probability. History of Economic Ideas, Vol. XXIX, no.3(November), pp.143-147.
  • Good, I.J. (1950). Probability and the Weighing of Evidence. London; C. Griffin.
  • Good, I.J. (1962). Subjective probability as the measure of a non-measurable set, in: E. Nagel, P. Suppes, A. Tarski (Eds.), Logic, Methodology and Philosophy of Science, Stanford University Press, Stanford, 1962, pp. 319–329.
  • Good, I.J. (1983a). Good Thinking. Minnesota; University of Minnesota Press.
  • Good, I. J. (1988). Causal Tendency. In Skyrms, B. and Harper, W. L. (1988). Causation, Chance and Credence, pp.22-46.
  • Hacking, I. (1980). The Theory of Probable Inference: Neyman, Pierce and Braithwaite. In Science, belief and behavior: Essays in honor of R B Braithwaite. ed. by D.H. Mellor. London; Cambridge University Press, pp.141-160, (Chapter 8).
  • Hailperin, T. (1965). Best possible inequalities for the probability of a logical function of events. American Mathematical Monthly, 72, 343-359.
  • ______. (1986). Boole’s Logic and Probability. Amsterdam: North Holland. 2nd edition.
  • Hishiyama, I. (1969). The Logic of Uncertainty according to J.M. Keynes. Kyoto University Economic Review, 39, no.1, pp. 22-44.
  • Hishiyama ,I.(2010). A Critical Reorientation of Keynes’s Economic and Philosophical Thoughts. In Silva Brandolini and R.Scazzieri,(eds.), Fundamental Uncertainty: Rationality and Plausible Reasoning. Palgrave Macmillan; London, pp.232-271.
  • Harris, M. (2021). Conceptualizing Uncertainty: The IPCC, Model Robustness and the Weight of Evidence. Ph.D., The London School of Economics and Political Sciences, Department of Philosophy. (October), pp.1-303.
  • Joyce, J. (2005). How probabilities reflect evidence. Philosophical Perspectives, 19, pp.153–178.
  • Kasser, J. (2016). Two conceptions of the Weight of Evidence in Peirce’s Illustrations of the Logic of Science.Erkinntnis,81, no.3, pp.629-648
  • Keynes, J.M. (1921). A Treatise on Probability. Macmillan, London, 1921.
  • Keynes, J. M. (1973). A Treatise on Probability. Macmillan, London. Volume 8. CWJMK edition of the A Treatise on Probability (with the editorial foreword of R. B Braithwaite, pp. xiv-xxii).
  • ____. F. P. Ramsey. In Essays in Biography, CWJMK (pp. 335-346), vol. X, London: Macmillan for the Royal Economic Society (reprinted from The New Statesman and Nation, 3 October 1931).
  • Levi, I. (2011). The Weight of Argument. In Brandolini, S. and Scazzieri, R.(eds.), Fundamental Uncertainty. Palgrave: Macmillan, pp.39-58.
  • Mellor, D. H. (1983). The Eponymous F. P. Ramsey. Journal of Graph Theory, Vol. 7, pp.9-13.
  • Mellor, D.H. (1995). “F.P. Ramsey”. Philosophy, 70, pp. 243-257.
  • Methven, S. J. (2015). Frank Ramsey and the realistic Spirit. Palgrave Macmillan; London.
  • Misak, C. (2016). The Subterranean influence of Pragmatism on the Vienna Circle: Pierce, Ramsey, Wittgenstein. Journal for the History of Analytical Philosophy ,4, no.5, pp.1-16.
  • Misak, C. (2020). Frank Ramsey: A Sheer Excess of Powers. Oxford: Oxford University Press.
  • Monk, R. (1991). Russell and Ramsey. London Reviews of Books, 29 August, pp. 11-13. Reprinted in Russell Society News, No. 72, (Nov. ,1991) pp. 25-26.
  • O’Donnell, R. (1989). Keynes: Philosophy, Economics and Politics. Palgrave Macmillan; London
  • O’Donnell, R.(2021a). Keynes and Knight: risk-uncertainty, distinctions, priority, coherence and change. Cambridge Journal of Economics,45(September), pp.1127-1144.
  • O’Donnell, R. (2021b) Keynes’s Treatise on Probability: The First Century. Review of Political Economy, (October), 33:4, pp.585-610.
  • Peden, W. (2018). Imprecise Probability and the Measurement of Keynes’s “Weight of Argument”. Journal of Applied Logics, Vol.5, no.3 , pp.677-708.
  • Ramsey, F. P. (1922). Mr. Keynes on Probability, Cambridge Magazine, Vol. XI, no. 1, (January), pp.3-5. Reprinted in British Journal of the Philosophy of Science, 40, [1989], pp.219-222.
  • ______. (1926). Truth and probability. In Mellor, D. H (Ed.) Foundations: Essays in Philosophy, Logic, Mathematics, and Economics, London: Routledge & Kegan Paul, [1978] and in Kyburg and Smokler (eds.), Studies in Subjective Probability,1980, (2nd ed.); New York; Krieger.pp.26-52.
  • Runde, J. (1990). Keynesian Uncertainty and the Weight of Arguments. Economics and Philosophy,6, pp.275-292.
  • Runde, Jochen (1994). Keynes after Ramsey: In Defense of A treatise on Probability. Studies in History and Philosophy of Science, Vol.25, no.1, pp.97-121.
  • Russell, B. (1922). Review of A treatise on Probability by John Maynard Keynes. Mathematical Gazette, Vol.11(July), pp.119-125.
  • Russell, B. (1948). Human Knowledge: Its Scope and Limits. Routledge; London,2009
  • Russell,B.(1959). My Philosophical Development. George Allen and Unwin; London, England.
  • Skidelsky, R. (1992). John Maynard Keynes: The Economist as Savior,1920-1937, Volume II. England; Penguin Publishers.
  • Townshend H. (1979 [1937]). Letter to Keynes, in Moggridge D. E. (ed.). CWK, XXIX: 236-7.
  • Townshend H. (1979 [1938]). Letter to Keynes. In Moggridge D. E. (ed.). CWK, XXIX: 240-5.
  • Townshend H. (1979 [1938]). Letter to Keynes. In Moggridge D. E. (ed.). CWK, XXIX: 257-8,288-294.
  • Vercelli, A. (2011). Weight of Argument and Economic Decisions. In Brandolini, S. and Scazzieri, R.(eds.), Fundamental Uncertainty. Palgrave: Macmillan, pp.151-170
  • Vercelli, A. (2013). Weight of Argument and liquidity preference: Keynes after Savage and Choquet. Department of Political Economy and Statistics University of Siena, pp.1-21
  • Vercelli, A. (2016). Weight of Argument and liquidity preference: Maynard Keynes and Victoria Chick. Department of Political Economy and Statistics University of Siena, pp.1-19.
  • Vercelli, A. (2018). Weight of Argument and liquidity preference: Maynard Keynes and Victoria Chick. In the General Theory and Keynes for the 21st Century. S Dow, J. Jesperson, and G. Tily, (eds.). Edward Elgar, London, pp.84-97.
  • Weatherson, B. (2002). Keynes, uncertainty, and interest rates. Cambridge Journal of Economics, 26, pp.47–62.
  • Wheeler, G. (2012). Commemorating the work of Henry E. Kyburg,Jr. Synthese, Vol.186, no.2, (May), pp.443-446.
  • Wilson, E.B. (1923). Keynes on Probability. Bulletin of the American Mathematical Society,29,7,319-322.
  • Zabell, S.L. (1991). Ramsey, Truth, and Probability. Theoria, vol.57, no.3(December), pp.211-238.
  • Zabell, S. L. (2005). Symmetry and its Discontents. Cambridge; Cambridge University Press.