I.J. Good’s Claim, That Keynes’s Evidential Weight of the Argument, V, a Logical Relation, is a Number, is False

  • Michael Emmett BRADY California State University, Dominguez Hills, College of Business Administration and Public Policy, Carson, California, USA

Abstract

All current assessments of how Keynes’s weight (evidential weight of the argument) concept is measured are erroneously based on a metaphor ignored by I.J. Good, which Keynes used before he presented the mathematical analysis involved in measuring weight in chapter 26 of the A Treatise on Probability, on page 77 of chapter 6 to measure weight.
Keynes’s chapter 26 is the omega while chapter 6 is the alpha. It is impossible to fully grasp Keynes’s evidential weight of the argument concept, first presented as a logical relation designated as V, which is then measured through the construction of an index of weight in chapter 26, without a detailed study of pp. 310-315 of chapter 26 of the A Treatise on Probability.
The misbelief that Keynes ‘s concept of the evidential weight of the evidence, V=V(a/h), in chapter 6 of the A Treatise on Probability, represented a measure of the absolute amount of Knowledge, defined as K by Good to represent a gross measure of weight, can be traced back to numerous book and journal article contributions made by I.J. Good between 1950 and 2000.
The most severe errors about chapter 6 of the A Treatise on Probability were repeated again and again by Good from 1950 to 1990 (Good 1950, 1960, 1962, 1965, 1967, 1967, 1968/70, 1970/71, 1975, 1983a, 1983b, 1985, 1988, 1988, Good and Toulmin 1968).
Good completely overlooked Keynes’s footnote 1 on page 76 of chapter 6 to chapter 26 of the A Treatise on Probability, where Keynes stated that he would discuss how to integrate weight into a discussion of “…the application of probability to practice.” This would require a mathematical analysis and, obviously, would require the restriction that V(a/h)=w, 0≤w≤1, and w is the degree of the completeness of the information so as to be able to combine it with 0≤α≤1, where P(a/h)=α and α is the probable degree of rational belief.

References

[1] Baylis, C.A. 1935. The Nature of Evidential Weight. The Journal of Philosophy, 32(11): 281-286. DOI:https://doi.org/10.2307/2015951
[2] 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, [1958]. Available at:https://www.gutenberg.org/files/15114/15114-pdf.pdf
[3] Brady, M. E. and Arthmar, R. 2012. Keynes, Boole, and the Interval approach to Probability. History of Economic Ideas, 20(3): 65-84. Available at: https://www.jstor.org/stable/23723682
[4] Brady, M. E. 2018a. Confusing Metaphors With Mathematics in Chapter 6 of the A Treatise on Probability, When Analyzing Keynes’s Modeling of the Evidential Weight of the Argument V (a/h), Leads to confusion: If V(a/h)=w, As Defined in Chapter 26, Where 0≤w≤1, Then It Is Mathematically Impossible That Keynes’s Weight Is Monotonically Increasing (October 21). DOI: http://dx.doi.org/10.2139/ssrn.3270409
[5] Brady, M. E. 2018b. Comparing Edgeworth’s, Russell’s, and Broad’s 1922 Assessments of Keynes’s Weight of the Evidence, Based on Chapters 6 and 26 of the A Treatise on Probability, With Levi’s, Runde’s, Weatherson’s, Joyce’s, Feduzi-Runde’s, Kasser’s and Peden’s Assessments of Keynes’s Weight of the Evidence Based on Chapter 6 of a Treatise on Probability Alone: Skipping Chapter 26 of the A Treatise on Probability Leads to a Number of Errors of Omission. DOI:http://dx.doi.org/10.2139/ssrn.3274122
[6] Brady, M. E. 2020a. On I.J. Good’s Inability to Grasp Keynes’s Complete Analysis of the Weight of the Argument: The Logical Part of the Analysis of Evidential Weight of the Argument in Chapter 6 and the Mathematical Part of the Analysis in Chapter 26 in the A Treatise on Probability (May 31). DOI:http://dx.doi.org/10.2139/ssrn.3614914
[7] Brady, M. E. 2020b. The Main Result of Keynes’s Evidential Weight of the Argument Analysis, in Chapter 6 of the A Treatise on Probability, Is That V=V(a/h) =V(a/h1, h2, h3, h4……hn, hn+1….) While the Main Result of Chapter 26 Is That V(a/h)=w, 0≤w≤1, Where w=K/[K+I] and 1-w=I/[K+I]. No Economist or Philosopher in the 20th or 21st Century Was Able to Obtain Keynes’s Final Results by Combining Them (May 28). DOI:http://dx.doi.org/10.2139/ssrn.3612516
[8] Brady, M. E. 2004a. J. M. Keynes’ Theory of Decision Making, Induction, and Analogy. The Role of Interval Valued Probability in His Approach. Philadelphia, Pennsylvania: Xlibris Corporation.
[9] Brady, M. E. 2004b. Essays on John Maynard Keynes and …. Philadelphia, Pennsylvania: Xlibris Corporation.
[10] 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. Available at: https://mountainscholar.org/bitstream/handle/10217/235951/Brekel_colostate_0053N_17497.pdf?sequence=1&isAllowed=y
[11] Broad, C.D. 1922. A Treatise on Probability. Mind, 31: 72–85.
[12] Derbyshire, J., Feduzi, A. and Runde, J. 2022. Borrowing from Keynes’ A Treatise on Probability: A non-probabilistic measure of uncertainty for scenario planning. European Management Review, 1-13. DOI:https://doi.org/10.1111/emre.12549
[13] Edgeworth, F.Y. 1922b. A Treatise on Probability, by John Maynard Keynes. Journal of the Royal Statistical Society, 85: 107–13.
[14] Good, I.J. 1965. The estimation of probabilities. Cambridge, Massachusetts; MIT Press.
[15] Good, I.J. 1967. Review of Ian Hacking, Logic of Statistical Inference. Math. Rev. 29, 560; and in Nature 213: 233–234, entitled ‘Probability or Support’.
[16] Good, I.J. 1967. On the Principle of Total Evidence. Brit. J. Phil. Sci. 17: 319–321.
[17] Good, I.J. 1970/71. The Probabilistic Explication of Information, Evidence, Surprise, Causality, Explanation, and Utility’, an invited lecture at the Waterloo Conference, April 1970, with appendix ‘Twenty-Seven Principles of Rationality’, in Foundations of Statistical Inference: Proc. Symposium on Foundations of Statistical Inference prepared under the auspices of the Réné Descartes Foundation and held at the Dept. of Statistics, Univ. of Waterloo, Ontario, Canada, from March 31 to April 9, 1970 (ed. by V. P. Godambe and D. A. Sprott), Holt, Rinehart and Winston of Canada, Ltd., Toronto and Montreal, pp. 108–141 (with discussion).
[18] Good, I.J. 1983b. Weight of evidence: a brief survey. North Holland, Amsterdam: Second Valencia International Meeting on Bayesian Statistics
[19] Good, I.J. 1985. Weight of Evidence: A Brief Survey. Bayesian Statistics, 2(1985): 249-70. Available at: https://www.cs.tufts.edu/~nr/cs257/archive/jack-good/weight-of-evidence.pdf
[20] Good, I.J. 1950. An error by Peirce concerning Weight of evidence. Journal od Statistical Computation and Simulation,13: 155-157.
[21] Good, I.J. 1950. Probability and the Weighing of Evidence. London ;C. Griffin.
[22] Good, I.J. 1960. Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments. Journal of the Royal Statistical Society. Series B (Methodological), 22(2): 319-331. DOI:https://doi.org/10.1111/j.2517-6161.1960.tb00378.x
[23] Good, I.J. 1962. Subjective probability as the measure of a non-measurable set. In Logic, Methodology, and Philosophy of Science, Nagel, D. and Tarski, A. (eds.), pp.319–329. Stanford University Press. Reprinted in Studies in Subjective Probability (H. E. Kyburg & H. E. Smokier, eds.; 2nd ed.) Huntington, N. Y.: Krieger, pp.133-146; and in Good (1983a), pp.73-82.
[24] Good, I.J. 1968/70. Contribution to the discussion of H. Vetter's paper ‘Logical Probability, Mathematical Statistics, and the Problem of Induction’, in Induction, Physics and Ethics [see de Finetti (1968/70)], pp. 103–104 and 113.
[25] Good, I.J. and Toulmin, G. H. 1968. Coding Theorems and Weight of Evidence. J. Inst. Math. Applics., 4: 94–105. DOI: https://doi.org/10.1093/imamat/4.1.94
[26] Good, I.J. 1975. Explicativity, corroboration, and the relative odds of hypotheses. Synthese, 30(March): 39–73. Available at: https://www.jstor.org/stable/20115014
[27] Good, I.J. 1983a. Good Thinking. Minnesota; University of Minnesota Press.
[28] Good, I.J. 1988.The Interface Between Statistics and Philosophy of Science. Statistical Science, 3(4): 386-397. Available at: http://www.jstor.org/stable/2245388
[29] Good, I.J. 1988. Causal Tendency. In Skyrms, B. and Harper, W. L. (1988). Causation, Chance and Credence, pp.22-46. DOI: https://doi.org/10.1007/978-94-009-2863-3_2
[30] 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. DOI: 10.21953/lse.00004355
[31] Hishiyama, I. 1969. The Logic of Uncertainty according to J. M. Keynes. Kyoto University Economic Review, 39(1): 22-44. DOI: https://doi.org/10.11179/ker1926.39.22
[32] Joyce, J. 2005. How probabilities reflect evidence. Philosophical Perspectives, 19: 153–178. DOI: https://doi.org/10.1111/j.1520-8583.2005.00058.x
[33] Kasser, J. 2016. Two conceptions of the Weight of Evidence in Peirce’s Illustrations of the Logic of Science. Erkinntnis, 81(3): 629-648. DOI: https://doi.org/10.1007/s10670-015-9759-5
[34] Keynes, J. M. 1921. A Treatise on Probability. London: Macmillan.
[35] Keynes, J. M. 1973. A Treatise on Probability. In The Collected Writings of John Maynard Keynes (CWJMK), vol. VIII. London: Macmillan.
[36] Kyburg, H. 2011. Logic, Empiricism and Probability Structures. In Brandolini, S. and Scazzieri, R. (eds.), Fundamental Uncertainty. Palgrave: Macmillan, pp.23-38.
[37] Levi, I. 2011. The Weight of Argument. In Brandolini, S. and Scazzieri, R.(eds.), Fundamental Uncertainty. Palgrave: Macmillan, pp.39-58.
[38] Peden, W. 2018. Imprecise Probability and the Measurement of Keynes’s “Weight of Argument”. Journal of Applied Logics, 5(3): 677-708. Available at: https://www.researchgate.net/publication/327446033_Imprecise_Probability_and_the_Measurement_of_Keynes's_Weight_of_Arguments
[39] Ramsey, F.P. 1922. Mr. Keynes on Probability, Cambridge Magazine, XI, 1, (Jan) 3-5. The British Journal of the Philosophy of Science, 40, [1989]: 219-222. Available at: https://www.journals.uchicago.edu/doi/abs/10.1093/bjps/40.2.219
[40] Ramsey, F.P. 1926. "Truth and Probability", in Ramsey, 1931, The Foundations of Mathematics and other Logical Essays, Ch. VII, p.156-198, edited by R.B. Braithwaite, London: Kegan, Paul, Trench, Trubner & Co., New York: Harcourt, Brace and Company. Available at: http://fitelson.org/probability/ramsey.pdf
[41] Ramsey, F.P. 1926. Truth and probability. In Mellor, D. H (Ed.) Foundations: Essays in Philosophy, Logic, Mathematics, and Economics, London: Routledge & Kegan Paul, [1978].
[42] Runde, J. 1990. Keynesian Uncertainty and the Weight of Arguments. Economics and Philosophy, 6: 275-292. DOI: https://doi.org/10.1017/S0266267100001255
[43] Russell, B. 1922. Review of A Treatise on Probability, by J. M. Keynes. Mathematical Gazette, 11(159): 119–25. DOI: https://doi.org/10.2307/3603283
[44] Vercelli, A. 2011. Weight of Argument and Economic Decisions. In Brandolini, S.M.D., Scazzieri, R. (eds.), Fundamental Uncertainty. Palgrave: Macmillan, London, pp.151-170. DOI:https://doi.org/10.1057/9780230305687_7
[45] 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 Available at: https://www.depfe.unam.mx/actividades/14/seminario-politicas-economicas/04_vercelli_2013.pdf
[46] 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. Available at: http://www.postkeynesian.net/downloads/downloads/events/GTVC80_VERCELLI.ppt
[47] 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. DOI: https://doi.org/10.4337/9781786439888.00014
[48] Weatherson, B. 2002. Keynes, uncertainty, and interest rates. Cambridge Journal of Economics, 26: 47–62. Available at: http://www.jstor.org/stable/23600357
Published
2023-06-26
How to Cite
BRADY, Michael Emmett. 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 Economic Fields, [S.l.], v. 14, n. 1, p. 5 - 15, june 2023. ISSN 2068-7710. Available at: <https://journals.aserspublishing.eu/tpref/article/view/7858>. Date accessed: 10 may 2024. doi: https://doi.org/10.14505/tpref.v14.1(27).01.