J. M. Keynes, The General Theory and George Boole: Keynes’s Uncertainty is based on Boolean Uncertainty as analyzed in The Laws of Thought
Abstract
This paper contributes to the literature on Keynes by showing that Keynes’s understanding and analysis of the role of uncertainty in decision making originated from his reading of George Boole’s The Laws of Thought. Boole’s The Laws of Thought was the first mathematically and logically advanced treatise(Thomas Aquinas and Adam Smith had both recognized that real world decision making could not be based on the purely mathematical laws of the probability calculus) on uncertainty, demonstrating that the purely mathematical laws of the probability calculus, based on additivity and linearity were, at best, only a limiting, special case that would rarely occur in the real world of decision making which were characterized by non-additivity and non-linearity. Keynes then developed the basic foundational analysis of Boole further in his A Treatise on Probability and General Theory .Keynes advanced Boole’s theory by developing his own version of Boole’s logical, objective, probability relation, theory of groups, upper-lower, interval bounded imprecise probabilities, as well as the evidential weight of the argument, which would allow a treatment of uncertainty in the form of a decision weight approach instead of by interval estimates. Keynes called this approach his conventional coefficient of weight and risk, c, in Chapter XXVI of the A Treatise on Probability.
References
[2] Brady, M. E. (2021a). How SIPTA overlooked Keynes’s major contributions to imprecise probability and decision making, 1999-2019. International Journal of Management Research and Economics, 1(3): 11-21. DOI: https://doi:10.51483/IJMRE.1.3.2021.11-21
[3] Brady, M.E. (2021b). 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, 24 (Special issue no.6): 1-19.
[4] Burris, S. N. (2022). Annotated Logic Chapters from Boole’s Algebra of Logic as presented in the first 15 chapters of his 1854 book An Investigation of The Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities.
[5] Clarke, P. (2023). Keynes at work. United Kingdom; Cambridge University Press. (ISBN-10: 1009255010, ISBN-13: 978-1009255011)
[6] Corcoran, J. (2003). Aristotle’s Prior Analytics and Boole’s Laws of Thought. History and Philosophy of Logic, 24: 261–288. DOI: https://doi.org/10.1080/01445340310001604707
[7] Ramsey, F. P. 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).
[8] Gerrard, B. (2023). Ramsey and Keynes Revisited. Cambridge Journal of Economics, 47(1): 195-213. DOI:https://doi.org/10.1093/cje/beac068
[9] Gerrard, B. (2023). Keynes, Ramsey, and Pragmatism. Journal of the History of Economic Thought, 45(3): 384 – 398. DOI: https://doi.org/10.1017/S1053837222000311
[10] Gerrard, B. (2023). The Development of Keynes’s Pragmatist Account of the Human Logic of Investment under conditions of Uncertainty. SSRN. Submitted to European Journal of the History of Economic Thought
[11] Gerrard, B. (2022). The Road Less Travelled: Keynes and Knight on Probability and Uncertainty. Review of Political Economy, pp. 1253-1278. DOI: https://doi.org/10.1080/09538259.2022.2114291
[12] Hailperin, T. (1986). Boole’s Logic and Probability. Amsterdam: North Holland. 2nd edition.
[13] Hishiyama, I. (1969). The Logic of Uncertainty according to J. M. Keynes. Kyoto University Economic Review, 39(1): 22-44. DOI: https://www.jstor.org/stable/i40126266
[14] Keynes, J. M. (1921[1973). A Treatise on Probability. London; Macmillan.
[15] Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. New York; Prometheus Books.
[16] Keynes, J. M. (1973). A Treatise on Probability. Macmillan, London. Volume 8. CWJMK edition of the A Treatise on Probability (with the erroneous error filled with editorial foreword of R. B Braithwaite, pp. xiv-xxii).
[17] Ramsey, F. P. (1922). Mr. Keynes on Probability, Cambridge Magazine, XI, 1 (Jan): 3-5. DOI:https://www.jstor.org/stable/687512. Reprinted in British Journal of the Philosophy of Science, (1989), 40: 219-222. DOI: 10.1093/bjps/40.2.219
[18] Ramsey, F. P. (1926). Truth and probability. In Mellor, D. H (Ed.) Foundations: Essays in Philosophy, Logic, Mathematics, and Economics, London: Routledge & Kegan Paul, (19780. Kyburg, H. E. & Smokler, H.(eds.). (1980). Studies in Subjective Probability, 2nd edition).
[19] Wilson, E.B. (1923). Keynes on Probability. Bulletin of the American Mathematical Society, 29(7): 319-322. Available: https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-29/issue-7
[20] Wilson, E. B. (1934). Boole’s Challenge Problem. Journal of the American, Statistical Association, 29(187): 301-304. Available at: https://www.researchgate.net›publication›31799732
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