Open Access Journal Article

An Examination of Ramsey's Critique: The Lack of Support in Dismissing Keynes's Logical Theory of Probability

by Michael Emmett Brady a,* orcid
a
College of Business Administration and Public Policy, California State University, Dominguez Hills, USA
*
Author to whom correspondence should be addressed.
EAL  2023, 21; 2(2), 21; https://doi.org/10.58567/eal02020003
Received: 25 March 2023 / Accepted: 7 May 2023 / Published Online: 15 May 2023
View Full-Text
Download PDF

Abstract

In his 1922 review for Cambridge Magazine of Keynes's A Treatise on Probability, and again in his 1926 review "Truth and Probability" (published in 1931 and republished in Kyburg and Smokler's 1980 edition), Ramsey provided examples critiquing Keynes's logical theory of probability. However, these examples do not disprove Keynes's theory as all of them are flawed. The flaws arise because all the pairs of propositions that Ramsey used to substantiate his criticisms are irrelevant to each other. Such irrelevant propositions are explicitly excluded from Keynes's theory in pages 4-6 of his A Treatise on Probability. This paper highlights that Ramsey's examples, which involve irrelevant propositions, do not disprove Keynes's Boolean, relational logic. The only other defense of Keynes's theory, put forth by Watt in 1989, was found to be deficient by Brady in 2022.

Keywords: Boolean logic; relational; propositional logic; premises; conclusions; argument form; conditional probability;
Copyright: © 2023 by Emmett Brady. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (Creative Commons Attribution 4.0 International License). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Share and Cite

ACS Style
Emmett Brady, M. An Examination of Ramsey's Critique: The Lack of Support in Dismissing Keynes's Logical Theory of Probability. Economic Analysis Letters, 2023, 2, 21. https://doi.org/10.58567/eal02020003
AMA Style
Emmett Brady M. An Examination of Ramsey's Critique: The Lack of Support in Dismissing Keynes's Logical Theory of Probability. Economic Analysis Letters; 2023, 2(2):21. https://doi.org/10.58567/eal02020003
Chicago/Turabian Style
Emmett Brady, Michael 2023. "An Examination of Ramsey's Critique: The Lack of Support in Dismissing Keynes's Logical Theory of Probability" Economic Analysis Letters 2, no.2:21. https://doi.org/10.58567/eal02020003
APA style
Emmett Brady, M. (2023). An Examination of Ramsey's Critique: The Lack of Support in Dismissing Keynes's Logical Theory of Probability. Economic Analysis Letters, 2(2), 21. https://doi.org/10.58567/eal02020003

Article Metrics

Article Access Statistics

References

  1. Boole, George. (1854). The Laws of Thought. New York; London.
  2. 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; Philadelphia, Pennsylvania.
  3. Brady, Michael Emmett. (2022a). No where in J M Keynes’s A Treatise on Probability (1921) did Keynes ever state that “…between any two non-self-contradictory propositions there holds a probability relation (Axiom I)…”(Ramsey,1922,p.3;1989,p.219). Journal of Insurance and Financial Management, Vol.6, No.1, pp.89-102. https://journal-of-insurance-and-financial-management.com/
  4. Brady, Michael Emmett. (2022b). On the Need for Insurance Analysts and Actuaries to reconsider Keynes’s Logical Theory of Probability, Part I: Russell’s Refutation of Ramsey’s Critique of Keynes’s Theory in 1922. Journal of Insurance and Financial Management, Vol.6, No.4, pp.89-94. https://journal-of-insurance-and-financial-management.com/
  5. Brady, Michael Emmett. (2022c). On the Need for Insurance Analysts and Actuaries to reconsider Keynes’s Logical Theory, Part II: On Ramsey’s Refusal to Recognize Russell’s Refutation of Ramsey. Journal of Insurance and Financial Management, Vol.6, No.5, pp.1-8. https://journal-of-insurance-and-financial-management.com/
  6. Brady, Michael Emmett. (2022d). D. E. Watt’s reply for Keynes to Ramsey in the British Journal for the Philosophy of Science in 1989 is defective. Theoretical and Practical Research in the Economic Fields, Volume XIII, Issue 2(26), (Winter), pp.109-115. https://doi.org/10.14505/tpref.v13.2(26).01
  7. Franklin, James. (2001). Resurrecting logical probability. Erkenntnis, 55, pp. 277–305. https://doi.org/10.1023/A:1012918016159
  8. Gerrard, Bill. (2023). Ramsey and Keynes revisited. Cambridge Journal of Economics, Vol.47, No.1, (January), pp.195-213. https://doi.org/10.1093/cje/beac068
  9. Gillies, D. (1972). The Subjective Theory of Probability. The British Journal for the Philosophy of Science, (May), Vol. 23, No. 2, pp. 138-157. 10.1093/bjps/23.2.138
  10. Keynes, J. M. (1936). The General Theory of Employment, Interest, and Money. Prometheus Books (1997); Amherst, New York.
  11. 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).
  12. Keynes, J.M. (1921). A Treatise on Probability. Macmillan, London, 1921.
  13. Kyburg, H. E. (1974). The Logical Foundations of Statistical Inference, Reidel, Dordrecht.
  14. Kyburg, H. E. Jr., & Smokler, H. E. (eds.). (1980). Introduction. In Kyburg and Smokler, Studies in Subjective Probability. New York: Wiley (2nd ed.), pp.25-52.
  15. Levi, I. (1974). On Indeterminate Probabilities. Journal of Philosophy, 71, pp. 391–418. 10.2307/2025161
  16. Misak, C. (2020). Frank Ramsey: A sheer excess of powers. United Kingdom; Oxford University Press.
  17. Misak, C., Naylor, C. D., Tonelli, M., et al. (2022). Case Report: What—or Who—Killed Frank Ramsey? Reflections on Cause of Death and the Nature of Medical Reasoning. Wellcome Open Research, 7:158. [Version 1; Peer Review: 1 Approved] https://doi.org/10.12688/wellcomeopenres.17759.1
  18. Pan, Y., & Yuan, B. (1997). Bayesian Inference of Fuzzy Probabilities. International Journal of General Systems, 26, pp. 73–90. https://doi.org/10.1080/03081079708945170
  19. Ramsey, F. P. (1922). Mr. Keynes on Probability. Cambridge Magazine, XI, 1, pp. 3-5. Reprinted in the British Journal of the Philosophy of Science, 40, (1989), pp. 219-222. https://doi.org/10.1093/bjps/40.2.219
  20. Ramsey, F. P. (1926). Truth and Probability. In D. H. Mellor (Ed.), Philosophical Papers. Cambridge University Press, (1990), pp. 52–94.
  21. Russell, B. (1922). Review of A Treatise on Probability by John Maynard Keynes. Mathematical Gazette, 11, pp. 119-125. https://doi.org/10.2307/3609931
  22. Sahlin, N.-E. (1990). The Philosophy of F.P. Ramsey. Cambridge University Press. Retrieved from https://www.nilsericsahlin.net/the-philosophy-of-f-p-ramsey
  23. Spiegelhalter, D. J., Dawid, A. P., Lauritzen, S. L., & Cowell, R. G. (1993). Bayesian Analysis in Expert Systems. Statistical Science, 8, pp. 219–283. https://www.jstor.org/stable/2245959
  24. Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall.