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

Michael E Brady


A historical myth has been created in the 20th and 21st centuries  that F P Ramsey uncovered major technical  and logical flaws in Keynes’s logical theory of Probability that was presented in his 1921 A Treatise on Probability.It has been accepted in academia   that Ramsey showed in 1922 ,in his book review in the January issue of Cambridge Magazine,and then again with greter force in his 1926 paper,titled “Truth and Probability”, that Keynes’s relational propositional logic contained serious logical mistakes that made it impossible to base probability and statistics on.

However,it has been completely overlooked for 100 years  that it  took Bertrand Russell only one small footnote to refute all of Ramsey’s claims , that supposedly demonstrated the logical errors in Keynes’s relational propositional logic as presented by Keynes on pp.4-6 and pp.53-56 of the A Treatise on Probability,with one small counter example that refutes Ramsey’s entire argument.Russell’s refutation  occurs in his July,1922 review ,published in the Mathematical Gazette on pp.119-125.Russell’s refutation takes place on page 120 in  a footnote.

This explains why Ramsey’s work on probability and statistics  is never mentioned by Russell in his monumental 1948 Human Knowledge :Its scope and limits.The reason is that Ramsey’s positive contributions to his own subjective theory of probability are severely marred because these positive contributions  are hopelessly intertwined with a series of false claims made about Keynes’s logical theory of probability.These false claims are identical in nature to the false claims contained in Ramsey’s first critique of Keynes in 1922.

It is thus imperative that insurance analysts seriously think about reconsidering Keynes’s theory as it is built upon a Boolean algebra and logic that is the foundation of many fields today such as artificial intelligence and computer languages.

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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.

______. (2004b). Essays on John Maynard Keynes and …. Xlibris Corporation; Philadelphia ,Pennsylvania.

Brady, Michael Emmett.(2021a).How SIPTA overlooked Keynes’s major contributions to imprecise probability and decision making,1999-2019.International Journal of Management Research and Economics,Volume 1,no.3,pp.11-21.

Brady, Michael Emmett.(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 science(s),Volume 24,no.6(special issue),pp.1-19.

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).

Kyburg, H. E. Jr., & Smokler, H. E. (1980). Introduction. In _Kyburg and Smokler,

Studies in Subjective Probability. New York: Wiley(2nd ed.).

Ramsey, F. P. (1922). Mr. Keynes on Probability, Cambridge Magazine, XI, 1, (Jan.).pp 3-5. Reprinted in the 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,

;Kyburg,H.E. and Smokler,H.E.(1980). Studies in Subjective Probability. New York: Wiley(2nd ed.).pp. 25-52.

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.


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