D. E. WATT’S REPLY FOR KEYNES TO RAMSEY IN THE BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE IN 1989 IS DEFECTIVE
D. E. Watt replied to Ramsey’s attacks on Keynes’s Logical Theory of, as originally contained in Keynes’s A Treatise on Probability, in the January 1922 issue of Cambridge Magazine, in the republished British Journal for the Philosophy of Science version.
Watt overlooks that all 15 of Ramsey’s paragraphs in the original Cambridge Magazine version of the paper are erroneous. Watt concentrates only on the issue of numerical versus non numerical probabilities that was raised by Ramsey. Watt is correct in his assessment that Keynes was right and Ramsey was wrong, but gives probability answers that would not have been given by Keynes, or Keynes and Russell. Watt overlooks the errors contained in each paragraph of Ramsey’s review.
Keynes’s main point on the issue of numerical versus non numerical probabilities is that many probabilities, especially initial or a priori probabilities, will have to be specified by interval probability. Keynes’s Principle of Indifference (POI) has nothing to do with this issue, due to Ramsey’s inchoate and erroneous understanding of the conditions Keynes laid out in the A Treatise on Probability for the sound application of the POI, as enunciated by Keynes on pp.52-56, and not on p.42, which is the Laplace -Bernoulli version of the POI. Sound applications of the Keynesian POI require that the alternatives must be a) discrete, b) indivisible, c) finite, d) represented by conditional probability, e) perfectly symmetrical, and f) based on the available, positive evidence. This, of course, rules out any application to states of equally balanced ignorance (no positive information). Of course, there will be only one answer that can be calculated by all rational decision makers. The obvious example is the first Ellsberg urn problem, which is nearly identical to the problem used by Keynes as an example on pp.75-76 of his A Treatise on Probability.
 Arthmar, R. and Brady, M. E. 2018. Boole, Ramsey and the Keynes-Townshend exchanges on subjective probability. Journal of Economic Thought and Policy, 2018(2): 55-74. https://www.francoangeli.it/riviste/Scheda_Rivista.aspx?IDArticolo=63027&Tipo=ArticoloPDF
 Bateman, B. 1987. Keynes’s changing conception of probability. Economics and Philosophy,3: 97-119. DOI: https://doi.org/10.1017/S0266267100002753
 Bateman, B. 1989. ”Human Logic” and Keynes’s Economics: A Comment. Eastern Economic Journal, 15(1): 63-67. Available at: https://www.jstor.org/stable/40325218
 Bateman, B. 1990. Keynes, Induction, and econometrics. History of Political economy, 22(2): 359-380. DOI: https://doi.org/10.1215/00182702-22-2-359
 Bateman, B. 2016. Review of Frank Ramsey (Margaret Paul). HOPE, 48: 181-183.
 Bateman, B. 2021. Introduction to Symposium: Celebrating the Centenary of Keynes’s Treatise on probability. Journal of the History of Economic Thought (December), 43(4). Available at: https://www.cambridge.org/core/journals/journal-of-the-history-of-economic-thought/article/abs/introduction-to-symposium-celebrating-the-centenary-of-keyness-treatise-on-probability/DA1DCE1E7B27406C69600A110600F1CE
 Bateman, B. 2021. Pragmatism and Probability: Re-Examining Keynes’s Thinking on Probability. Journal of the History of Economic Thought, 43(4): 619-632. DOI:https://doi.org/10.1017/S1053837221000365
 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 Science(s), 24(6)(special issue): 1-19. Available at: https://www.abacademies.org/articles/on-the-correction-of-all-thirty-five-errors-contained-in-ramseys-1922-and-1926-reviews-of-keyness-treatise.pdf
 Brady, M.E. 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, M.E. 2004b. Essays on John Maynard Keynes and… Xlibris Corporation. (Pennsylvania; Philadelphia)
 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.org/10.51483/IJMRE.1.3.2021.11-21
 Braithwaite, R.B. 1973. Editorial Foreword to A treatise on Probability, Vol.8, CWJMK edition. London, Macmillan, pp.xiv-xxii).
 Hailperin, T. 1965. Best possible inequalities for the probability of a logical function of events. American Mathematical Monthly, 72: 343-359. DOI: https://doi.org/10.2307/2313491
 Hailperin, T. 1986. Boole’s Logic and Probability. Amsterdam: North-Holland. 2nd edition, eBook ISBN: 9780080880051
 Hailperin, T. 1996. Sentential Probability Logic. Bethlehem: Lehigh University Press.
 Keynes, J. M. 1921. A treatise on probability. London: Macmillan
 Misak, C. 2020. Frank Ramsey: A Sheer Excess of Powers. Oxford: Oxford University Press.
 Ramsey, F. 1926. Truth and probability. In Mellor, D. H. (Ed.) Foundations: Essays in Philosophy, Logic, Mathematics, and Economics, London: Routledge & Kegan Paul, 1978]; Kyburg, H.E. and Smokler, H.E. (1980). Studies in Subjective Probability. New York: Wiley (2nd ed.), pp. 25-52.
 Ramsey, F. P. 1922. Mr. Keynes on Probability. Cambridge Magazine, XI, 1, (Jan.): 3-5. Reprinted in the British Journal of the Philosophy of Science, 40, [1989, June]: 219-222. Available at: https://www.journals.uchicago.edu/doi/abs/10.1093/bjps/40.2.219
 Russell, B. 1922. Review of A treatise on Probability by John Maynard Keynes. Mathematical Gazette, 11(July): 119-125.
 Watt, D. E. 1989. Not Very Likely: A Reply to Ramsey. The British Journal for the Philosophy of Science, (June), 40(2): 223-227.
Non-Exclusive License under Attribution 4.0 International Public License (CC BY 4.0):
This ‘Article’ is distributed under the terms of the license CC-BY 4.0., which lets others distribute, remix, adapt, and build upon this article, even commercially, as long as they credit this article for the original creation. ASERS Publishing will be acknowledged as the first publisher of the Article and a link to the appropriate bibliographic citation (authors, article title, volume issue, page numbers, DOI, and the link to the Published Article on ASERS Publishing’ Platform) must be maintained.