A Treatise on Probability [1] is a book published by John Maynard Keynes in 1921. it was a development of his 1909 King's College, Cambridge mathematical Fellowship Treatise originally prepared for publication in 1913 but delayed by the Great War and subsequently revised in 1920.[2]

The Treatise developed the approach of John Venn's Logic of Chance [3] [4], and provides a much broader logic of uncertainty than the more familiar and straightforward 'classical' probability [5] [6].[7] This has since become known as a "logical-relationist" approach.[8] In a 1922 review, Bertrand Russell, the co-author of Principia Mathematica, called it "undoubtedly the most important work on probability that has appeared for a very long time," and said that the "book as a whole is one which it is impossible to praise too highly."[9]

The Treatise presented an approach to uncertainty that was more subject to variation with evidence than the highly quantified classical probability. [10] Keynes's conception of this broader notion of probability is that it is a strictly logical relation between evidence and hypothesis, a degree of partial implication. Keynes's Treatise is the classic account of the logical interpretation of probability (or probabilistic logic), a view of probability that has been continued by such later works as Carnap's Logical Foundations of Probability and E.T. Jaynes Probability Theory: The Logic of Science.

Keynes saw numerical probabilities as special cases of probability, which did not have to be quantifiable or even comparable.[5] [11]

Keynes, in chapter 3 of the "A Treatise on Probability", used the example of taking an umbrella in case of rain to express the idea of uncertainty that he dealt with by the use of interval estimates in chapters 3, 15, 16, and 17 of the "A Treatise on Probability". Intervals that overlap are not greater than, less than or equal to each other. They can't be compared[6].

Is our expectation of rain, when we start out for a walk, always more likely than not, or less likely than not, or as likely as not? I am prepared to argue that on some occasions none of these alternatives hold, and that it will be an arbitrary matter to decide for or against the umbrella. If the barometer is high, but the clouds are black, it is not always rational that one should prevail over the other in our minds, or even that we should balance them, though it will be rational to allow caprice to determine us and to waste no time on the debate.[12]

Keynes noted the limitations of 'mathematical expectation' for 'rational' decision making [13], a point taken up in his more well-known General Theory of Employment, Interest and Money, specifically underpinning his thinking on the nature and role of long-term expectation in economics, notably on Animal spirits. However it has often been regarded as more philosophical in nature despite extensive mathematical formulations.[14]

References

  1. ↑ Keynes, John Maynard (1921), Treatise on Probability, London: Macmillan & Co.
  2. ↑ Skidelsky, Robert (1992). John Maynard Keynes: the Economist as Saviour 1920-1937. London: Macmillan.
  3. ↑ Venn, John (1888). The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability, with especial reference to its logical bearings and its application to moral and social sciences and to Statistics (PDF) (3rd ed.). London and New York: Macmillan. Retrieved 30 November 2023.
  4. ↑ See Keynes' Bibliography
  5. 1 2 e.g. pgs 34, 112 of the Treatise, with examples from pg 22.
  6. 1 2 Skidelsky, Robert (September 14, 2009). Keynes: Return of the Master. PublicAffairs.
  7. ↑ Keynes discusses the logical use of the term 'certainty' on pg 15 of the Treatise.
  8. ↑ "John Maynard Keynes, 1883-1946". The New School. Archived from the original on July 23, 2011.
  9. ↑ Russell, Bertrand (July 1948). "Review: A Treatise on Probability by John Maynard Keynes". Mathematical Gazette. 32 (300): 152–159. doi:10.2307/3609931. JSTOR 3609931.
  10. ↑ e.g pg 169 of the Treatise considers evidence about the fairness of a coin obtained from coin tossing.
  11. ↑ Gerrad, Bill (2003). John Edward King (ed.). The Elgar Companion to Post Keynesian Economics. Edward Elgar Publishing. p. 161. ISBN 978-1-84064-630-6.
  12. ↑ Keynes, John (2004). A Treatise on Probability. New York: Dover Publications. p. 30. ISBN 978-0-486-49580-4.
  13. ↑ pgs 311-316
  14. ↑ Broad, C. D. (January 1922). "Review: A Treatise on Probability by J. M. Keynes". Mind. New Series. Oxford University Press on behalf of the Mind Association. 31 (121): 72–85. doi:10.1093/mind/XXXI.121.72. JSTOR 2249688.
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