A Treatise on Probability,[1] published by John Maynard Keynes in 1921, provides a much more general logic of uncertainty than the more familiar and straightforward 'classical' theories of probability.
[notes 1][3][notes 2]
This has since become known as a "logical-relationist" approach,[5][notes 3]
and become regarded as the seminal and still 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.[8]
Keynes's conception of this generalised notion of probability is that it is a strictly logical relation between evidence and hypothesis, a degree of partial implication. It was in part pre-empted by Bertrand Russell's use of an unpublished version.[9][notes 4]
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."[17][notes 5]
With recent developments in machine learning to enable 'artificial intelligence' and behavioural economics the need for a logical approach that neither assumes some unattainable 'objectivity' nor relies on the subjective views of its designers or policy-makers has become more appreciated, and there has been a renewed interest in Keynes's work.[20][21]
^Keynes 1921.
^Keynes 1921, p. 34,112.
^Skidelsky 2009.
^Keynes 1921, p. 15.
^"John Maynard Keynes, 1883-1946". The New School. Archived from the original on July 23, 2011.
^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.
^Keynes' Bibliography, page 429ff.
^Peden, William (September 2021). "Probability and arguments: Keynes's legacy". Cambridge Journal of Economics. 45 (5): 933–950. Retrieved 29 December 2023.
^Preface to Russell, Bertrand (1912). The Problems of Philosophy. London: Williams and Norgate.
^Keynes 1949.
^Skidelsky 1983, p. 55, 132-160.
^Moore, George Edward (1903). Principia Ethica. Cambridge: Cambridge University Press.
^Russell, Bertrand (1903). The Principles of Mathematics. Cambridge: Cambridge University Press.
^Skidelsky 1983, pp. 254–256, 259, 273–4, 285, 381.
^Skidelsky 1992, pp. 57–89.
^Harrod 1951, p. 153.
^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.
^Russell, Bertrand (1948). Human Knowledge: Its Scope and Limits. London: George Allen and Unwin. p. 397.
^Gaifman, H.; Snir, M. (1982). "Probabilities over rich languages, testing and randomness". J. Symb. Log. 47 (3): 495–548. doi:10.2307/2273587.
^Hosni, Hykel; Landes, Jurgen (June 19, 2023). "Logical perspectives on the foundations of probability". Open Mathematics. 21 (1). Retrieved 29 December 2023.
^Arena, Richard; Nasica, Eric (2021). "Keynes's methodology and the analysis of economic agent behavior in a complex world". Revue d'économie politique. 131 (3): 371–402. doi:10.3917/redp.313.0053.
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