''A Treatise on Probability'' is a book published by

John Maynard Keynes John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...

while at

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the world' ...

in 1921. The ''Treatise'' attacked the classical theory of

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...

and proposed a "logical-relationist" theory instead. In a 1922 review,

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...

, the co-author of ''

Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...

'', 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." The ''Treatise'' is fundamentally philosophical in nature despite extensive mathematical formulations. The ''Treatise'' presented an approach to probability that was more subject to variation with evidence than the highly quantified classical version. Keynes's conception 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 The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one be ...

(or

probabilistic logic Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A diffic ...

), a view of probability that has been continued by such later works as

Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. ...

's ''Logical Foundations of Probability'' and

E.T. Jaynes Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis, Missouri, St. Louis. He wrote extensively on statistical mechanics and on foundations of prob ...

''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. 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.

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.

References

{{DEFAULTSORT:Treatise on Probability Keynesian economics Probability books 1921 non-fiction books Books by John Maynard Keynes Macmillan Publishers books Treatises