A Treatise on Probability
There is, first of all, the distinction between that part of our belief which is rational and that part which is not. If a man believes something for a reason which is preposterous or for no reason at all, and what he believes turns out to be true for some reason not known to him, he cannot be said to believe it rationally, although he believes it and it is in fact true. On the other hand, a man may rationally believe a proposition to be probable, when it is in fact false. -from Chapter II: Probability in Relation to the Theory of Knowledge" His fame as an economist aside, John Maynard Keynes may be best remembered for saying, "In the long run, we are all dead." That phrase may well be the most succinct expression of the theory of probability every uttered. For a longer explanation of the premise that underlies much of modern mathematics and science, Keynes's A Treatise on Probability is essential reading. First published in 1920, this is the foundational work of probability theory, which helped establish the author's enormous influence on modern economic and even political theories. Exploring aspects of randomness and chance, inductive reasoning and logical statistics, this is a work that belongs in the library of any interested in numbers and their application in the real world. AUTHOR BIO: British economist JOHN MAYNARD KEYNES (1883-1946) also wrote The Economic Consequences of the Peace (1919), The End of Laissez-Faire (1926), The Means to Prosperity (1933), and General Theory of Employment, Interest and Money (1936).
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actual alternatives application argue argument arise arithmetic mean assert assume assumption axioms Bernoulli's Theorem binary stars cause certainty Chapter characteristic conclusion correlation Daniel Bernoulli defined definition degree of probability depends determine discussed event evidence example existence experience fact favour finite probability follows formula frequency theory fundamental generalisation given greater hypothesis independent inference inverse inverse probability irrelevant judgments knowledge known Laplace law of error Laws of Thought Least Squares Leibniz less limits logical magnitude mathematical mean method Multiplication Theorem negative analogy number of instances numerical measurement objective chance observed occur particular possible posteriori precise premisses Principle of Indifference priori probability prob probable value problem proportion pure induction quantity question random rational belief reason reference relations of probability relative relevant result sense solution statistical frequency suppose Theory of Probabilities tion true valid weight white balls
Page 13 - ... propositions. The mental process by which we pass from direct knowledge to indirect knowledge is in some cases and in some degree capable of analysis. We pass from a knowledge of the proposition a to a knowledge about the proposition by perceiving a logical relation between them. With this logical relation we have direct acquaintance.
Page 19 - Confusion of thought is not always best avoided by technical and unaccustomed expressions, to which the mind has no immediate reaction of understanding; it is possible, under cover of a careful formalism, to make statements, which, if expressed in plain language, the mind would immediately repudiate.
Page 22 - Instead it declared in a more formalist way, that 'probability is the ratio of the number of favourable cases to the total number of equally likely cases'.