




A Treatise On Probability  Unabridged [Hardcover]
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Item description for A Treatise On Probability  Unabridged by John Maynard Keynes...
An Unabridged Printing, With Bibliography And A Comprehensive Index. Chapters Include: The Meaning Of Probability  Probability In Relation To The Theory Of Knowledge  The Measurement Of Probabilities  The Principle Of Indifference  Other Methods Of Determining Probabilities  The Weight Of Arguments  Historical Retrospect  The Frequency Theory Of Probability  The Theory Of Groups, With Special Reference To Logical Consistence, Inference, And Logical Priority  The Definitions And Axioms Of Inference And Probability  The Fundamental Theorems Of Necessary Inference  The Fundamental Theorems Of Probable Inference  Numerical Measurement And Approximation Of Probabilities  Some Problems In Inverse Probability, Including Averages  The Nature Of Argument By Analogy  The Value Of Multiplication Of Instances, Or Pure Induction  Some Historical Notes On Induction  The Meanings Of Objective Chance, And Of Randomness  Some Problems Arising Out Of The Discussion Of Chance  The Application Of Probability To Conduct  The Nature Of Statistical Inference  The Law Of Great Numbers  The Theorems Of Bernoulli, Poisson, And Tchebycheff  Etc., Etc. Promise Angels is dedicated to bringing you great books at great prices. Whether you read for entertainment, to learn, or for literacy  you will find what you want at promiseangels.com!
Item Specifications...
Pages 480
Est. Packaging Dimensions: Length: 9.1" Width: 5.9" Height: 1.4" Weight: 1.75 lbs.
Binding Hardcover
Release Date May 5, 2007
Publisher Watchmaker Publishing
ISBN 1929148763 ISBN13 9781929148769

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More About John Maynard Keynes


John Maynard Keynes (18831946) is widely considered to have been the most influential economist of the 20th century. His key books include The Economic Consequences of the Peace (1919); A Treatise on Probability (1921); A Tract on Monetary Reform (1923); A Treatise on Money (1930); and his magnum opus, the General Theory of Employment, Interest, and Money (1936). Robert Skidelsky is Emeritus Professor of Political Economy at the University of Warwick, England, and a member of the House of Lords. His threevolume biography of Keynes received numerous awards, including the Lionel Gelber Prize and the Council on Foreign Relations Prize.
John Maynard Keynes was born in 1883 and died in 1946 and has an academic affiliation as follows  University of Cambridge.
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 The best book ever written on probability,induction and analogy May 14, 2007 
In this path breaking contribution to the logic of probability,Keynes showed how to adapt the work of George Boole for the purpose of estimating probabilities.Keynes is the first scholar in history to explicitly emphasize the importance of interval estimates in decision making.For Keynes there are only two types of probability estimates,point estimates and interval estimates;ordinal ranking can be incorporated in the interval classification.Unfortunately,Keynes decided to call interval estimates " nonnumerical " probabilities.His reasoning is really quite obvious.A precise estimate of probability used a single numeral for the point estimate.Therefore,an imprecise estimate of probability used two numerals to denote an interval(set).Thus, an interval estimate is not based on the use of a single number or numeral but two numbers or numerals. These types of probabilities are thus " nonnumerical " because you are not using a single numeral.In 1922 and 1926,Frank Ramsey reviewed Keynes's book based on his very brief and haphazard reading of parts of chapters 14 plus 3 pages from Part II and 4 pages from Part V.Keynes's discussion of nonnumerical probabilities takes place in detail in chapters 5,10,15 and 17,although there is a clear discussion of intervals for the careful reader in chapter 3.Keynes then applies his new approach to induction and analogy in chapters 20 and 22,using his concept of " finite probability " ,which applies to both precise ,numerical probabilities and imprecise, nonnumerical probabilities.All of Keynes's discoveries ,however,were ignored by the ignorant Ramsey.It is unfortunate that the editorial foreword to the 1973 Collected Writings of JMK edition of the TP, written by Richard Braithwaite ,simply repeats all of the errors made by Ramsey in his reviews.Consider Braithwaite's paraphrase of Ramsey's argument that " On Keynes's theory it is something of a mystery why the probability relations should be governed by the probability calculus."(p.xx,1973).The answer is quite simple. First,the " non numerical " interval estimates will not be governed by the probability calculus.Second,numerical probability calculations,such as the bluegreen taxi cab problem of Tversky and Kahneman,will only satisfy the probability calculus if the weight of the evidence,w,is equal to 1,where w is defined as an element on the unit interval between 0 and 1 and measures the relative completeness of the available evidence upon which the probability estimates are to be calculated.[To this day(2007)one can regularly read about Keynes's " strange,mysterious,unfathomable,undefined " nonnumerical probabilities in literally hundreds of economics and philosophy journal articles and books that have been written about Keynes's approach to probability since the Ramsey reviews were first published 80 years ago.These reviews are still cited as " overwhelming " evidence that Keynes agreed that Ramsey's critique had completely demolished the entire structure of his logical approach to probability.Nothing could be further from the truth.Ramsey's theory is a special case that holds when all probabilities are numerical.This requires that the weight of the evidence ,w, be equal to 1 so that the probability calculus(addition and multiplication rules) of mathematical probability can be applied.Ramsey's reviews were so poor that Keynes and Bertrand Russell attempted to downplay their relevance so as to save Ramsey from being embarrassed in the academic community.]Keynes then showed that interval estimates,because they frequently overlap and/or will be contained inside another interval,would very likely also,in many cases,be nonmeasurable,noncomparable and/or nonrankable if a decision maker used such order preserving operators like " greater than or equal to " or "less than or equal to " or "equal to".While this is quite obvious to any reader of Part II of the TP,it went completely over Ramsey's head. Keynes's second major advance was to create his "conventional coefficient of weight and risk ", c=p/(1+q)[2w/(1+w)] in sections 7 and 8 of chapter 26 . The goal of the decision maker is to Maximize cA,where A is some outcome.This decision rule solves most of the paradoxes and anomalies that plague subjective expected utility theory.A major accomplishment made by Keynes in chapter 26 of the TP was to specify that the weight of the evidence variable,w,was defined on the unit interval [0,1].It would be forty years before Daniel Ellsberg would define his practically identical variable,rho,on the unit interval between 0 and 1 also,where rho measured the degree of confidence in the decision maker's information base.Since these two measures are one to one onto and isomorphic,Keynesian weight(uncertainty in the General Theory) and Ellsbergian ambiguity measure the same thing and are interchangeable.This means that Ellsberg's analysis can be applied when studying the GT and used to buttress Keynes's theory of liquidity preference in the GT.In Part 5 of this book ,Keynes showed how one could use Chebyshev's Inequality as a lower bound to the normal probability distributions overly precise and inaccurate point estimate . Part 5 of the Treatise,which is based on Part III's analysis of induction and analogy, also includes Keynes's advocacy of the Lexis Q test for the stability of a statistical frequency[law of large numbers].It is this part of the TP that forms the basis,along with chapter 17,of Keynes's exchange with Tinbergen over the logical foundations of econometrics in the Economic Journal in 19391940.Keynes pointed out that ,in order to justify his assumption of normality,Tinbergen needed to apply the Lexis Q test to his time series data.Tinbergen never applied either that test or the Chi Square test for goodness of fit.TINBERGEN NEVER APPLIED ANY GOODNESS OF FIT TEST TO HIS TIME SERIES DATA IN HIS LIFETIME.This will then bring the reader back to Keynes's chapter 8 of the Treatise ,where he presents his own logical frequency interpretation of probability as a special case of his general logical approach to probability.This chapter includes his criticism of Venn's particular version of a frequency approach.
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