A Treatise On Probability | 
 enlarge | Author: John Maynard Keynes
Publisher: Rough Draft Printing
Category: Book
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Rating:  6 reviews
Sales Rank: 239407
Media: Paperback
Pages: 480
Number Of Items: 1
Shipping Weight (lbs): 1.8
Dimensions (in): 9.2 x 7.5 x 1.1
ISBN: 1603861181
Dewey Decimal Number: 512
EAN: 9781603861182
ASIN: 1603861181
Publication Date: June 19, 2008
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Product Description
An Unabridged, Digitally Enlarged Printing: 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. - Bibliography And Comprehensive Index
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| Customer Reviews: Read 1 more reviews...
 Very extravagant November 16, 2008
R. NAIQUE
0 out of 4 found this review helpful
In fact the copy I received contains only blank pages, without any text, absolutly none. I don't know if it is odd. May be it is a singular copy. In any case, I am intending to keep the copy I received,and if there is a normal text available, I certainly would like to order one.
R.A.Naique, Lisbon (PORTUGAL)
 Historically important ... but. November 2, 2008
J. Hall (El cajon, ca United States)
1 out of 3 found this review helpful
The author introduces key concepts for the first time. He also introduces some ideas that I had not seen before. The book is historically important. However, the author's writing style is very much a product of his time - obviously brevity was not considered a virtue. The book is really, painfully long. If you are a historian, great. If you are looking for key concepts in statistical theory, there are other books that will get to the point much quicker.
 Oustanding! February 14, 2008
Jean-claude Couture
2 out of 4 found this review helpful
This is an outstanding book from an outstanding mind better known from his revolutionary economic ideas.
Contains the first mathematically designed interval estimate approach to probability in history August 11, 2007
Michael Emmett Brady (Bellflower, California ,United States)
1 out of 8 found this review helpful
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 into the interval estimate classification.Unfortunately,Keynes decided to call interval estimates " non-numerical " probabilities.His reasoning is really quite obvious.A precise estimate of probability used a single numeral for the point estimate.Therefore,an imprecise,indeterminate 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.This is what Ramsey fundamentally objected to. These types of probabilities are ,thus ," non-numerical " because you are not using a single numeral.In 1922 and 1926,Frank Ramsey reviewed Keynes's book based on his very brief,partial, and haphazard reading of parts of chapters 1-4 plus 3 pages from Part II and 4 pages from Part V.Keynes's discussion of non-numerical probabilities takes place in detail in chapters 5,10,15 and 17,although there is a clear discussion of intervals for the careful reader contained 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, non-numerical 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 really quite simple. First,the " non numerical " interval estimates will not be governed by the probability calculus rules of conjunction and disjunction.Second,numerical probability calculations,such as the blue-green 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 calculatedKeynes was the first scholar in history to define and create an index to measure the weight of the evidence .[To this day(2007)one can regularly read about Keynes's " strange,mysterious,unfathomable,undefined " non-numerical 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.Ramsey's 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 only when all the probabilities are numerical,additive,precise, and unique.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 who has covered pp.160-163 and pp.186-194 of the TP or the comparable pages from Booles 1854 classic,p.268,pp.276-278,pp.281-283,etc.,it went completely over Ramsey's head.Ramsey had never comprehended what it was that Booole was doing in Part V of the Laws of Thought. 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.You simply substitute rho for w in the c formula above or substitute w for rho in Ellsberg's decision rules.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 dynamic stability of a statistical frequency[law of large numbers]over time.It is this part of the TP that forms the basis,along with chapter 17's analysis of the misuse of the Normal distribution in science and social science,of Keynes's exchange with Tinbergen over the logical foundations of econometrics(the use of multiple regression and correlation analysis in the study of time series data) in the Economic Journal in 1939-1940.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.
Treats mathematical probability as a limiting case of logical probability September 18, 2006
Michael Emmett Brady (Bellflower, California ,United States)
8 out of 13 found this review helpful
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.Unfortunately,Keynes decided to call interval estimates " non-numerical "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 a single numeral but two. These types of probabilities are thus " non-numerical "because you are not using a single numeral.In 1922 and 1926,Frank Ramsey reviewed Keynes's book based on his reading of chapters 1-4 plus 3 pages from Part II and 4 pages from Part V.Keynes's discussion of non-numerical probabilities takes place in chapters 5,10,15 and 17.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, non-numerical 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 blue-green 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(2006)one can regularly read about Keynes's " strange,mysterious,unfathomable,undefined " non-numerical 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 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,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 ".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 also includes Keynes's advocacy of the Lexis Q test for 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 1939-1940.Keynes pointed out that ,in order to justify his assumption of normality,Tinbergen needed to apply the Lexis Q test.Tinbergen never applied either that test or the Chi- Square test for goodness of fit.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 after criticizing Venn's particular version of a frequency approach.
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