A Treatise On Probability - Unabridged [Hardcover]

John Maynard Keynes (Author)

Book Description

ISBN-10: 1929148763 | ISBN-13: 978-1929148769 | Publication Date: May 5, 2007 | Edition: Unabridged

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.

Product Details

• Hardcover: 480 pages
• Publisher: Watchmaker Publishing; Unabridged edition (May 5, 2007)
• Language: English
• ISBN-10: 1929148763
• ISBN-13: 978-1929148769
• Product Dimensions: 9.1 x 5.9 x 1.4 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #916,493 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

12 of 17 people found the following review helpful:

5.0 out of 5 stars The best book ever written on probability,induction and analogy, May 14, 2007

By 

Michael Emmett Brady "mandmbrady" (Bellflower, California ,United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: A Treatise On Probability - Unabridged (Hardcover)

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 " 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 the use of a single number or numeral but two numbers or numerals. 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 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 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 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(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.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 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.

4 of 6 people found the following review helpful:

5.0 out of 5 stars this is a book to be read by people interested in the foundations of Probability, October 5, 2008

By 

Antonio L. Rodriguez "arlc" (Spain) - See all my reviews
(REAL NAME)   

This review is from: A Treatise On Probability - Unabridged (Hardcover)

Keynes is very clear in his writings. The book is an amplification of his disertation thesis. It is easy to read and not out of date. The book has special value from the philosophical point of view. It is also a compulsory reading for the students and people interested in the history of Mathematics.