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Author: Michael Emmett Brady
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Languages : en
Pages : 0
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J M Keynes's A Treatise on Probability is built on the mathematical and logical foundations of G E Boole's 1854 The Laws of Thought. Boole introduced the first technical attempt (Adam Smith was the first to specify and solve two such indeterminate problems in The Wealth of Nations) at systematically solving indeterminate, probability problems (where, under uncertainty, relevant knowledge or evidence is missing) using interval valued probability. His systematic techniques were presented in chapters 16-21 of The Laws of Thought. Fisher's review of the A Treatise on Probability demonstrates an astounding degree of ignorance on his part. Fisher has no idea of what an indeterminate probability is. For Fisher, ALL probabilities MUST be point estimates. We will show that Fisher, a biologist wedded to the Limiting (Relative) Frequency interpretation of probability, had no idea about what Keynes was doing or talking about in Parts I-IV of the A Treatise on Probability. We will conclude that Fisher was foolish to attempt a review of the A Treatise on Probability knowing that he had not read Boole. This conclusion is then shown to apply to practically all modern, twentieth and twenty-first century writers on the A Treatise on Probability.
Author: Michael Emmett Brady
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Languages : en
Pages : 0
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J M Keynes's A Treatise on Probability is built on the mathematical and logical foundations of G E Boole's 1854 The Laws of Thought. Boole introduced the first technical attempt (Adam Smith was the first to specify and solve two such indeterminate problems in The Wealth of Nations) at systematically solving indeterminate, probability problems (where, under uncertainty, relevant knowledge or evidence is missing) using interval valued probability. His systematic techniques were presented in chapters 16-21 of The Laws of Thought. Fisher's review of the A Treatise on Probability demonstrates an astounding degree of ignorance on his part. Fisher has no idea of what an indeterminate probability is. For Fisher, ALL probabilities MUST be point estimates. We will show that Fisher, a biologist wedded to the Limiting (Relative) Frequency interpretation of probability, had no idea about what Keynes was doing or talking about in Parts I-IV of the A Treatise on Probability. We will conclude that Fisher was foolish to attempt a review of the A Treatise on Probability knowing that he had not read Boole. This conclusion is then shown to apply to practically all modern, twentieth and twenty-first century writers on the A Treatise on Probability.
Author: Michael Emmett Brady
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Languages : en
Pages : 0
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Arne Fisher attempted a cover up of an important footnote in chapter 29 of the A Treatise on Probability (1921), in which Keynes made it clear that he was not going to use the modern Method of Moments, which used a Moment Generating Function approach based on a Taylor Series expansion very similar to the Maclaurin Series, a special case of the Taylor series expansion, used by Keynes in chapter 17 of the A Treatise on Probability. Cumulants and semi-invariants, which A. Fisher claimed Keynes had no inkling of and did not understand, are simply terms used to describe particular parts of the Taylor series expansion carried out to provide the optimal estimate of a series using the Moment Generating Function technique. A. Fisher attempted to create the illusion that Keynes had made a number of very critical comments about the mathematical capabilities of Laplace, Bernoulli, and Poisson on pp. 358-361 of the A Treatise on Probability. These are figments of Fisher's own imagination. A. Fisher's “review” is really about one section of one chapter, chapter 29, sections 16-18, pp. 358-361, of the A Treatise on Probability. Nowhere in these pages will a reader find any such comments. A. Fisher, in his “review,” also sought to create the illusion that there were many mathematical errors in the A Treatise on Probability in these sections. In reality, there are no mathematical errors in these sections. Keynes simply used an older method of generating values for the Poisson distribution instead of using the most modern approach, the Method of Moments, which used the Moment Generating Function, with which Keynes was well acquainted with. A. Fisher gambled that no one reading his “review” would go back and check to see if his comments were correct. His gambit worked for nearly 94 years.
Author: Michael Emmett Brady
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Languages : en
Pages : 0
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R. Pearl's attempt to review J M Keynes's A Treatise on Probability for Science is only a near fiasco compared with the failed attempt made by Ronald Fisher to review Keynes's book for the Eugenics Society. It provides the educated reader with minimal value. How this review made it through the referees, associate editors, and editors at the journal, Science, is a mystery worthy of investigation. Again, anyone attempting to read or review Keynes' A Treatise on Probability, without having any knowledge or familiarity of how J M Keynes made use in the A Treatise on Probability of George Boole's application of his logic to probability in chapters 16-21 of The Laws of Thought (1854), is foolish.
Author: Michael Brady
Publisher: Xlibris Corporation
ISBN: 1524544892
Category : Philosophy
Languages : en
Pages : 179
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Book Description
The standard view of the economics profession is that Keynes was a brilliant, intuitive, nonrigorous innovator. These essays show that Keynes backed up his intuitions with a rigorous mathematical and logical supporting analysis, which has been overlooked.
Author: John Maynard Keynes
Publisher:
ISBN:
Category : Probabilities
Languages : en
Pages : 494
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Author: Michael Emmett Brady
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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C. D. Broad presents an excellent, overall view of how the A Treatise on Probability (1921) was written and constantly checked by internationally recognized and acclaimed philosophers and mathematical logicians, such as Bertrand Russell, Alfred North Whitehead, John Nevile Keynes, C. D. Broad himself, and especially William Ernest Johnson. Broad was the only reviewer to explicitly reveal the substantial role played by the applied mathematician and philosopher W. E. Johnson.Broad also carefully assessed Keynes's weight of the argument (evidence) criteria in Chapter 6 of the A Treatise on Probability, as did F. Y. Edgeworth. Neither of them found any errors.
Author: Michael Emmett Brady
Publisher:
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Category :
Languages : en
Pages : 13
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Ramsey's 1922 “review” of J M Keynes's A Treatise on Probability (1921) is an intellectual mess. Ramsey fails to score even one point against Keynes. It was most likely published because of Ramsey's alleged reputation as the “boy genius”. There are myriad errors in the review. For just one instance, consider the claim that Part III of the A Treatise on Probability relies only on Mills' Method of Agreement. This would mean that Keynes only considered a concept of similarity, a concept that Ramsey had no clue about. In fact, Keynes's analysis is based on degrees of similarity and dissimilarity. It is quite impossible to understand Part III if the reader has not mastered the Boolean framework erected by Keynes in Part II. Ramsey did not have the slightest clue about the interval estimate approach used by Keynes in Part II of the TP. Ramsey had no idea that Keynes rejected the axiom of additivity except in the special case where the weight of the evidence, w, equaled one and the decision maker had linear probability preferences.
Author: John Maynard Keynes
Publisher:
ISBN: 9780333496374
Category :
Languages : en
Pages : 514
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 466
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Author: Michael Emmett Brady
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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F. Y. Edgeworth, in 1922, demonstrated a very deep and penetrating understanding of the technical, mathematical, logical and statistical analysis provided by J M Keynes in 1921 in his magnum opus, the A Treatise on Probability. No other reviewer, except Bertrand Russell, showed such a great understanding of Keynes's book. Edgeworth's two reviews are, however, carried out with very high technical and analytic standards of mathematical, logical, statistical, and philosophical care. Edgeworth understood, like no other reviewer at that time or since, the great strengths of Keynes's breakthroughs, as well as what the limitations of Keynes's theory were.The Keynesian Fundamentalists lacked the technical training in mathematics, logic, and statistics that would be required to follow and duplicate what Edgeworth was doing in these reviews. Therefore, the two Edgeworth reviews and their content were skipped over by the Keynesian Fundamentalists, as well as by all other philosophers and economists. This unfortunate result was probably strengthened by the appearance in 2002 of a strange piece written on the history of economic thought at the interface between economics and statistics by Steven Stigler that erroneously claimed that Edgeworth's reviews of Keynes's A Treatise on Probability were as highly critical of Keynes's work as was the empty diatribe published by Ronald Fisher in 1923 in the Eugenics Review. Nothing could be further from the truth.This paper demonstrates that there is no Keynesian Fundamentalist, philosopher or economist who is even close to Edgeworth in his grasp and understanding of the detailed mathematical and logical analysis provided by Keynes in 1921.All of the valuable summaries, analysis, commentary, support, and criticism of the positions presented by Keynes in the formulation of his logical approach to probability, made by Edgeworth in his two reviews of Keynes's A Treatise on Probability (1921) in 1922, were lost in the years between 1922 and 2016.
