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Michael Emmett Brady - One of the best experts on this subject based on the ideXlab platform.
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keynes rejected the concepts of probabilistic truth true expected values true expectations true probability distributions and true probabilities probability begins and ends with probability keynes 1921
Social Science Research Network, 2020Co-Authors: Michael Emmett BradyAbstract:Ramsey’s many, many confusions and errors about Keynes’s Logical Theory of Probability all stemmed from his failure to a) read more than just the first four chapters of Keynes’s A Treatise on Probability(1921),b) his gross ignorance of Boole’s 1854 logical theory of probability that Keynes had built on in Parts II, III, IV, and V of the A Treatise on Probability, c) his complete and total ignorance of real world decision making under time constraint in financial markets(bond, money, stocks, commodity futures),government, industry and business, and d) his complete and total ignorance of the role that intuition and perception played in tournament chess competition under time constraint, a role that was taught to J M Keynes by his father, J N Keynes, a rated chess master who played first board for Cambridge University in the late 1870’s and early 1880’s.Keynes simply generalized the important role of intuition and perception in decision making in tournament chess competition under time constraint (OTB) to real world decision making under time constraint, where there was missing information, unavailable information, incomplete information, unclear information, and conflicting information. Keynes successfully applied his logical theory of probability in 1913 in his Indian Currency and Finance, in 1919 in his Economic Consequences of the Peace, and was a millionaire with vast first hand knowledge, expertise,and experience (only Alan Greenspan had comparable hands on knowledge, experience and expertise. His 2004 paper on the role of uncertainty in the making of monetary policy from 1987 till 2004 shocked and stunned the economics profession) of how decision making under time constraint was done in financial markets(real estate, bonds, money, stocks, commodity futures), government, industry and business. Academia was strictly a part time sideline for Keynes. Against this back drop, an 18 year old boy appeared at Cambridge University who had absolutely NO real world knowledge of what Keynes had mastered.His name was Frank Ramsey.Keynes’s theory was a theory of real world decision making. For just one example ,Keynes realized that ,in the real world of non additive and nonlinear probability, applications involving interval valued probability and decision weights,like his own conventional coefficient, c, Ramsey’s Dutch Book Argument simply did not apply. However, in the academic world of additive probability, where academicians served to provide the “…forces of banking and finance …” with a variety of “…pretty, polite techniques, made for a well paneled Board Room and a nicely regulated market…”,Keynes saw that there was a place for Ramsey ,where he would be dominating .Ramsey was a very keen and sharp thinker who would have a great career publishing articles and Books- in academia. Keynes also liked those who challenged him intellectually,even if they were quite wrong. After Ramsey published an error filled paper in the 1922 Cambridge Magazine challenging Keynes, which it is clear was never refereed, a myth arose that Ramsey had single handedly confronted Keynes in person one-one-one and showed Keynes that his logical theory of probability was full of all types of logical, philosophical ,and epistemological holes .According to Misak (2020),Ramsey “….shook Keynes’s confidence in his newly published probability theory…” .Supposedly, Keynes then quickly agreed with Ramsey and adopted Ramsey’s subjective ,additive, linear theory of probability in 1931. The problem here is that MIsak is completely and totally ignorant and confused, since ,at best, Ramsey’s theory, which is additive, linear, and deals with mere degrees of belief is a SPECIAL case of Keynes’s general theory, which is non additive, non linear,and deals with degrees of RATIONAL belief. Keynes was never shaken by Ramsey’s theory ,as he was conversant with Borel’s earlier work that also used a betting quotient approach as a foundation for subjective probability. Anyone who has read Parts II, III, IV and V of the A Treatise on Probability can avoid coming to the conclusion that Keynes was “shaken” by Ramsey, since Keynes had been applying his theory successfully in the real world since 1909. Unfortunately, this myth has been given new life in C. Misak’s ( 2020,p.xxvi) biography of Ramsey, where it is asserted that Ramsey easily demolished Keynes’s logical theory of probability and convinced Keynes himself to repudiate his incomprehensible, strange, unfathomable and mysterious beliefs in “ non numerical” probabilities. Of course, It would have been quite impossible for Keynes, the only economist and philosopher in the 20th and 21st centuries to have mastered Boole’s approach, to have accepted Ramsey’s position as it directly contradicted that of Boole, who, according to Bertrand Russell ,was the greatest mathematical logician who ever lived. Of course, since Keynes’s work in the A Treatise on Probability in Parts II-V is directly based on Boole’s theory of interval valued probability, that defined lower and upper probabilities in chapters 16 -21 of the 1854 The Laws of Thought,that are non additive and non linear, and which Keynes applied successfully in the period from 1912 to 1921, Keynes actually took Ramsey’s approach with a grain of salt. Ramsey had made a major advance in strengthening the theoretical and logical foundations of additive and linear probability with his betting quotient-Dutch Book approach to degrees of belief. However, this theory had nothing to offer decision makers operating in a world of nonlinear and non additive probability and degrees of rational belief. For example, Ramsey’s approach is applicable only to rated Correspondence Chess (postal-CC) and never to Over -The -Board (OTB) rated Tournament chess.
Colin Howson - One of the best experts on this subject based on the ideXlab platform.
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beyond finite additivity
2019Co-Authors: Colin HowsonAbstract:Abstract. There is a Dutch Book Argument for the axiom of countable additivity for subjective probability functions, but de Finetti famously rejected the axiom, arguing that it wrongly renders a uniform distribution impermissible over a countably infinite lottery. Dubins however showed that rejecting countable additivity has a strongly paradoxical consequence which a much weaker rule than countable additivity blocks. I argue that this rule, which also prohibits the de Finetti lottery itself, has powerful independent support in a desirable closure principle. I leave it as an open question whether countable additivity itself should be adopted.
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de finetti countable additivity consistency and coherence
The British Journal for the Philosophy of Science, 2008Co-Authors: Colin HowsonAbstract:Many people believe that there is a Dutch Book Argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book Argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea to deductive logic and its own concept of consistency. This I do, showing that at one level the definitions of deductive and probabilistic consistency are identical, differing only in the nature of the constraints imposed. In the probabilistic case I believe that R.T. Cox's ‘scale-free’ axioms for subjective probability are the most suitable candidates.
Pinto Sílvio - One of the best experts on this subject based on the ideXlab platform.
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El Bayesianismo y la Justificación de la Inducción
2002Co-Authors: Pinto SílvioAbstract:The appearance of Bayesian inductive logic has prompted a renewed optimism about the possibility of justification of inductive rules The justifying Argument for the 'rides of such a logic is the famous Dutch Book Argument (Ramsey-de Finetti’s theorem) The issue winch divides the theoreticians of induction concerns the question of whether this Argument can indeed legitimize Bayesian conditionalization rides Here I will be firstly interested in showing that the Ramsey de Finetti's Argument cannot establish that the use of the mentioned conditionalization rides is the best option against Dutch Book betting strategies except in special circum stances I suggest secondly that some presuppositions of the Ramsey de Finetti’s theorem (for instance, the principle of maximization of expected utility) themselves demand a justification.The appearance of Bayesicin inductive logic lias prompted a renewed op tirrusm about the posstbdity of justification of tnductwe rules The justifying Argument for the 'rides of such a logic is the famous Dutch Book Argument (Ramsey-de Finettes theorent) The issue winch divides the theoreticians of induction concerns the question of whether this Argument can indeed legitimize Bayesian conditmalization rides Here I will be firstly interested in showing that the Ramsey de Finetti's Argument cannot establish that the use of the rnentioned conditionalization rides is the best option against Dutch Book betting strategnes except in special circum stances I suggest secondly that some presuppositicms of the Ramsey de Finetti s theorem (for instance, the principie of maximizaticrn of expected utility) themselves demand a justtfication
Sílvio Pinto - One of the best experts on this subject based on the ideXlab platform.
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El Bayesianismo y la Justificación de la Inducción
Universidade Federal de Santa Catarina, 2002Co-Authors: Sílvio PintoAbstract:The appearance of Bayesian inductive logic has prompted a renewed optimism about the possibility of justification of inductive rules The justifying Argument for the 'rides of such a logic is the famous Dutch Book Argument (Ramsey-de Finetti’s theorem) The issue winch divides the theoreticians of induction concerns the question of whether this Argument can indeed legitimize Bayesian conditionalization rides Here I will be firstly interested in showing that the Ramsey de Finetti's Argument cannot establish that the use of the mentioned conditionalization rides is the best option against Dutch Book betting strategies except in special circum stances I suggest secondly that some presuppositions of the Ramsey de Finetti’s theorem (for instance, the principle of maximization of expected utility) themselves demand a justification
Darrell Patrick Rowbottom - One of the best experts on this subject based on the ideXlab platform.
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the insufficiency of the Dutch Book Argument
Studia Logica, 2007Co-Authors: Darrell Patrick RowbottomAbstract:It is a common view that the axioms of probability can be derived from the following assumptions: (a) probabilities reflect (rational) degrees of belief, (b) degrees of belief can be measured as betting quotients; and (c) a rational agent must select betting quotients that are coherent. In this paper, I argue that a consideration of reasonable betting behaviour, with respect to the alleged derivation of the first axiom of probability, suggests that (b) and (c) are incorrect. In particular, I show how a rational agent might assign a ‘probability’ of zero to an event which she is sure will occur.
