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Rating: 
Summary: Again,Hacking gets it right except for Keynes's theory
Review: Moving from Pascal and Bernoulli in the 16th and 17th centuries through Keynes, Carnap,Ramsey, de Finetti and Heisenberg in the 20th century,Hacking(H)does a commendable job blending the philosophy and history of science with the history and philosophy of probability.H's tie in of Pascal's Wager and decision theory is just one example of his ability to connect the ideas of different centuries to each other.However,there is one small criticism that must be made.It is in regards to J M Keynes's logical theory of probability put forth in A Treatise on Probability(TP) in 1921.H bases his assessment of Keynes's theory on one chapter of the TP alone.That chapter,chapter 3,was to be regarded as an introduction only.Keynes's point was that,in general,a probability could not be measured by a single number or numeral alone,i.e.,probabilities were "nonnumerical"or not by a single numeral(number).In general,Keynes argued that most probabilities required TWO numbers to specify the probability estimate,a lower bound and an upper bound.In Part II of the TP Keynes refers to his theory of "approximation".In modern terminology,Keynes's interval estimates are "indeterminate" or"imprecise" probabilities.Given the above summary of Keynes's approach to probability,the following statement by H is incorrect and very misleading:"Indeed Keynes argued masterfully in Chapter 3 of his A Treatise on Probability that many comparisons of probability are necessarily qualitative and cannot be represented by real numbers."(Hacking,p.73)While it is true that most probabilities cannot be represented by A SINGLE REAL NUMBER,most probabilities can be represented by TWO REAL NUMBERS in Keynes's approach.A strictly qualitative approach would be practically useless.Probability would not be the guide to life.
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Summary: A stimulating tour de force
Review: This is a great book. Hacking describes the development of probability and statistics from the Renaissance to David Hume. His central questions are: What were Pascal, Huygens, Leibniz, Jacques Bernoulli, and all the others really doing? What problems were they trying to solve? What limitations were they working under? How did all this fit into other intellectual and mathematical problems of the day? How did all this affect the subsequent development of probability and statistics? Some of this clears up minor details that I had never grasped before, such as what was the problem with two dice that Pascal solved for the Chevalier de Mere. More important is the description of the intellectual implications of the development of modern probability and statistics. I had not known that the very name "probability" grew out of a profound religious and intellectual argument between the Jansenist Pascal and the Jesuits.The book is full of historical gems. For example, the Dutch and English governments in the seventeenth century became infatuated with annuities as a way to finance theor expenses, especially wars. Most of the schemes were actuarially unsound. The early statisticians devoted a lot of energy to this problem and this led to major advances. Unfortunately the governments were not always pleased to be told they had no clothes. It all sounds terribly up to date. In summary, this book covers material that is important not only in a histroical context but also for its relvance to many contemporary issues. It is well written and concise. If you want to know what the early probabilists were thinking about and how that affected the way we all think about uncertainty today, this is the book for you.
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