Betting on Theories

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Cambridge University Press, Feb 26, 1993 - Mathematics - 309 pages
1 Review
This book is a major new contribution to decision theory, focusing on the question of when it is rational to accept scientific theories. The author examines both Bayesian decision theory and confirmation theory, refining and elaborating the views of Ramsey and Savage. He argues that the most solid foundation for confirmation theory is to be found in decision theory, and he provides a decision-theoretic derivation of principles for how many probabilities should be revised over time. Professor Maher defines a notion of accepting a hypothesis, and then shows that it is not reducible to probability and that it is needed to deal with some important questions in the philosophy of science. A Bayesian decision-theoretic account of rational acceptance is provided together with a proof of the foundations for this theory. A final chapter shows how this account can be used to cast light on such vexing issues as verisimilitude and scientific realism.
 

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Patrick Maher has reversed, in an interesting way, the usual steps in the construction of verisimilitude measures. He starts from a Bayesian framework, where it can be proved in a representation theorem that a scientist will have a cognitive utility function.
He gives conditions (resembling TR1, TR2, and TR3) for the cognitive utility u(h, x) of accepting proposition h when x is the true state of the world. This function is 'subjective' in the sense that it depends on the scientist's cognitive interests and preferences.
The truthlikeness v(h, x) of h relative to state x is then defined by v(h,x) = (u(h,x) - u(t,x))/(u({x},x) - u(t,x)) where t is tautology. This function is normalized so that v({x}, x ) = l and v(t, x) = 0. On the basis of v(h, x), Maher defines measures of information c(h) and distance from being true d(h, x), which allow him to express the truthlikeness measure in a combination of the form v(h, x) = yc(h) - d(h, x), where y > 0 which is a generalization of Levi's epistemic utility in the direction of Niiniluoto's min-sum measure.
Maher's book is wonderfully clear and accessible to readers with little mathematical sophistication. His proof of his representation theorem is more accessible than those written by and for mathematicians. By developing a concept of rational cognitive decision making, Betting on Theories opens promising and exciting research programs for both decision making theory and the philosophy of science .In short it is a tour de force for research of this genre and further proof, if any were needed, of Maher's combination of word economy, and lucid realization of his subject matter.
WGP
 

Contents

II
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III
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IV
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V
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VI
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VIII
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IX
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LXII
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