# Betting on Theories

Cambridge University Press, Feb 26, 1993 - Mathematics - 309 pages
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 2 III 6 IV 10 V 13 VI 20 VII 22 VIII 24 IX 26
 LXII 136 LXIII 138 LXIV 140 LXV 144 LXVI 148 LXVII 150 LXVIII 153 LXIX 156

 X 30 XI 35 XII 37 XIV 39 XV 43 XVI 46 XVII 48 XVIII 49 XIX 50 XX 52 XXI 54 XXII 58 XXIII 61 XXIV 64 XXVI 67 XXVII 71 XXVIII 75 XXIX 77 XXX 80 XXXI 82 XXXII 83 XXXIII 84 XXXIV 85 XXXV 87 XXXVI 89 XXXVII 92 XXXVIII 94 XXXIX 95 XL 96 XLI 97 XLII 98 XLIII 100 XLIV 103 XLV 106 XLVI 107 XLVII 108 XLVIII 111 XLIX 114 L 115 LI 117 LII 121 LIII 122 LIV 124 LV 126 LVI 127 LVII 128 LVIII 129 LIX 131 LX 134 LXI 135
 LXX 157 LXXI 159 LXXII 162 LXXIII 163 LXXIV 170 LXXV 174 LXXVI 182 LXXVII 183 LXXVIII 186 LXXIX 187 LXXX 188 LXXXI 189 LXXXII 191 LXXXIII 193 LXXXIV 194 LXXXV 196 LXXXVI 198 LXXXVII 199 LXXXVIII 201 LXXXIX 203 XC 204 XCI 207 XCII 209 XCIII 210 XCIV 211 XCV 214 XCVI 215 XCVII 217 XCVIII 219 XCIX 221 C 225 CI 228 CII 232 CIV 235 CV 238 CVI 241 CVII 246 CIX 250 CX 251 CXI 260 CXII 266 CXIV 268 CXVII 270 CXVIII 274 CXIX 282 CXX 288 CXXI 293 CXXII 308 Copyright