Conclusion
The philosophical controversy concerning the logical status of MAXENTmay be in large measure due to the conflation of two distinct logical roles:(1) A general inductive principle for updating subjective probabilities (2)a supposing rule for moving from one chance probability to another.When judged under standards of dynamic coherence appropriate to (1),MAXENT is found wanting. When judged in terms of the logic appro-priate to (2) MAXENT yields for convex closed constraint sets a reason-able selection function with interesting connections with sufficiency andconditioning. Indeed it is just the features of MAXENT which make itappropriate for (2) which make it inappropriate for (1). MAXENT canbe thought of as part of Bayesian logic. But it is part of the logic ofsupposition rather than the logic of induction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, E.: 1962, ‘On rational betting systems’, Archive für mathematische Logik und Grundlagenforschung 6, 7–29, 112–128.
Adams, E.: 1970, ‘Subjunctive and indicative conditionals’, Foundations of Language 6, 89–94.
Adams, E.: 1975, The Logic of Conditionals, D. Reidel, Dordrecht.
Armendt, B.: 1980, ‘Is there a Dutch book, argument for probability kinematics?’, Philosophy of Science 47, 583–588.
Cheesman, P.: 1983, ‘A method of computing generalized Bayesian probability values for expert systems’, Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, 198–202.
Cheesman, P.: 1985, ‘In defense of probability’, Proc. AAAI-85, 1002–1009.
Csizar, I.: 1975, ‘I-divergence geometry of probability distributions and minimization problems’, Annals of Probability 3, 146–158.
Dawid, A. P. and Stone, M.: 1972, ‘Expectation consistency of inverse probability distributions’, Biometrika 59, 486–489.
Dawid, A. P. and Stone, M.: 1973, ‘Expectation consistency and generalized Bayes inference’, The Annals of Statistics 1, 478–485.
de Finetti, B.: 1937, ‘La prévision: ses lois logiques, ses sources subjectives’, Annales de l'Institut Henri Poincaré 7, 1–68. Tr. as ‘Foresight: Its logical laws, its subjective sources’, in Studies in Subjective Probability, ed. H. E. Kyburg Jr. and H. Smokler (Huntington, N.Y.: Krieger, 1980).
Dempster, A. P.: 1967, ‘Upper and lower probabilities induced by a multivalued mapping’, Annals of Mathematical Statistics 38, 325–339.
Dempster, A. P.: 1968, ‘A generalization of Bayesian inference’, Journal of the Royal Statistical Society, Series B 30, 205–249.
Diaconis, P. and Zabell, S.: 1982, ‘Updating subjective probability’, Journal of the American Statistical Association 77, 822–830.
Diaconis, P. and Zabell, S.: 1983, ‘Some alternatives to Bayes' rule’, Technical Report 205, Dept. of Statistics, Stanford University.
Diaconis, P. and Freedman, D. A.: 1985, ‘Partial exchangeability and sufficiency’, Statistics: Applications and New Directions, ed. J. Goshand J. Roy (Indian Statistical Institute: Calcutta), pp. 205–236.
Dias, P. M. C. and Shimon, A.: 1981, ‘A critique of Jaynes' maximum entropy principle’, Advances in Applies Mathematics 2, 172–211.
Domotor, Z.: 1980, ‘Probability kinematics and the representation of belief change’, Philosophy of Science 47, 384–403.
Dynkin, E.: 1978, ‘Sufficient statistics and extreme points’, Annals of Probability 6, 705–730.
Freedman, D. A.: 1962, ‘Invariants under mixing which generalize de Finetti's theorem’, Annals of Mathematical Statistics 33, 916–923.
Freedman, D. A. and Purves, R. A.: 1969, ‘Bayes method for bookies’, The Annals of Mathematical Statistics 40, 1177–1186.
Frieden, B. R.: 1972, ‘Restoring with maximum likelihood and maximum entropy’, Journal of the Optical Society of America 62, 511–518.
Friedman, K. and Shimony, A.: 1971, ‘Jaynes's maximum entropy prescription and probability theory’, Journal of Statistical Physics 3, 381–384.
Gaifman, H.: forthcoming, ‘A theory of higher order probabilities’, in Probability and Causation: Proceedings of the Irvine Conference, ed. Harper, W. and Skyrms, B., D. Reidel, Dordrecht, Holland.
Gibbard, A.: 1981, ‘Two recent theories of conditionals’, in Ifs, ed. Harper et al., D. Reidel, Dordrecht.
Goldstein, M.: 1983, ‘The prevision of a prevision’, Journal of the AMerican Statistical Association 78, 817–819.
Good, I. J.: 1950, Probability and the Weighing of Evidence, Hafner, New York.
Good, I. J.: 1963, ‘Maximum entropy or hypothesis formation, especially for multidimensional contingency tables’, Annals of Mathematical Statistics 34, 911–934.
Good, I. J.: 1981, ‘The weight of evidence provided by uncertain testimony or from an uncertain event’, Journal of Statistical Computation and Simulation 13, 56–60.
Hacking, I.: 1967, ‘Slightly more realistic personal probability’, Philosophy of Science 34, 311–325.
Heath, D. and Sudderth, W.: 1972, ‘On a theorem of de Finetti, oddsmaking and game theory’, Annals of Mathematical Statistics 43, 2072–2077.
Heath, D. and Sudderth, W.: 1978, ‘On finitely additive priors, coherence, and extended admissibility’, Annals os Statistics 6, 333–345.
Hipp, C.: 1974, ‘Sufficient statistics and exponential families’, Annals of Statistics 2, 1283–1292.
Hunter, D.: 1986, ‘Uncertain reasoning using maximum entropy inference’, in Uncertainty in Artificial Intelligence, ed. L. K. Konol and J. F. Lemmaer, Elsevier Science Publishers, Amsterdam.
Jaynes, E. T.: 1957, ‘Information theory and statistical mechanics’, Physical Review 106, 620–630.
Jaynes, E. T.: 1963, ‘Information theory and statistical mechanics’, in Statistical Physics, ed. Ford, Benjamin, N.Y., pp. 181–218.
Jaynes, E. T.: 1967, ‘Foundations of probability theory and statistical mechanics’, Delaware Seminar in the Foundations of Physics, ed. Bunge, Springer, Berlin, 77–101.
Jaynes, E. T.: 1974, Probability Theory with Applications in Science and Engineering, Department of Physics Washington Univeristy, St. Louis.
Jaynes, E. T.: 1980, ‘Where do we stand on maximum entropy’, in The Maximum Entropy Formalism, ed. Levine and Tribus, MIT Press, Cambridge, 15–118.
Jeffrey, R.: 1965, The Logic of Decision, McGraw Hill, N.Y. (2nd ed., University of Chicago Press: Chicago, 1983).
Jeffrey, R.: 1968, ‘Probable knowledge’, in The Problem of Inductive Logic, ed. Lakatos, North Holland, Amsterdam.
Kemeny, J.: 1955, ‘Fair bets and inductive probabilities’, Journal of Symbolic Logic 20, 263–273.
Koopman, B. O.: 1936, ‘On distributions admitting a sufficient statistic’, Transactions of the American Mathematical Society 39, 399–409.
Kullback, S. and Liebler, R.: 1951, ‘On information and sufficiency’, Annals of Mathematical Statistics 23, 8–102.
Kullback, S.: 1959, Information Theory and Statistics, Wiley, New York.
Kupperman, M.: 1958, ‘Probabilities of hypotheses and information-statistics in sampling from exponential class populations’, Annals of Mathematical Statistics 29, 571–574.
Lane, D. and Sudderth, W.: 1983, ‘Coherent and continuous inference’, The Annals of Statistics 11, 114–120.
Lehman, R.: 1955, ‘On confirmation and rational betting’, Journal of Symbolic Logic 20, 251–262.
Lewis, David: 1976, ‘Probabilities of conditionals and conditional probabilities’, Philosophical Review 85, 297–315.
Lewis, David: 1973, Counterfactuals, Blackwell, Oxford.
May, S. and Harper, W.: 1976, ‘Toward an omtimization procedure for applying minimum change principles in probability kinematics’, Foundations of Probability Theory, Inductive Inference, and Statistical Theories of Science 1 (Reidel: Dordrecht), pp. 137–166.
Ramsey, F. P.: 1931, ‘Truth and probability’, in The Foundations of Mathematics and Other Essays, ed. R. B. Braithwaite (N.Y.: Harcourt Brace), and in Studies in Subjective Probability, ed. H. Kyburg and H. Smokler (Huntington, N.Y.: Krieger, 1980).
Seidenfeld, T.: ‘Entropy and uncertainty’, forthcoming in Philosophy of Science.
Shafer, G.: 1976, A Mathematical Theory of Evidence, Princeton University Press, Princeton, N.J.
Shafer, G.: 1981, ‘Jeffrey's rule of conditioning’, Philosophy of Science 48, 337–362.
Shimony, A.: 1955, ‘Coherence and the axioms of confirmation’, Journal of Symbolic Logic 20, 1–28.
Shimony, A.: 1973, ‘Comment on the interpretation of inductive probabilities’, Journal of Statistical Physics 9, 187–191.
Shore, J. and Johnson, R.: 1980, ‘Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy’, IEEE Transactions in Information Theory It-26 1, 26–37.
Skyrms, B.: 1980a, Causal Necessity, Yale University Press, New Haven, Appendix 2.
Skyrms, B.: 1980b, ‘Higher order degrees of belief’, in Prospects for Pragmatism, ed. D. H. Mellor, Cambridge University Press, Cambridge.
Skyrms, B.: 1983, ‘Zeno's paradox of measure’, in Physics, Philosophy, and Psychoanalysis, ed. R. S. Cohen and L. Laudan, D. Reidel, Dordrecht, Holland, 223–254.
Skyrms, B.: 1984, Pragmatics and Empiricism, Yale University Press, New Haven, Conn.
Skyrms, B.: 1985, ‘Maximum entropy inference as a special case of conditionalization’, Synthese 63, 55–74.
Skyrms, B.: (1987a), ‘Dynamic coherence and probability kinematics’, in Philosophy of Science 54, 1–20.
Skyrms, B.: (1987b), ‘Dynamic coherence’, in Advances in the Statistical Sciences VII Foundations of Statistical Inference, ed. I. B. MacNeill and G. Umphrey, D. Reidel, Dordrecht, 233–243.
Skyrms, B.: (1987c), ‘Coherence’, in Scientific Inquiry in Philosophical Perspective, ed. N. Rescher, University of Pittsburgh Press, Pittsburgh, 225–242.
Skyrms, B.: (forthcoming), ‘The value of knowledge’, in Justification Discovery, and Evolution of Scientific Theories, ed. C. Wade Savage, University of Minnesota Press, Minneapolis.
Stalnaker, R. C.: 1968, ‘A theory of conditionals’, Studies in Logical Theory, ed. N. Rescher, Blackwell, London.
Teller, P.: 1973, ‘Conditionalization and observation’, Synthese 26, 218–258.
Teller, P.: 1976, ‘Conditionalization, observation, and change of preference’, in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, ed. W. Harper and C. Hooker (D. Reidel), (Dordrecht-Holland), pp. (205–253).
Tjur, T.: 1974, Conditional Probability Distributions, Lecture Notes 2, Institute of Mathematical Statistics, University of Copenhagen, Sections 36, 37.
van Campenhout, J. and Cover, T.: 1981, ‘Maximum entropy and conditional probability’, IEEE Transactions on Information Theory IT-27, 483–489.
van Fraassen, B.: 1980, ‘Rational belief and probability kinematics’, Philosophy of Science 47, 165–187.
van Fraassen, B.: 1981, ‘A problem for relative information minimizers in probability kinematics’, British Journal for the Philosophy of Science 32, 375–379.
van Fraassen, B.: 1984, ‘Belief and the will’, Journal of Philosophy 81, 235–256.
Williams, P. M.: 1980, ‘Bayesian conditionalization and the principle of minimum information’, British Journal for the Philosophy of Science 31, 131–144.
Zabell, S.: 1974, ‘A limit theorem for conditional expectations with applications to probability theory and statistical mechanics’, PhD. Dissertation, Harvard University Cambridge, Massachusetts.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Skyrms, B. Updating, supposing, and maxent. Theor Decis 22, 225–246 (1987). https://doi.org/10.1007/BF00134086
Issue Date:
DOI: https://doi.org/10.1007/BF00134086