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In Defence of Objective Bayesianism$

Jon Williamson

Print publication date: 2010

Print ISBN-13: 9780199228003

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199228003.001.0001

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(p.173) References

(p.173) References

In Defence of Objective Bayesianism
Oxford University Press

Bibliography references:

Abraham, J. A. (1979). An improved algorithm for network reliability. IEEE Transactions on Reliability, 28, 58–61.

Aczél, J. and Daróczy, Z. (1975). On measures of information and their characterizations. Academic Press, New York.

Alchourrón, C. E., Gärdenfors, P., and Makinson, D. (1985). On the logic of theory change: partial meet functions for contraction and revision. Journal of Symbolic Logic, 50, 510–30.

Amari, Shun‐ichi and Nagaoka, Hiroshi (1993). Methods of information geometry (2000 edn). American Mathematical Society/Oxford University Press. Providence, RI.

Bacchus, Fahiem, Kyburg, Jr., Henry E., and Thalos, Mariam (1990). Against conditionalization. Synthese, 84(3), 475–506.

Baillie, Patricia (1973). Confirmation and the Dutch book argument. The British Journal for the Philosophy of Science, 24(4), 393–7.

Barnett, O. W. and Paris, J. B. (2008). Maximum entropy inference with quantified knowledge. Logic Journal of the IGPL, 16, 85–98.

Bayes, Thomas (1764). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.

Bernoulli, Jakob (1713). Ars Conjectandi (2006 edn). The Johns Hopkins University Press, Baltimore. Translated by Edith Dudley Sylla.

Billingsley, Patrick (1979). Probability and measure (Third (1995) edn). Wiley, New York.

Borel, Emile (1943). Probabilities and life (1962 edn). Dover, New York.

Bovens, Luc and Rabinowicz, Wlodek (2006). Democratic answers to complex questions‐an epistemic perspective. Synthese, 150, 131–53.

Carnap, Rudolf (1950). Logical foundations of probability. Routledge and Kegan Paul, London.

—— (1952). The continuum of inductive methods. University of Chicago Press, Chicago, IL.

Chopra, Samir, Ghose, Aditya, and Meyer, Thomas (2006). Social choice theory, belief merging, and strategy‐proofness. Information Fusion, 7(1), 61–79.

Corfield, David (2001). Bayesianism in mathematics. In Foundations of Bayesianism (eds. D. Corfield and J. Williamson), pp. 175–201. Kluwer, Dordrecht.

Cover, Thomas M. and Thomas, Joy A. (1991). Elements of information theory. Wiley, New York.

(p.174) Cox, R. T. (1946). Probability, frequency and reasonable expectation. American Journal of Physics, 14(1), 1–3.

Dawid, A. P. (1982). The well‐calibrated Bayesian. Journal of the American Statistical Association, 77, 604–13. With discussion.

de Cooman, Gert and Miranda, Enrique (2007). Symmetry of models versus models of symmetry. In Probability and Inference: Essays in Honour of Henry E. Kyburg Jr. (eds. W. Harper and G. Wheeler), pp. 67–149. College Publications, London.

de Finetti, Bruno (1937). Foresight: its logical laws, its subjective sources. In Studies in Subjective Probability (Second (1980) edn) (eds. H. E. Kyburg and H. E. Smokler), pp. 53–118. Robert E. Krieger Publishing Company, Huntington, New York.

Deakin, Michael A. B. (2006). The wine/water paradox: background, provenance and proposed resolutions. The Australian Mathematical Society Gazette, 33, 200–5.

del Val, Alvaro and Shoham, Yoav (1994). A unified view of belief revision and update. Journal of Logic and Computation, 4(5), 797–810.

Delgrande, James P. and Schaub, Torsten (2007). A consistency‐based framework for merging knowledge bases. Journal of Applied Logic, 5(3), 459–77.

Dias, Penha Maria Cardoso and Shimony, Abner (1981). A critique of Jaynes' maximum entropy principle. Advances in Applied Mathematics, 2(2), 172–211.

Dietrich, Franz and List, Christian (2007). Arrow's theorem in judgment aggregation. Social Choice and Welfare, 29(1), 19–33.

Earman, John (1992). Bayes or bust? MIT Press, Cambridge, MA.

Fantl, Jeremy and McGrath, Matthew (2007). On pragmatic encroachment in epistemology. Philosophy and Phenomenological Research, 75, 558–789.

Festa, Roberto (1993). Optimum inductive methods: a study in inductive probability, Bayesian statistics, and verisimilitude. Kluwer, Dordrecht.

Fienberg, Stephen E. (2006). When did Bayesian inference become “Bayesian”? Bayesian Analysis, 1(1), 1–40.

Foley, Richard (1993). Working without a net. Oxford University Press, New York.

Franklin, James (2001). Resurrecting logical probability. Erkenntnis, 55, 277–305.

Fridlyand, J., Snijders, A. M., Ylstra, B., Li, H., Olshen, A., Segraves, R., Dair‐ kee, S., Tokuyasu, T., Ljung, B. M., Jain, A. N., McLennan, J., Ziegler, J., Chin, K., Devries, S., Feiler, H., Gray, J. W., Waldman, F., Pinkel, D., and Albertson, D. G. (2006). Breast tumor copy number aberration phenotypes and genomic instability. BMC Cancer, 6, 96.

Friedman, Kenneth and Shimony, Abner (1971). Jaynes's maximum entropy prescription and probability theory. Journal of Statistical Physics, 3(4), 381–4.

(p.175) Gaifman, H. and Snir, M. (1982). Probabilities over rich languages. Journal of Symbolic Logic, 47(3), 495–548.

Gauwin, Olivier, Konieczny, Sébastien, and Marquis, Pierre (2005). Conciliation and consensus in iterated belief merging. In Proceedings of the 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 514–26. Springer, Berlin.

Gillies, Donald (1991). Intersubjective probability and confirmation theory. British Journal for the Philosophy of Science, 42, 513–33.

—— (2000a). Philosophical theories of probability. Routledge, London and New York.

—— (2000b). Varieties of propensity. British Journal for the Philosophy of Science, 51, 807–35.

Good, I. J. (1952). Rational decisions. Journal of the Royal Statistical Society. Series B, 14(1), 107–14.

Gottfried, Kurt and Wilson, Kennth G. (1997). Science as a cultural construct. Nature, 386, 545–7. With discussion in vol. 387 p. 543.

Grove, Adam J. and Halpern, Joseph Y. (1997). Probability update: conditioning vs. cross‐entropy. In Proceedings of the 13th Annual Conference on Uncertainty in Artificial Intelligence, pp. 208–14. Morgan Kaufmann, San Francisco, CA.

Grünwald, Peter (2000). Maximum entropy and the glasses you are looking through. In Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence, pp. 238–46. Morgan Kaufmann. San Francisco, CA.

—— and Dawid, A. Philip (2004). Game theory, maximum entropy, minimum discrepancy, and robust Bayesian decision theory. Annals of Statistics, 32(4), 1367–433.

Hacking, Ian (1971). Jacques Bernoulli's art of conjecturing. British Journal for the Philosophy of Science, 22(3), 209–29.

Haenni, R. (2007). Climbing the hills of compiled credal networks. In ISIPTA'07, 5th International Symposium on Imprecise Probabilities and Their Applications (eds. G. de Cooman, J. Vejnarová, and M. Zaffalon), Prague, Czech Republic, pp. 213–22.

—— (2009). Probabilistic argumentation. Journal of Applied Logic, 7(2), 155–76. Berlin.

Haenni, R., Kohlas, J., and Lehmann, N. (2000). Probabilistic argumentation systems. In Handbook of Defeasible Reasoning and Uncertainty Management Systems (eds. D. M. Gabbay and P. Smets), Volume 5: Algorithms for Uncertainty and Defeasible Reasoning, pp. 221–88. Kluwer Academic Publishers, Dordrecht.

—— Romeijn, Jan‐Willem, Wheeler, Gregory, and Williamson, Jon (2010). Probabilistic logic and probabilistic networks. Synthese Library. Springer.

Halpern, Joseph Y. (1999a). A counterexample to theorems of Cox and Fine. Journal of Artificial Intelligence Research, 10, 67–85.

(p.176) Halpern, Joseph Y. (1999b). Cox's theorem revisited. Journal of Artificial Intelligence Research, 11, 429–35.

—— (2003). Reasoning about uncertainty. MIT Press, Cambridge, MA.

Halpern, Joseph Y. and Koller, Daphne (1995). Representation dependence in probabilistic inference. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI 95) (ed. C. S. Mellish), pp. 1853–60. Morgan Kaufmann, San Francisco, CA.

Harman, Gilbert (2004). Practical aspects of theoretical reasoning. In The Oxford Handbook of Rationality (eds. A. R. Mele and P. Rawling), pp. 45–56. Oxford University Press, Oxford.

—— (2007). Epistemology as methodology. In A Companion to Epistemology (second edn) (eds. J. Dancy and E. Sosa). Blackwell. Oxford.

Harremoës, Poul, Gee, David, MacGarvin, Malcolm, Stirling, Andy, Keys, Jane, Wynne, Brian, and Vaz, Sofia Guedes (eds.) (2002). The precautionary principle in the 20th century: late lessons from early warnings. Earthscan, London.

Hartmann, Stephan, Pigozzi, Gabriella, and Sprenger, Jan (2007). Reliable methods of judgment aggregation. Technical Report 3593 (http://philsci-archive.pitt.edu/archive/00003593/), Philsci Archive.

Hawthorne, James and Makinson, David C. (2007). The quantitative/qualitative watershed for rules of uncertain inference. Studia Logica, 86, 247–97.

Hilbert, David (1925). On the infinite. In Philosophy of Mathematics: Selected Readings (second edn) (eds. P. Benacerraf and H. Putnam). Cambridge University Press (1983), Cambridge.

Hild, Matthias, Jeffrey, Richard, and Risse, Mathias (2008). Preference aggregation after harsanyi. In Justice, Political Liberalism, and Utilitarianism: Themes from Harsanyi and Rawls (eds. M. Fleurbaey, J. A. Weymark, and M. Salles). Cambridge University Press, Cambridge.

Hobson, Arthur (1971). Concepts in statistical mechanics. Gordon and Breach, New York.

Hosni, H. and Paris, J. B. (2005). Rationality as conformity. Synthese, 144(3), 249–85.

Howson, Colin (1997). Bayesian rules of updating. Erkenntnis, 45, 195–208.

—— (2000). Hume's problem: induction and the justification of belief. Clarendon Press, Oxford.

—— (2001). The logic of Bayesian probability. In Foundations of Bayesianism (eds. D. Corfield and J. Williamson), pp. 137–59. Kluwer, Dordrecht.

—— (2008). De finetti, countable additivity, consistency and coherence. The British Journal for the Philosophy of Science, 59, 1–23.

—— (2009). Can logic be combined with probability? Probably. Journal of Applied Logic, 7(2), 177–87.

—— —— and Urbach, Peter (1989a). Scientific reasoning: the Bayesian approach (Second (1993) edn). Open Court, Chicago, IL.

(p.177) —— —— (1989b). Scientific reasoning: the Bayesian approach (Third (2006) edn). Open Court, Chicago, IL.

Jaynes, E. T. (1957a). Information theory and statistical mechanics. The Physical Review, 106(4), 620–30.

—— (1957b). Information theory and statistical mechanics II. The Physical Review, 108(2), 171–90.

—— (1973). The well‐posed problem. Foundations of Physics, 3, 477–92.

—— (2003). Probability theory: the logic of science. Cambridge University Press, Cambridge.

Jeffreys, Harold (1931). Scientific inference (Second (1957) edn). Cambridge University Press, Cambridge.

—— (1939). Theory of Probability (Third (1961) edn). Clarendon Press, Oxford.

Johnson, W. E. (1932a). Probability: axioms. Mind, 41(163), 281–96.

—— (1932b). Probability: the deductive and inductive problems. Mind, 41(164), 409–23.

—— (1932c). The relations of proposal to supposal. Mind, 41(161), 1–16.

Kass, Robert E. and Wasserman, Larry (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91, 1343–70.

Katsuno, Hirofumi and Mendelzon, Alberto O. (1991). On the difference between updating a knowledge base and revising it. In P roceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, pp. 387–94. Morgan Kaufmann, San Francisco, CA.

Kelly, J. L. (1956). A new interpretation of information rate. Bell Systems Technical Journal, 35, 917–26.

Keynes, John Maynard (1921). A treatise on probability. Macmillan (1948), London.

Kolmogorov, A. N. (1933). The foundations of the theory of probability. Chelsea Publishing Company (1950), New York.

Konieczny, Sébastien and Pino Pérez, Ramón (1998). On the logic of merging. In Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning, pp. 488–98. Morgan Kaufmann, San Francisco, CA.

—— —— (2002). Merging information under constraints: a logical framework. Journal of Logic and Computation, 12(5), 773–808.

Kornhauser, L. A. and Sager, L. G. (1986). Unpacking the court. Yale Law Journal, 96, 82–117.

Kraus, Sarit, Lehmann, Daniel, and Magidor, Menachem (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.

Kullback, S. and Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22, 79–86.

(p.178) Kyburg Jr, Henry E. (1968). Bets and beliefs. American Philosophical Quarterly, 5(1), 54–63.

—— (1970). Two world views. Noûs, 4(4), 337–48.

—— (2003). Are there degrees of belief? Journal of Applied Logic, 1, 139–49.

—— and Pittarelli, Michael (1996). Set‐based bayesianism. IEEE Transactions on Systems, Man, and Cybernetics, 26(3), 324–39.

Kyburg Jr, Henry E. and Teng, Choh Man (1999). Choosing among interpretations of probability. In Proceedings of the 15th Annual Conference on Uncertainty in Artificial Intelligence (UAI‐99), pp. 359–65. Morgan Kaufmann Publishers, San Francisco, CA.

—— —— —— (2001). Uncertain inference. Cambridge University Press, Cambridge.

—— —— —— and Wheeler, Gregory (2007). Conditionals and consequences. Journal of Applied Logic, 5(4), 638–50.

Lange, Mark (1999). Calibration and the epistemological role of Bayesian con‐ ditionalization. The Journal of Philosophy, 96, 294–324.

Laplace (1814). A philosophical essay on probabilities. Dover (1951), New York. Pierre Simon, marquis de Laplace.

Levi, Isaac (1980). The enterprise of knowledge: an essay on knowledge, credal probability, and chance. MIT Press, Cambridge, MA.

Levine, Raphael D. and Tribus, Myron (ed.) (1979). The maximum entropy formalism. MIT Press, Cambridge, MA.

Lewis, David K. (1980). A subjectivist's guide to objective chance. In Philosophical Papers, Volume 2, pp. 83–132. Oxford University Press (1986), Oxford.

—— (1994). Humean supervenience debugged. Mind, 412, 471–490.

—— and —— (1998). Merging databases under constraints. International Journal of Cooperative Information Systems, 7(1), 55–76.

List, C. and Pettit, P. (2002). Aggregating sets of judgments. An impossibility result. Economics and Philosophy, 18, 89–110.

—— —— (2004). Aggregating sets of judgments. Two impossibility results compared. Synthese, 140, 207–35.

Makinson, David (2005). Bridges from classical to nonmonotonic logic. King's College Publications, London.

Meyer, Thomas, Ghose, Aditya, and Chopra, Samir (2001). Social choice, merging and elections. In Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (eds. Benferhat and Besnard), pp. 466–77. Springer. Volume 2143 of Lecture Notes in Artificial Intelligence. Berlin.

Mikkelson, Jeffrey M. (2004). Dissolving the wine/water paradox. British Journal for the Philosophy of Science, 55, 137–45.

(p.179) Miller, David (1966). A paradox of information. British Journal for the Philosophy of Science, 17, 59–61.

Mongin, Phillippe (2001). The paradox of the Bayesian experts. In Foundations of Bayesianism (eds. D. Corfield and J. Williamson), pp. 309–38. Kluwer, Dordrecht.

Nagl, Sylvia, Williams, Matt, and Williamson, Jon (2008). Objective Bayesian nets for systems modelling and prognosis in breast cancer. In Innovations in Bayesian networks: theory and applications (eds. D. Holmes and L. Jain), pp. 131–167. Springer, Berlin.

Nau, Robert F. (2001). De Finetti was right: probability does not exist. Theory and Decision, 51, 89–124.

Neapolitan, Richard E. (1990). Probabilistic reasoning in expert systems: theory and algorithms. Wiley, New York.

Nilsson, Nils J. (1986). Probabilistic logic. Artificial Intelligence, 28, 71–87.

Oaksford, Mike and Chater, Nick (2007). Bayesian rationality: the probabilistic approach to human reasoning. Oxford University Press, Oxford.

Paris, J. B. (1994). The uncertain reasoner's companion. Cambridge University Press, Cambridge.

—— (2003). Lecture notes on nonmonotonic logic. Department of Mathematics, University of Manchester. www.maths.man.ac.uk/~jeff/lecture-notes/mt4181.ps.

—— and Vencovská, A. (1990). A note on the inevitability of maximum entropy. International Journal of Approximate Reasoning, 4, 181–223.

—— —— (1997). In defence of the maximum entropy inference process. International Journal of Approximate Reasoning, 17, 77–103.

—— —— (2001). Common sense and stochastic independence. In Foundations of Bayesianism (eds. D. Corfield and J. Williamson), pp. 203–40. Kluwer, Dordrecht.

—— —— (2003). The emergence of reasons conjecture. Journal of Applied Logic, 1(3–4), 167–95.

Pauly, Marc and van Hees, Martin (2006). Logical constraints on judgement aggregation. Journal of Philosophical Logic, 35, 568–85.

Pearl, Judea (1988). Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San Mateo, CA.

Pigozzi, Gabriella (2006). Belief merging and the discursive dilemma: an argument‐based account to paradoxes of judgment aggregation. Synthese, 152(2), 285–98.

Press, S. James and Tanur, Judith M. (2001). The subjectivity of scientists and the Bayesian approach. Wiley, Chichester.

Ramsey, Frank Plumpton (1926). Truth and probability. In Studies in Subjective Probability (Second (1980) edn) (eds. H. E. Kyburg and H. E. Smokler), pp. 23–52. Robert E. Krieger Publishing Company, Huntington, New York.

(p.180) Ramsey, Frank Plumpton (1928). Reasonable degree of belief. In Philosophical Papers (1990 edn) (ed. D. H. Mellor). Cambridge University Press, Cambridge.

Reichenbach, Hans (1935). The theory of probability: an inquiry into the logical and mathematical foundations of the calculus of probability (1949 edn). University of California Press, Berkeley and Los Angeles. Translated by Ernest H. Hutten and Maria Reichenbach.

Rissanen, Jorma (1987). Stochastic complexity. Journal of the Royal Statistical Society. Series B, 49(3), 223–39.

Rosenkrantz, Roger D. (1977). Inference, method and decision: towards a Bayesian philosophy of science. Reidel, Dordrecht.

Rowbottom, Darrell P. (2007). The insufficiency of the Dutch Book argument. Studia Logica, 87, 65–71.

—— (2008). On the proximity of the logical and ‘objective Bayesian’ interpretations of probability. Erkenntnis, 69, 335–49.

Russo, Federica and Williamson, Jon (2007). Interpreting probability in causal models for cancer. In Causality and Probability in the Sciences (eds. F. Russo and J. Williamson), Texts in Philosophy, pp. 217–41. College Publications, London.

Salmon, Wesley C. (1967). Foundations of Scientific Inference. University of Pittsburgh Press, Pittsburgh.

—— (1990). Rationality and objectivity in science, or Tom Kuhn meets Tom Bayes. In Scientific Theories (ed. C. Wade Savage), pp. 175–204. University of Minnesota Press, Minneapolis, MN. Minnesota Studies in the Philosophy of Science 14.

—— (2005). Reality and rationality. Oxford University Press, Oxford. Edited by Phil Dowe and Merrilee H. Salmon.

Savage, L. J. (1954). The foundations of statistics. Wiley. New York. John Wiley & Sons.

Scott, Dana and Kraus, Peter (1966). Assigning probabilities to logical formulas. In Aspects of Inductive Logic (eds. J. Hintikka and P. Suppes), pp. 219–64. North‐Holland, Amsterdam.

Seidenfeld, Teddy (1979). Why I am not an objective Bayesian. Theory and Decision, 11, 413–40.

—— (1986). Entropy and uncertainty. Philosophy of Science, 53(4), 467–91.

—— Schervish, M. J., and Kadane, J. B. (1990). When fair betting odds are not degrees of belief. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1990, 517–24.

Shafer, Glenn (1996). The art of causal conjecture. MIT Press, Cambridge, MA.

—— and Pearl, Judea (eds.) (1990). Readings in uncertain reasoning. Morgan Kaufmann, San Mateo, CA.

Shannon, Claude (1948). A mathematical theory of communication. The Bell System Technical Journal, 27, 379–423 and 623–56.

(p.181) Shimony, Abner (1973). Comment on the interpretation of inductive probabilities. Journal of Statistical Physics, 9(2), 187–91.

—— (1985). The status of the principle of maximum entropy. Synthese, 63, 35–53.

Skyrms, Brian (1985). Maximum entropy inference as a special case of condi‐ tionalization. Synthese, 63, 55–74.

—— (1987). Coherence. In Scientific Inquiry in Philosophical Perspective (ed. N. Rescher), pp. 225–42. University Press of America, Lanham, MD.

Smith, Cedric A. B. (1961). Consistency in statistical inference and decision. Journal of the Royal Statistical Society Series B, 23, 1–37. With discussion.

Sturgeon, Scott (2008). Reason and the grain of belief. Noûs, 42(1), 139–65.

Teller, Paul (1973). Conditionalisation and observation. Synthese, 26, 218–58.

Topsϕe, F. (1979). Information theoretical optimization techniques. Kyber‐ netika, 15, 1–27.

Tribus, Myron (1961). Thermostatics and thermodynamics: an introduction to energy, information and states of matter, with engineering applications. Van Nostrand, Princeton, NJ.

—— (1969). Rational descriptions, decisions and designs. Pergamon Press, New York.

Uffink, Jos (1996). The constraint rule of the maximum entropy principle. Studies in History and Philosophy of Modern Physics, 27, 47–79.

van Fraassen, Bas C. (1981). A problem for relative information minimizers in probability kinematics. British Journal for the Philosophy of Science, 32, 375–79.

—— (1984). Belief and the will. Journal of Philosophy, 81(5), 235–56.

—— (1987). Symmetries of personal probability kinematics. In Scientific inquiry in philosophical perspective (ed. N. Rescher), pp. 183–223. University Press of America, Lanham, MD.

—— (1989). Laws and symmetry. Clarendon Press, Oxford.

—— (2002). The empirical stance. Yale University Press, New Haven, CT.

—— (2009). On stance and rationality. Synthese, doi 10.1007/s11229‐009‐9520‐1.

—— Hughes, R. I. G., and Harman, G. (1986). A problem for relative information minimisers, continued. British Journal for the Philosophy of Science, 37, 453–75.

Venn, John (1866). Logic of chance: an essay on the foundations and province of the theory of probability (Second (1876) edn). Macmillan, London.

von Kries, Johannes (1886). Die Principien der Wahrscheinlichkeits‐Rechnung: Eine logische Untersuchung. Mohr, Tübingen.

von Mises, Richard (1928). Probability, statistics and truth (Second (1957) edn). Allen and Unwin, London.

Walley, Peter (1991). Statistical reasoning with imprecise probabilities. Chapman and Hall, London.

(p.182) Wheeler, Gregory and Williamson, Jon (2010). Evidential probability and objective Bayesian epistemology. In Handbook of the Philosophy of Statistics (eds. P. S. Bandyopadhyay and M. Forster). Elsevier, Amsterdam.

Williams, Peter M. (1980). Bayesian conditionalisation and the principle of minimum information. British Journal for the Philosophy of Science, 31, 131–44.

Williamson, Jon (1999). Countable additivity and subjective probability. British Journal for the Philosophy of Science, 50(3), 401–16.

—— (2001). Foundations for Bayesian networks. In Foundations of Bayesianism (eds. D. Corfield and J. Williamson), pp. 75–115. Kluwer, Dordrecht.

—— (2002). Maximising entropy efficiently. Electronic Transactions in Artificial Intelligence Journal, 6. www.etaij.org.

—— (2005a). Bayesian nets and causality: philosophical and computational foundations. Oxford University Press, Oxford.

—— (2005b). Objective Bayesian nets. In We Will Show Them! Essays in Honour of Dov Gabbay (eds. S. Artemov, H. Barringer, A. S. d'Avila Garcez, L. C. Lamb, and J. Woods), Volume 2, pp. 713–30. College Publications, London.

—— (2007a). Inductive influence. British Journal for the Philosophy of Science, 58(4), 689–708.

—— (2007b). Motivating objective Bayesianism: from empirical constraints to objective probabilities. In Probability and Inference: Essays in Honour of Henry E. Kyburg Jr. (eds. W. L. Harper and G. R. Wheeler), pp. 151–79. College Publications, London.

—— (2008a). Objective Bayesian probabilistic logic. Journal of Algorithms in Cognition, Informatics and Logic, 63, 167–83.

—— (2008b). Objective Bayesianism with predicate languages. Synthese, 163(3), 341–56.

—— (2009a). Aggregating judgements by merging evidence. Journal of Logic and Computation, 19, 461–73.

—— (2009b). Objective Bayesianism, Bayesian conditionalisation and voluntarism. Synthese, doi 10.1007/s11229‐009‐9515‐y.

—— (2009c). Philosophies of probability. In Handbook of the Philosophy of Mathematics of the Handbook of the Philosophy of Science volume 4 (ed. A. Irvine), pp. 493–533. North‐Holland, Amsterdam.

Williamson, Timothy (2000). Knowledge and its limits. Oxford University Press, Oxford.