, Volume 139, Issue 2, pp 225–240 | Cite as

A Counterexample to Six Fundamental Principles of Belief Formation

  • Hans Rott


In recent years there has been a growing consensus that ordinary reasoning does not conform to the laws of classical logic, but is rather nonmonotonic in the sense that conclusions previously drawn may well be removed upon acquiring further information. Even so, rational belief formation has up to now been modelled as conforming to some fundamental principles that are classically valid. The counterexample described in this paper suggests that a number of the most cherished of these principles should not be regarded as valid for commonsense reasoning. An explanation of this puzzling failure is given, arguing that a problem in the theory of rational choice transfers to the realm of belief formation.


Fundamental Principle Rational Choice Classical Logic Rational Belief Belief Formation 
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  1. Alchourrón, Carlos, Peter Gärdenfors and David Makinson: 1985, ‘On the Logic of Theory Change: Partial Meet Contraction Functions and Their Associated Revision Functions’, Journal of Symbolic Logic 50, 510–530.Google Scholar
  2. Brewka, Gerd: 1991, ‘Cumulative Default Logic: In Defense of Non-Monotonic Inference Rules’, Artificial Intelligence 50, 183–205.CrossRefGoogle Scholar
  3. Dennett, Daniel: 1971, ‘Intentional Systems’, Journal of Philosophy 68, 87–106. The page reference is to the reprint in D.D.: 1978, Brainstorms, MIT Press, Cambridge, MA, pp. 3-22Google Scholar
  4. Gärdenfors, Peter: 1986, ‘Belief Revisions and the Ramsey Test for Conditionals’, Philosophical Review 95, 81–93.Google Scholar
  5. Gärdenfors, Peter: 1988, Knowledge in Flux. Modeling the Dynamics of Epistemic States, Bradford Books, MIT Press, Cambridge, MA.Google Scholar
  6. Gärdenfors, Peter and Hans Rott: 1995, ‘Belief Revision’, in D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming Volume IV: Epistemic and Temporal Reasoning, Oxford University Press, Oxford, pp. 35–132.Google Scholar
  7. Giordano, Laura and Alberto Martelli: 1994, ‘On Cumulative Default Logics’, Artificial Intelligence 66, 161–179.CrossRefGoogle Scholar
  8. Hansson, Sven O.: 1999, A Textbook of Belief Dynamics: Theory Change and Database Updating, Kluwer Academic Publishers, Dordrecht.Google Scholar
  9. Kalai, Gil, Ariel Rubinstein, and Ran Spiegler: 2002, ‘Rationalizing Choice Functions by Multiple Rationales’, Econometrica 70, 2481–2488.CrossRefGoogle Scholar
  10. Kyburg, Henry E., Jr.: 2001, ‘Real Logic is Nonmonotonic’, Minds and Machines 11, 577–595.Google Scholar
  11. Levi, Isaac: 1986, Hard Choices, Cambridge University Press, Cambridge.Google Scholar
  12. Lindström, Sten: 1991, ‘A Semantic Approach to Nonmonotonic Reasoning: Inference Operations and Choice’, Uppsala Prints and Preprints in Philosophy, Department of Philosophy, University of Uppsala.Google Scholar
  13. Lindström, Sten and Wlodek Rabinowicz: 1999, ‘DDL Unlimited: Dynamic Doxastic Logic for Introspective Agents’, Erkenntnis 50, 353–385.CrossRefGoogle Scholar
  14. Luce, R. Duncan and Howard Raiffa: 1957, Games and Decisions, John Wiley & Sons, New York.Google Scholar
  15. Makinson, David: 1994, ‘General Patterns in Nonmonotonic Reasoning’, in D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming,Vol. 3: Nonmonotonic Reasoning and Uncertain Reasoning, Oxford University Press, Oxford, pp. 35–110.Google Scholar
  16. Makinson, David and Peter Gärdenfors: 1991, ‘Relations between the Logic of Theory Change and Nonmonotonic Logic’, in A. Fuhrmann and M. Morreau (eds.), The Logic of Theory Change, Springer LNAI 465, Berlin, pp. 185–205.Google Scholar
  17. McGee, Van: 1985, ‘A Counterexample toModus Ponens’, Journal of Philosophy 82, 462–471.Google Scholar
  18. Morgan, Charles G.: 2000, ‘The Nature of Nonmonotonic Reasoning’, Minds and Machines 10, 321–360.CrossRefGoogle Scholar
  19. Moulin, Hervé: 1985, ‘Choice Functions over a Finite Set: A Summary’, Social Choice and Welfare 2, 147–160.CrossRefGoogle Scholar
  20. Reiter, Raymond: 1980, ‘A Logic of Default Reasoning’, Artificial Intelligence 13, 81–132.CrossRefGoogle Scholar
  21. Roos, Nico: 1998, ‘Reasoning by Cases in Default Logic’, Artificial Intelligence 99, 165–183.CrossRefGoogle Scholar
  22. Rott, Hans: 1989, ‘Conditionals and Theory Change: Revisions, Expansions, and Additions’, Synthese 81, 91–113.CrossRefGoogle Scholar
  23. Rott, Hans: 1993, ‘Belief Contraction in the Context of the General Theory of Rational Choice’, Journal of Symbolic Logic 58, 1426–1450.Google Scholar
  24. Rott, Hans: 2001, Change, Choice and Inference, Oxford Logic Guides, Vol. 42, Clarendon Press, Oxford.Google Scholar
  25. Sen, Amartya K.: 1993, ‘Internal Consistency of Choice’, Econometrica 61, 495–521.Google Scholar
  26. Sen, Amartya K.: 1995, ‘Is the Idea of Purely Internal Consistency of Choice Bizarre?’, in J. E. J. Altham and R. Harrison (eds.), World, Mind, and Ethics. Essays on the Ethical Philosophy of Bernard Williams, Cambridge University Press, Cambridge, pp. 19–31.Google Scholar
  27. Stalnaker, Robert C.: 1984, Inquiry, Bradford Books, MIT Press, Cambridge, MA.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Hans Rott
    • 1
  1. 1.Department of PhilosophyUniversity of RegensburgRegensburgGermany

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