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BELIEF-REVISION, THE RAMSEY TEST, MONOTONICITY, AND THE SO-CALLED IMPOSSIBILITY RESULTS

  • NEIL TENNANT (a1)
  • DOI: http://dx.doi.org/10.1017/S1755020308090023
  • Published online: 01 December 2008
Abstract

Peter Gärdenfors proved a theorem purporting to show that it is impossible to adjoin to the AGM-postulates for belief-revision a principle of monotonicity for revisions. The principle of monotonicity in question is implied by the Ramsey test for conditionals. So Gärdenfors’ result has been interpreted as demonstrating that it is impossible to combine the Ramsey test for conditionals with the basic postulates for rational belief-revision. It is shown here that this interpretation of Gärdenfors’ result is unwarranted. A new diagnosis is offered of a methodological error made in the statement of the key principle of monotonicity. Crucial applications of this principle in Gärdenfors’ proof require one to regard as revisions what are really expansions. If monotonicity is stated only for genuine revisions, then Gärdenfors’ proof does not go through. Nor can it; for, when the monotonicity principle for revisions is correctly formulated, one can actually establish a contrary consistency result. This requires only a slight adjustment to the postulates of AGM-theory, in order to ensure that the three operations of expansion, contraction, and revision trichotomize the domain of theory-changes. It is further shown that being careful in this way about the proper domains of definition of the three operations of expansion, contraction, and revision also disposes of another, more direct, impossibility result, due to Arló-Costa, that targets the Ramsey test.

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*DEPARTMENT OF PHILOSOPHY THE OHIO STATE UNIVERSITY COLUMBUS, OH 43210 E-mail:tennant.9@osu.edu
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

H. L. Arló-Costa , & I Levi . (1996). Two notions of epistemic validity. Synthese, 109(2), 217262.

P. Gärdenfors (1986). Belief revision and the Ramsey test for conditionals. Philosophical Review, 95, 8193.

S. O Hansson . (1992). In defense of the Ramsey test. Journal of Philosophy, 89(10), 522540.

S. O Hansson . (1999). A Textbook of Belief Dynamics. Dordrecht, The Netherlands: Kluwer Academic Publishers.

N. Tennant (2003). Theory-contraction is NP-complete. The Logic Journal of the IGPL, 11(6), 675693.

N. Tennant (2006b). New foundations for a relational theory of theory-revision. Journal of Philosophical Logic, 35(5), 489528.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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