David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Journal of Philosophical Logic 40 (2):155-191 (2011)
According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α > β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α > (β > γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals.
|Keywords||Ramsey test conditionals belief change iterated revision impossibility theorem preservation|
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References found in this work BETA
David K. Lewis (1973). Counterfactuals. Blackwell.
Carlos E. Alchourrón, Peter Gärdenfors & David Makinson (1985). On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. Journal of Symbolic Logic 50 (2):510-530.
Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J., Littlefield, Adams.
Isaac Levi (1967). Gambling with Truth. Cambridge: MIT Press.
Citations of this work BETA
Georg Brun & Hans Rott (2013). Interpreting Enthymematic Arguments Using Belief Revision. Synthese 190 (18):4041-4063.
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