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Extra resources for Logics & Experimental Science
H could be inconsistent with K yet consistent with the consensus. Strictly speaking condition (2) will also be violated because when K is open with respect to h and $h, 11 For further discussion, see Levi (1996, ch. 3). Counterlogical supposition and conditional modal judgment is also entertainable when we abandon consistency preservation. 12 35 Supposition and Belief Change one does not expand by adding h to K but to the consensus between K and K0 . Thus, the pure indicative ‘‘if Oswald did not kill Kennedy, somebody else did’’ is appropriately uttered by someone engaged in colloquy with someone who thinks Oswald did not kill Kennedy.
I have adopted the approach of representing the potential state K by K in L. But why not represent it by the deductive closure in LM of K and the judgments of serious possibility and impossibility represented in LM supported by K? If we use K as a standard for serious possibility along lines I have suggested and along lines reinforced by the use of positive and negative Ramsey Tests that are based on AGM revision or Ramsey revision, when neither h nor $h is in K, we can consistently expand K in L but we cannot consistently expand KM in LM .
To be sure, the inquirer should somehow retreat from inconsistency. Consider the net effect of stumbling into inconsistency plus retreating. The retreat might lead to retaining the input and giving up some elements of the initial state of belief. The result is a reasonable facsimile of an AGM revision. But that is not the only possibility (see Hansson, 1991 and Levi, 1991, ch. 4). The net effect of expanding into inconsistency and then contracting might be that the input is given up. The net effect will then (roughly speaking) be return to the status quo ex ante.