Restricting preservation: a response to Hill

Brian Hill argues for a restriction of the Preservation condition that is based on a notion of epistemic, as opposed to logical, consistency. In this reply I consider possible criteria for epistemic consistency and suggest that a natural candidate for one leads to a more severe restriction on the Preservation condition than Hill proposes. I also question whether his proposed restriction is either necessary or sufficient to avoid the impossibility results for the Preservation condition, suggesting that it is the way in which belief expansion is characterized within the AGM framework that is the real source of the problem. Finally, I draw on the notion of belief undermining to support a different resolution of the problem.