 One might think that an immediate corollary to Gilbert’s definition is that Gilbert-common knowledge implies the hierarchical common knowledge of Proposition 2.5. However, this claim follows only on the assumption that an agent knows all of the propositions that her smooth-reasoner counterpart reasons through. Gilbert does not explicitly endorse this position, although she correctly observes that Lewis and Aumann are committed to something like  it.[17]  Gilbert maintains that her account of common knowledge expresses our intuitions with respect to common knowledge better than Lewis’ and Aumann’s accounts, since the notion of open*-ness presumably makes explicit that when a proposition is common knowledge, it is “out in the open”, so to speak.