 Lewis is credited with the idea of characterizing common knowledge as a hierarchy of ‘\(i\) knows that \(j\) knows that … knows that \(A\)’ propositions. However, Lewis is aware of the difficulties that such an infinitary definition raises. A first problem is whether it is possible to reduce the infinity inherent in the hierarchical account into a workable finite definition. A second problem is the issue that finite agents cannot entertain the infinite amount of epistemic states which is necessary for common knowledge to obtain. Lewis tackles both problems, but his presentation is informal. Aumann is often credited with presenting the first finitary method of generating the common knowledge hierarchy (Aumann 1976), even though (Friedell 1969) in fact predates both Aumann’s and Lewis’s work. Recently, Cubitt and Sugden (2003) have argued that Aumann’s and Lewis’ accounts of common knowledge are radically different and irreconcilable.