 Lewis formulated an account of common knowledge which generates the hierarchy of ‘\(i\) knows that \(j\) knows that … \(k\) knows that \(A\)’ propositions in order to ensure that in his account of convention, agents have correct beliefs about each other. But since human agents obviously cannot reason their way through such an infinite hierarchy, it is natural to wonder whether any group of people can have full common knowledge of any proposition. More broadly, the analyses of common knowledge reviewed in §3 would be of little worth to social scientists and philosophers if this common knowledge lies beyond the reach of human agents.