 Barwise (1988) proposes another definition of common knowledge that avoids explicit reference to the hierarchy of ‘\(i\) knows that \(j\) knows that … knows that \(A\)’ propositions. Barwise’s analysis builds upon an informal proposal by Harman (1977). Consider the situation of the guest and clumsy waiter in Example 1 when he announces that he was at fault. They are now in a setting where they have heard the waiter’s announcement and know that they are in the setting. Harman adopts the circularity in this characterization of the setting as fundamental, and propses a definition of common knowledge in terms of this circularity. Barwise’s formal analysis gives a precise formulation of Harman’s intuitive analysis of common knowledge as a fixed point. Given a function \(f, A\) is a fixed point of \(f\) if \(f(A)=A.\) Now note that