 Fortunately for Lewis’ program, there are strong arguments that common knowledge is indeed attainable. Lewis (1969) argues that the common knowledge hierarchy should be viewed as a chain of implications, and not as steps in anyone’s actual reasoning. He gives informal arguments that the common knowledge hierarchy is generated from a finite set of axioms. We saw in §2 that it is possible to formulate Lewis’ axioms precisely and to derive the common knowledge hierarchy from these axioms and a public event functioning as a basis for common knowledge. Again, the basic idea behind Lewis’ argument is that for a set of agents, if a proposition \(A\) is publicly known among them and each agent knows that everyone can draw the same conclusion \(p\) from \(A\) that she can, then \(p\) is common knowledge. These conditions are obviously context dependent, just as an individual’s knowing or not knowing a proposition is context dependent. Yet there are many cases where it is natural to assume that a public event generates common knowledge, because it is properly broadcast, agents in the group are in ideal conditions to perceive it, the inference from the public event to the object of common knowledge is immediate, etc. However, common knowledge could fail if some of the people failed to perceive the public event, or if some of them believed that some of the others could not understand the announcement, or hear it, or could not draw the necessary inferences, and so on.