Being realistic about common knowledge: a Lewisian approach

Defined and formalized several decades ago, widely used in philosophy and game theory, the concept of common knowledge is still considered as problematic, although not always for the right reasons. I suggest that the epistemic status of a group of human agents in a state of common knowledge has not been thoroughly analyzed. In particular, every existing account of common knowledge, whether formal or not, is either too strong to fit cognitively limited individuals, or too weak to adequately describe their state. I provide a realistic definition of common knowledge, based on a formalization of David Lewis’ seminal account and show that it is formally equivalent to probabilistic common belief. This leads to a philosophical analysis of common knowledge which answers several common criticisms and sheds light on its nature.