Normality judgements are frequently used in everyday communication as well as in biological and social science. Moreover they became increasingly relevant to formal logic as part of defeasible reasoning. This paper distinguishes different kinds of normality statements. It is argued that normality laws like “Birds can normally fly” should be understood essentially in a statistical way. The argument has basically two parts: firstly, a statistical semantic core is mandatory for a descriptive reading of normality in order to explain the logical (...) features of normality laws. Secondly, a statistical justification of normality statements can be derived by game theoretic considerations if the normality law is understood as communication convention. (shrink)