Are Statistical Laws Genuine Laws ? A Concern of Poincaré and Boltzmann

Usually a law is understood as a rule which governs all the things of a certain area to which the law is applicable. Since statistical laws govern most of the things of such an area but allow exceptions for some of them – even if those exceptions are very improbable – there is the question whether statistical laws are genuine laws at all. This paper deals with four questions : – 1, Can all laws be reduced to dynamical laws ?; – 2, Are all laws (ultimately) statistical laws ?; – 3, The Discovery of Chaotic Motion; – 4, Boltzmann versus Poincaré : is Boltzmann’s statistical mechanics as an explanation for time-irreversible processes incompatible with Poincaré’s recurrence theorem ?