  The Ehrenfests' reading of Boltzmann's intentions has thus some undeniable advantages. However, there is no evidence that Boltzmann really had the ergodic hypothesis in mind. It seems m more likely that he relied on a naive identification of the various meanings of probability. Further, nobody has ever succeeded in proving a statistical H-theorem on the basis of the ergodic hypothesis, or on the basis of a modern relative such as the hypothesis of ‘metrical transitivity’. Much stronger dynamical and probabilistic conditions seem to be needed for such a proof, and even then it remains a difficult problem whether these are satisfied in a realistic gas model.