At this point, it might be useful to take a retrospective look at some of the major questions posed throughout this book, asking ourselves to what extent the questions have been answered and to what extent important puzzling issues still remain to be resolved. The reader will not be surprised by now, I expect, to discover that it is the author's view that many of the most important questions still remain unanswered in very fundamental and important ways.

A reasonable understanding of the role played by probabilistic assertions in statistical mechanics requires, I believe, some version of an interpretation of probability that views it as frequency or proportion in the physical world. Although “subjectivist” or “logicist” interpretations certainly are suggested by the role played by symmetry principles and principles of indifference in generating the posited probabilities, and although, as we have seen, the probabilities can sometimes be generated out of the lawlike structure of the underlying dynamics alone, still an understanding of how these probabilities are then used to describe the evolution of systems and to explain that behavior requires that they be understood in the manner of proportions.

But, as we have also seen, this understanding of probability is fraught with subtle difficulties.