We do know how to do the calculations, we can determine the probabilities for various experiments, real or imagined. In fact, an amazing machinery of methods and tools has been developed over decades for this purpose; A cornerstone of modern physics and science in general.
And yet, important foundational questions remain unanswered.
I am talking, of course, about statistics and our theories of probability.
Recently I found this:
"This book is about one of the greatest intellectual failures of the twentieth
century - several unsuccessful attempts to construct a scientific theory of
probability. Probability and statistics are based on very well developed
mathematical theories. Amazingly, these solid mathematical foundations
are not linked to applications via a scientific theory but via two mutually
contradictory and radical philosophies. One of these philosophical theories
(frequency) is an awkward attempt to provide scientific foundations for
probability. The other theory (subjective) is one of the most confused
theories in all of science and philosophy. A little scrutiny shows that in
practice, the two ideologies are almost entirely ignored, even by their own supporters."
But I guess before I buy the book I will browse the blog a bit more...
added later: ... and read some reviews: negative and positive. (I thank Jonathan for the links.)