What remains of probability?

1. When I say “probability” I do not mean a Kolmogorovian ‘probability measure’ or similar mathematical notion. Of course, a definition—both coordinative1 and logical— plays a constitutive role in the very concept to be defined. Nevertheless, there seems no reason to include into the definition of probability that it “satisfies the Kolmogorovian axioms of probability theory”. For, once we know—supposedly from the rest part of the definition—what “probability” is in our world, it becomes a contingent fact of the world whether it satisfies the Kolmogorovian axioms or not; which can be known by a posteriori means. In other words, the aim of the so called “interpretations” of probability is not to find an interpretation of the Kolmogorovian axioms, but to give a sound meaning to scientific statements containing the term “probability”. For example, consider the following assertions of quantum mechanics or statistical mechanics: