  The crucial but very confidential fact is brought into evidence that, as
Kolmogorov himself repeatedly claimed, the mathematical theory of probabilities
cannot be applied to physical, factual probabilistic situations because the
factual concept of probability is not defined : it is nowhere specified how to
construct, for a given physical random phenomenon, the specific numerical
distribution of relative frequencies of outcomes from the universe of
elementary events produced by that phenomenon, that constitutes the factual
probability law to be asserted on this universe; nor is it known what
significance to associate to the assertion of mere 'existence' of such a
factual probability law. An algorithm of semantic integration of the factual
probability law to be asserted in any given factual probabilistic situation, is
then constructed. This algorithm, developed inside a general method of
relativized conceptualization, involves a quantification of the factual concept
of probability. These results, while solving Kolmogorov's aporia, fully
organize the general classical concept of probability, both syntactic and
factual. As for quantum mechanical 'probabilities', it comes out, surprisingly,
that, factually, they cannot be defined in an effective way: fundamental
quantum mechanics seems to be confined (observationally and even in principle)
to the establishment of only statistical distributions which, as far as finite
data can guarantee, are endowed with stability.
