On a Crucial Problem in Probabilities and Solution

TL;DR

This paper discusses the fundamental issue that an abstract theory of probabilities is incomplete due to the lack of a clear method to construct factual probability laws, and proposes an algorithm for semantic integration to identify these laws.

Contribution

It introduces an algorithm of semantic integration to determine factual probability laws, addressing a longstanding conceptual gap in probability theory.

Findings

Identifies the absence of a concrete method to construct probability laws

Develops an algorithm for semantic integration to find factual probabilities

Provides a new approach to foundational issues in probability theory

Abstract

First the crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, there exists no abstract theory of probabilities, simply because the factual concept of probability is itself unachieved: it is nowhere specified how to construct the factual probability law to be asserted on a given physical random phenomenon. Then an algorithm of semantic integration is built that permits to identify this factual probability law.