Probability Meaning and Assessment: a Reconciliation

Abstract

The point of interpreting events — and then probability — in terms of bets is to get an unmistakable, concrete and operational meaning, valid for any kind of event: in fact betting is conceivable in any circumstance that can be expressed by a sensible proposition, and not only in those corresponding to the classic combinatorial or frequentist evaluations. Moreover, notice that the so-called “subjective view” is based on hypothetical bets: the force of the argument does not depend on whether or not one actually has the possibility or intends to bet. So, even if the above discussion aims at giving a possible “semantic” interpretation of the concept of coherence, nevertheless we may just refer (thanks to the alternative theorem) to the mathematical side of the problem, which rests essentially on the compatibility of system (4.1).