Probability as a theory dependent concept (Q1969695)

Objectivists, we are told, explain probabilities in terms of events (Kolmogorov) or propensities (Popper), while on the other hand subjectivists refer to hypotheses (Keynes, Carnap) or degrees of belief (Ramsay, de Finetti). The aim of this paper is to unite the two facets, the objective and the subjective, in one single description: theory dependent probability. The authors take the notion of a stochastic theory as fundamental (it supposedly differs from a deterministic theory in assigning intervals rather than values to quantities), and probability distributions are secondary, theory-dependent quantities derived from this, which are tested by but not defined in terms of relative frequencies. It is claimed this combines subjectivity in that theories not events are primary, but is also objective in that predictions are tested by experiment. In support the authors first consider the difficulties of either a purely objectivist or purely subjectivist interpretation, discuss confidence levels derived from their analysis, and argue from simple classical conditional examples as well as from Bose-Einstein quantum statistics, that Kolmogorov axioms such as equiprobability are not a priori true. Sections 5 and 6 then compare classical and quantum probability games to highlight the difference between classical predictions and an analogous spin quantum experiment, concluding that the quantum correlations that lead to the successful game strategy only seem spooky if one is blinkered by the erroneous view that classical probability is the necessary framework for a theory about the relative frequencies. The argument that quantum theory uses its own probability theory is hardly new and indeed has more compelling features than are presented in this short paper. Furthermore there are key questions left unanswered by this rather sketchy treatment, for example what does characterize probabilities if not the Kolmogorov axioms, why are quantum predictions in some circumstances precise, why are quantum predictions so different from their classical counterparts? To conclude that probabilities express beliefs about experiment outcomes does not shed much light on such issues. However this short paper is clearly written. It provides a concise exposition of standard approaches to probability and illustrates some key differences between quantum and classical predictions in a clear and straightforward way.