Even those generally skeptical of propensity interpretations of probability must now grant the following two points. First, the above single-case propensity interpretation meets recognized formal conditions for being a genuine interpretation of probability. Second, this interpretation is not logically reducible to a hypothetical relative frequency interpretation, nor is it only vacuously different from such an interpretation.The main objection to this propensity interpretation must be not that it is too vague or vacuous, but that it is metaphysically too extravagant. It asserts (...) not only that there are physical possibilities in nature, but further that nature itself contains innate tendencies toward these possibilities, tendencies which have the logical structure of probabilities. Thus the basic dispute between advocates of an actualist relative frequency interpretation and a single-case propensity interpretation is not a matter of epistemology, but metaphysics. The frequency theorist wishes to maintain that claims about physical probabilities are nothing more than claims about relative frequencies that will occur in the actual history of the world, be it infinite or no. It is a substantial, though hardly conclusive, argument for the propensity view that the mathematical structures commonly employed in studies of stochastic processes and statistical inference are richer than can be accommodated by a relative frequency interpretation. Whether it is possible to bridge this gap without going beyond an actualist metaphysics remains to be seen.38. (shrink)

Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone determination condition (...) that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory. (shrink)

I argue that to the extent to which philosophical theories of objective probability have offered theoretically adequateconceptions of objective probability (in connection with such desiderata as causal and explanatory significance, applicability to single cases, etc.), they have failed to satisfy amethodological standard — roughly, a requirement to the effect that the conception offered be specified with the precision appropriate for a physical interpretation of an abstract formal calculus and be fully explicated in terms of concepts, objects or phenomena understood independently (...) of the idea of physical probability. The significance of this, and of the suggested methodological standard, is then briefly discussed. (shrink)

This book deals not so much with statistical methods as with the central concept of chance, or statistical probability, which statistical theories apply to nature.