Probability and Objectivity in Deterministic and Indeterministic Situations

Abstract

This paper pursues the question, “To what extent does the propensity approach to probability contribute to plausible solutions to various anomalies which occur in quantum mechanics?” The position I shall defend is that of the three interpretations – the frequency, the subjective, and the propensity – only the third accommodates the possibility, in principle, of providing a realistic interpretation of ontic indeterminism. If these considerations are correct, then they lend support to Popper’s contention that the propensity construction tends to remove (at least some of) the mystery from quantum phenomena.

This paper is an expanded and revised version of a lecture presented at the University of Colorado in February and at New College in April 1983. I am grateful to Paul Humphreys and to Stephen Brush for their comments and inquiries. In particular, Professor Brush has raised the issue of the Aspect experiments – which seem to confirm action at a distance – in relation to the approach defended here. As Popper (1982, p. xviii) has noted, this result need not undermine realism; but it would be remarkable if quantum mechanics could be true only if relativity were false. If situations involve propensities if and only if they are indeterministic in character, as my position implies, then if experiments such as Aspect’s, Einstein-Podolsky-and-Rosen’s, and others are indeterministic, then propensities are involved. If they are both indeterministic and action at a distance cannot be avoided (by appealing to non-causal, but not therefore non-lawful, relations, for example), which I doubt, then indeterministic causal concepts as well as deterministic causal concepts will almost certainly require revision. In any case, while the propensity approach can contribute to the resolution of some of the anomalies arising within the quantum domain, others – some involving questions of completeness – no doubt remain.