Why Propensities Cannot be Probabilities

Abstract

The notion that probability theory is the theory of chance has an immediate appeal. We may allow that there are other kinds of things to which probability can address itself, things such as degrees of rational belief and degrees of confirmation, to name only two, but if chance forms part of the world, then probability theory ought, it would seem, to be the device to deal with it. Although chance is undeniably a mysterious thing, one promising way to approach it is through the use of propensities-indeterministic dispositions possessed by systems in a particular environment, exemplified perhaps by such quite different phenomena as a radioactive atom's propensity to decay and my neighbor's propensity to shout at his wife on hot summer days. There is no generally accepted account of propensities, but whatever they are, propensities must, it is commonly held, have the properties prescribed by probability theory. My contention is that they do not and, that rather than this being construed as a problem for propensities, it is to be taken as a reason for rejecting the current theory of probability as the correct theory of chance. The first section of the paper will provide an informal version of the argument, indicating how the causal nature of propensities cannot be adequately represented by standard probability theory. In the second section a full version of the argument will be given so that the assumptions underlying the informal account can be precisely identified. The third section examines those assumptions and deals with objections that could be raised against the argument and its conclusion. The fourth and final section draws out some rather more general consequences of accepting the main argument. Those who find the first section sufficiently persuasive by itself may wish to go immediately to the final section, returning thereafter to the second and third sections as necessary. ? Copyright 1985 Paul Humphreys

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