Probability and Propensities

Retrospective reflections are provided on the papers “Why Propensities Cannot Be Probabilities,” “Some Considerations on Conditional Chances,” and “Probability Theory and Its Models” by Paul Humphreys. A discussion of whether probability theory is a mathematical or an empirical theory is provided and the point made that mathematical theories are not revised but replaced when used as models of empirical phenomena. Probability theory qua formal theory has a mathematical interpretation but any empirical interpretation, contra Quine, is completely detachable. A replacement for Quine’s web metaphor is suggested. The author assesses Donald Gillies’ response to Humphreys’ Paradox, and reasons not to abandon the single case propensity interpretation of probabilities are given. Responses to the paradox by Mauricio Suárez, Isabelle Drouet, Leslie Ballentine, and David Miller are discussed, and an argument given that the temporal evolution approach is primary for absolute propensities.

The Propensity Interpretation

The propensity interpretation of probability was introduced by Popper in 1957, and the chapter begins with a discussion of Popper’s initial account of propensities and a comparison with Peirce’s related ideas. The original propensity interpretation had a number of strands, some of which could be accepted while others were rejected. This meant that the propensity interpretation could be, and was, developed in different ways by different philosophers of science. One point at issue was whether propensities were objective probabilities of single events. This led to a distinction between (i) single-case propensity theories, and (ii) long-run propensity theories. Another problem concerned the relation between propensities and causes – if propensities had a causal import, because of what is known as the Humphreys’ paradox they might not satisfy the standard axioms of probability. The chapter concludes by discussing how propensities might be connected to observed frequencies via the theory of statistical testing.