Academic journal article Review of Social Economy

On Popper, Probabilities and Propensities

Academic journal article Review of Social Economy

On Popper, Probabilities and Propensities

Article excerpt

A puzzling feature of the many contributions in economics that refer to Karl Popper's writings is how few of them mention his propensity interpretation of probability.(1) This may well be because this interpretation was initially proposed with physics in mind (Popper 1967). Yet by the end of his life it had become clear that his propensity theory had developed into something with much wider implications. As he puts in his last book, after he had first proposed it in the 1950s the "theory had further grown so that it was only in the last year that I realized its cosmological significance. I mean that we live in a worm of propensities, and that this fact makes our world both more interesting and more homely than the world as seen by earlier states of the sciences" (Popper 1990: 9). My aim in this paper is to document this development, to point out its affinities with Critical Realism (CR), and to raise some implications for two prominent Popperian themes in economics.

One of the difficulties in reporting Popper's views on propensities is that there is some slippage over time in the way that he uses the term. In his earlier writings he leans toward the view that propensities are dispositions, generated in particular experimental situations, toward the realization of certain experimental outcomes. These dispositions are interpreted as holistic properties of experimental situations, but expressed in terms of the possible outcomes or effects of the situation concerned (rather than the generating factors - forces, fields, and so on - which, in conjunction with the relevant boundary conditions, combine to cause those effects).(2) In his last book, however, Popper also refers to forces as propensities, suggesting that propensities may be regarded as causal factors as well as what is generated by the operation of causal factors. To avoid confusion I shall use the term propensity in the former sense, in the first two sections below. Some ambiguities that arise in Popper's later interpretation are considered at the end of the paper.

I. PROBABILITIES AS PROPENSITIES

Popper introduced his propensity theory of probability in two papers published during the 1950s. I shall concentrate on the second of these, his 1959 paper in the British Journal for the Philosophy of Science.(3) The purpose of this paper is to provide an interpretation of probability, or more accurately, of statements of the form "the probability of a given b is r" (where r is a real number in the interval [0,1]). In symbols, this statement may be written:

p(a, b) = r

Popper divides into two broad categories the different ways statements of this kind are interpreted: the subjective interpretation (sometimes called the epistemic interpretation) and the objective interpretation (sometimes called the aleatory interpretation).(4) On the subjective interpretation, probability is regarded as a property of our knowledge of the external world. Here r is regarded as the degree of belief that a knowledge of b confers on a. As Popper consistently rejected the subjective interpretation throughout his career, I shall say no more about it here (other than that he does concede that there may be something like a measure of rational belief r in a given b, but that this measure is unlikely to conform to the standard probability axioms).

On the objective interpretation, probability is regarded as a property of the external world. Here a represents the possible outcome of some experiment b and r the relative frequency with which a occurs in a sufficiently long series of repetitions of b. Before developing his propensity theory, Popper had been a proponent of the "purely statistical" version of the objective interpretation of probability. On this interpretation, p(a, b) = r is an estimate or hypothesis "asserting nothing but that the relative frequency of the event a in a sequence of trials defined by b is equal to r" (1959b: 26). Popper went on to abandon this view due to problems connected with the interpretation of quantum theory and because of its inability to account for single-case probabilities (probabilities that can be ascribed to a single event occurring at a particular spatio-temporal location). …

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