Propensity Probability - History - Karl Popper

Karl Popper

A later propensity theory was proposed by philosopher Karl Popper, who had only slight acquaintance with the writings of Charles S. Peirce, however. Popper noted that the outcome of a physical experiment is produced by a certain set of "generating conditions". When we repeat an experiment, as the saying goes, we really perform another experiment with a (more or less) similar set of generating conditions. To say that a set of generating conditions has propensity p of producing the outcome E means that those exact conditions, if repeated indefinitely, would produce an outcome sequence in which E occurred with limiting relative frequency p. For Popper then, a deterministic experiment would have propensity 0 or 1 for each outcome, since those generating conditions would have same outcome on each trial. In other words, non-trivial propensities (those that differ from 0 and 1) only exist for genuinely indeterministic experiments.

Popper's propensities, while they are not relative frequencies, are yet defined in terms of relative frequency. As a result, they face many of the serious problems that plague frequency theories. First, propensities cannot be empirically ascertained, on this account, since the limit of a sequence is a tail event, and is thus independent of its finite initial segments. Seeing a coin land heads every time for the first million tosses, for example, tells one nothing about the limiting proportion of heads on Popper's view. Moreover, the use of relative frequency to define propensity assumes the existence of stable relative frequencies, so one cannot then use propensity to explain the existence of stable relative frequencies, via the Law of large numbers.