“The treatment of probability has been confused by the mathematicians. .... The problem of probable inference is much bigger than those problems which constitute the field of the calculus of probability. Only preoccupation with the mathematical treatment could result in the prejudice that probability always means frequency.Hoppe (2007: 1) contends that Frank Knight and Ludwig von Mises held a frequency interpretation of probability and regarded probability theory of limited use in economics, especially in economic forecasting. Hoppe sees Ludwig von Mises as essentially following his brother Richard von Mises’s frequentism as well as rejecting the idea of a priori probability (Hoppe 2007: 3).
A further error confused the problem of probability with the problem of inductive reasoning as applied by the natural sciences. The attempt to substitute a universal theory of probability for the category of causality characterizes an abortive mode of philosophizing, very fashionable only a few years ago.
A statement is probable if our knowledge concerning its content is deficient. We do not know everything which would be required for a definite decision between true and not true. But, on the other hand, we do know something about it; we are in a position to say more than simply non liquet or ignoramus.
There are two entirely different instances of probability; we may call them class probability (or frequency probability) and case probability (or the specific understanding of the sciences of human action). The field for the application of the former is the field of the natural sciences, entirely ruled by causality; the field for the application of the latter is the field of the sciences of human action, entirely ruled by teleology.” (Mises 2008: 106–107).
Ludwig von Mises’s class probability is essentially the same as the frequency interpretation of probability.
But from Mises’s statements that
(1) the “problem of probable inference is much bigger than those problems which constitute the field of the calculus of probability” andsuggest that he conceived of probability theory in a broader sense, as incorporating not only objective probabilities (derivable from relative frequencies), but also probable inferences inferred in inductive reasoning.
(2) “only preoccupation with the mathematical treatment could result in the prejudice that probability always means frequency”
The latter appear to be close to what Mises calls “case probabilities” and do not have numerical values. Instances where people give numerical values for case probabilities are called mere “metaphors” by Mises (Mises 2008: 114).
Hauwe (2011) argues that Ludwig von Mises’s views on probability have a close affinity with those of Keynes, but I leave this as an open question.
Hauwe, Ludwig van den. 2011. “John Maynard Keynes and Ludwig von Mises on Probability,” Journal of Libertarian Studies 22: 471–507.
Hoppe, Hans-Hermann. 2007. “The Limits of Numerical Probability: Frank H. Knight and Ludwig von Mises and the Frequency Interpretation,” Quarterly Journal of Austrian Economics 10.1: 1–20.
Mises, L. 2008. Human Action: A Treatise on Economics. The Scholar’s Edition. Mises Institute, Auburn, Ala.