Crovelli On Probability: A Critique
According to that old adage, if you are going to attack the king, you had better kill him. Mises, of course, is our emperor. Crovelli (2010) has launched a denunciation of him. In our view, he has not at all succeeded. The monarch, of course, cannot respond, but we, his courtiers, can. In this paper we will attempt to refute the former in defense of the latter.
Crovelli, more than once, upbraids Mises for not defining probability; for using the concepts of case and class probability, without ever explicating what these two branches have in common. And, this is a legitimate, although somewhat minor, criticism of Ludwig von Mises. In fact we observe that “probability” is essentially mathematical in meaning, whether we consult Wolfram MathWorld which states:
“Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes’ relative likelihoods and distributions. In common usage, the word “probability” is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.
There are several competing interpretations of the actual “meaning” of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure that endeavors to estimate parameters of an underlying distribution based on the observed distribution”,1
or the OED:
“probability, n. 3. Mathematics. As a measurable quantity: the extent to which a particular event is likely to occur, or a particular situation be the case, as measured by the relative frequency of occurrence of events of the same kind in the whole course of experience, and expressed by a number between 0 and 1.
An event that cannot happen has probability 0; one that is certain to happen has probability 1. Probability is commonly estimated by the ratio of the number of successful cases to the total number of possible cases, derived mathematically using known properties of the distribution of events, or estimated logically by inferential or inductive reasoning (when mathematical concepts may be inapplicable or insufficient).”
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