Abstract: In previous publications on probability, I have followed I.J. Good in arguing that probability must be defined subjectively if we accept that the world is causally deterministic. In this article I go significantly beyond this position, arguing that we are forced to accept a subjective definition of probability if we use any probabilistic methods at all. In other words, all probabilistic methods tacitly assume a subjective definition of probability.
Abstract: My claim that probability ought to be defined as a purely subjective measure of human belief has been challenged in a recent and interesting article on these pages by Arnold Baise (2011). Baise argues that probability ought to be defined, not as a purely subjective measure of human belief, as I have claimed, but rather in the following way:
Probability P(A|I) is a number between 0 and 1 that indicates how plausible it is that proposition A is true, based on information I. In addition, one could add that a probability of 1 indicates certainty that the proposition is true, while a probability of 0 indicates certainty that the proposition is false. (2011, p.3).
The reasoning that leads Baise to advance this definition for probability, however, is seriously and apodictically flawed. As a consequence, his definition for probability must be rejected as a viable alternative to my purely subjective definition.
Abstract: The most interesting and completely overlooked aspect of Ludwig von Mises’s theory of probability is the total absence of any explicit definition for probability in his theory. This paper examines Mises’s theory of probability in light of the fact that his theory possesses no definition for probability. It is argued, first, that Mises’s theory differs in important respects from his brother’s famous theory of probability. A defense of the subjective definition for probability is then provided, which is subsequently used to critique Ludwig von Mises’s theory. It is argued that only the subjective definition for probability comports with Mises’s other philosophical positions. Since Mises did not provide an explicit definition for probability, it is suggested that he ought to have adopted a subjective definition.
Download Paper: 23. “A Challenge to Ludwig von Mises’s Theory of Probability”
Abstract: In my recent article on these pages (Crovelli 2009) I argued that members of the Austrian School of economics have adopted and defended a faulty definition of probability. I argued that the definition of probability necessarily depends upon the nature of the world in which we live. I claimed that if the nature of the world is such that every event and phenomenon which occurs has a cause of some sort, then probability must be defined subjectively; that is, “as a measure of our uncertainty about the likelihood of occurrence of some event or phenomenon, based upon evidence that need not derive solely from past frequencies of ‘collectives’ or ‘classes.’” I further claimed that the nature of the world is indeed such that all events and phenomena have prior causes, and that this fact compels us to adopt a subjective definition of probability.
David Howden has recently published what he claims is a refutation of my argument in his article “Single Trial Probability Applications: Can Subjectivity Evade Frequency Limitations” (Howden 2009). Unfortunately, Mr. Howden appears to not have understood my argument, and his purported refutation of my subjective definition consequently amounts to nothing more than a concatenation of confused and fallacious ideas that are completely irrelevant to my argument. David Howden has thus failed in his attempt to vindicate Richard von Mises’s definition of probability.
Abstract: Both Ludwig von Mises and Richard von Mises claimed that numerical probability could not be legitimately applied to singular cases. This paper challenges this aspect of the von Mises brothers’ theory of probability. It is argued that their denial that numerical probability could be applied to singular cases was based solely upon Richard von Mises’ exceptionally restrictive definition of probability. This paper challenges Richard von Mises’ definition of probability by arguing that the definition of probability necessarily depends upon whether the world is governed by time-invariant causal laws. It is argued that if the world is governed by time-invariant causal laws, a subjective definition of probability must be adopted. It is further argued that both the nature of human action and the relative frequency method for calculating numerical probabilities both presuppose that the world is indeed governed by time-invariant causal laws. It is finally argued that the subjective definition of probability undercuts the von Mises claim that numerical probability cannot legitimately be applied to singular, non-replicable cases.