Hauwe sees two fundamental conceptual divisions in probability theory (Hauwe 2011: 472), which I expand upon below:
(1) Epistemological (or epistemic) probability theory, further divided intoAn epistemological/epistemic probability assignment measures a degree of knowledge, a degree of rational belief, or a degree of belief (Hauwe 2011: 473).(i.) the logical interpretation;(2) Objective probability theory, further divided into
(ii.) the subjective interpretation;
(iii.) the intersubjective interpretation, and(i.) the frequency interpretation;(Gillies 2000: 2).
(ii.) the propensity interpretation.
In contrast, objective probability interpretations see probability assignments as a characteristic of the material world (Hauwe 2011: 473).
Hauwe (2011: 473) charges that many members of the Austrian school (such as Rothbard 2004: 553) have simply assumed that Mises adopted the frequentist interpretation of probability of his brother Richard von Mises, when Ludwig von Mises really ascribed to an epistemological/epistemic probability interpretation.
Richard von Mises’s frequentism held that probabilities are based on collectives or sets of things, events, or phenomena, and formulated his limiting frequency definition of probability.
“An important implication of Richard von Mises’s frequency theory is that, when dealing with unique events, statistical or stochastic methods will be essentially useless. Where collectives do not exist, probability theory and the calculations based on it will add nothing to our knowledge concerning the world of reality. Only where previous experience has established that events can be considered as belonging to a collective, can statistical methods play a role.” (Hauwe 2011: 484).And furthermore,
“Richard von Mises thus advocated a monist view of probability, that is, he asserts that there is only one concept of probability that is of scientific importance, in contradistinction to his brother Ludwig von Mises who espoused a dualist view of probability.” (Hauwe 2011: 486, n. 24).According to Hauwe, Keynes adopted a logical interpretation of probability. Keynes argued that probability is a degree of partial entailment, but primarily in regard to propositions, and involving a logic of inductive reasoning. Thus Keynes conceived of probability as “a branch of logic” (Hauwe 2011: 488).
There is some confusion over the question whether Keynes’s theory was a subjective or objective one. But Keynes himself thought that “probability was [sc. a] degree of rational belief not simply degree of belief” (Hauwe 2011: 488). Therefore his theory must be understood as having a strong objective element.
Hauwe summarises the differences between Richard von Mises and Keynes on the fundamental nature of probability as follows:
Richard von MisesThe following crucial difference is seen by Hauwe:
– held that probability is a branch of empirical science;
– held that probability is to be defined as a limiting frequency;
– held that the axioms of probability are obtained by abstraction from two empirical laws;
– held that the only scientifically important theory of probability is the frequentist interpretation.
– held that probability is a logic of induction, and thus an extension of deductive logic;
– held that probability is a degree of rational belief;
– held that the axioms of probability are perceived by direct logical intuition;
– held a broader definition of probability beyond mere relative frequencies. (Hauwe 2011: 489).
”For Richard von Mises only probabilities defined within an empirical collective can be evaluated and only these probabilities have any scientific interest. The remaining uses of probability are examples of a crude prescientific concept towards which he takes a dismissive attitude. For Keynes on the other hand all probabilities are essentially on a par. They all obey the same formal rules and play the same role in our thinking. Certain special features of the situation allow us to assign numerical values in some cases, though not in general. Through the acknowledgement that frequency probability does not cover all we mean by probability, Keynes’s position is thus also closer to that of other economists such as Ludwig von Mises and John Hicks. Finally the position of statistics is different in the two accounts. For von Mises it is a study of how to apply probability theory in practice, similar to applied mechanics. For Keynes statistical inference is a special kind of inductive inference and statistics is a branch of the theory of induction.” (Hauwe 2011: 497).Now Ludwig von Mises’s notion of “class probability” appears to correspond to Richard von Mises’s frequency probability (Hauwe 2011: 500), but Hauwe contends that ultimately Ludwig von Mises held an epistemological/epistemic view of probability:
“On the one hand Ludwig von Mises clearly relates the idea of probability to the state of knowledge of the knowing subject. This is true both of class probability and of case probability. A statement is probable if our knowledge concerning its content is deficient. This view is shared by all adepts of an epistemological interpretation of the concept of probability, including John Maynard Keynes. Richard von Mises, to the contrary, very explicitly rejects the idea that the concept of probability refers to a state of partial or deficient knowledge. On the other hand, Ludwig von Mises clearly recognizes that the meaning of probability is different according to the field of knowledge in which it is used or according to the kind of phenomena to which it is applied. He thus embraces a dualist view in the philosophy of probability. But in this respect his view is again clearly different from and opposed to that of his brother Richard von Mises who obviously embraces a monist theory of probability.” (Hauwe 2011: 489)Hauwe contends that Ludwig von Mises regarded his category of “case probability” as “important scientific status” (Hauwe 2011: 500). But Mises held that case probability can never be given a strict numerical value, and Keynes also thought that many probabilities are not capable of numerical estimate, and in some case cannot be ranked on an ordinal scale (Hauwe 2011: 501).
Gillies, Donald. 2000. Philosophical Theories of Probability. Routledge, London and New York.
Hauwe, Ludwig van den. 2008. “John Maynard Keynes and Ludwig von Mises on Probability,” Procesos De Mercado Revista Europea de Economía Política 5.1: 11–50.
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. 1998. Human Action: A Treatise on Economics. The Scholar’s Edition. Mises Institute, Auburn, Ala.
Rothbard, M. N. 2004. Man, Economy, and State, The Scholar’s Edition. Ludwig von Mises Institute, Auburn, Ala.