Frequency Theory of Probability

Discipline: Philosophy

Theory due to German philosopher and mathematician Richard von Mises (1883-1954) in Probability, Statistics and Truth (1928, 2nd edition translated 1939).

Here he defined the probability of something in terms of the relative frequency of its occurrence on occasions when it might occur.

Von Mises limits his definition to cases where we have a collective, or potentially infinite sequence of cases satisfying certain conditions of randomness (for example throws of a die).

Since any frequency in a finite run is compatible with almost any frequency in a sufficiently long run, we must define the probability (for example, of a six on our die) as the limiting frequency of sixes as the number of throws extends indefinitely, assuming that there is such a limit.

Objections to the theory include the narrrowness of its scope (for example, it has no strict application to the probability of single events, still less to that of theories and so on); and the difficulties of ensuring, first, that the randomness conditions are satisfied; and second, that there is a limiting frequency.

With regard to this latter objection, we seem in danger of being reduced to saying that probably there is a limiting frequency, with this 'probably' being unexplained impossibility of a gambling system.

Source:
H E Kyburg, Probability and Inductive Logic (1970), ch.4

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