A unified interpretation of probability

Abstract:In this article I revisit the frequency interpretation of probability of von Mises, and argue that it contains the key elements of any coherent interpretation of scientific probability - notwithstanding the heavy criticisms von Mises collected from mathematicians and philosophers alike. I propose a modified definition that is not based on von Mises' "infinite collectives" but retains an essential ingredient of his interpretation, namely that probability can only quantitatively be defined for events that are, or can be, repeated in similar conditions and that exhibit frequency stabilisation. New is that the mentioned "conditions" should be "partitioned". Thus, I will partition probabilistic systems into object and environment, or in object, initiating, and probing subsystem, and show that such partitioning solves a series of classic problems. Other consistent interpretations can be unified with frequentism, e.g. Bayesianism à la Jaynes. I explore in detail the tantalising subjective or operationalist touch of probability, and argue that it can be put on objective grounds. One further upshot of the model is that several quantum puzzles can be seen as deriving from an imprecise interpretation of probability.

This is the penultimate version of Chapter 4 of my book "Problem solving in philosophy. How to do philosophy in the age of ultra-intelligent AI" (cf. this https URL). The present article is for 99.99% identical to the book chapter (which is the last version)

History and Overview (math.HO); Probability (math.PR); Quantum Physics (quant-ph)

arXiv:2609.38293 [math.HO]

(or arXiv:2609.38293v1 [math.HO] for this version)

https://doi.org/10.48550/arXiv.2609.38293 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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