A unified interpretation of probability

@misc{vervoort2026unified,
  title = {{A unified interpretation of probability}},
  author = {Louis Vervoort},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38293},
  eprint = {2609.38293},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38293},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - A unified interpretation of probability
AU  - Louis Vervoort
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38293
UR  - https://arxiv.org/abs/2609.38293
AB  - 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.
ER  -