A conception of probability as an irreducible feature of the physical world is outlined. Propensity analyses of probability are examined and rejected as both formally and conceptually inadequate. It is argued that probability is a non-dispositional property of trial-types; probabilities are attributed to outcomes as event-types. Brier's Rule in an objectivist guise is used to forge a connection between physical and subjective probabilities. In the light of this connection there are grounds for supposing physical probability to obey some standard set (...) of axioms. However, there is no a priori reason why this should be the case. (shrink)

Kolmogorov's account in his [1933] of an absolute probability space presupposes given a Boolean algebra, and so does Rényi's account in his [1955] and [1964] of a relative probability space. Anxious to prove probability theory ‘autonomous’. Popper supplied in his [1955] and [1957] accounts of probability spaces of which Boolean algebras are not and [1957] accounts of probability spaces of which fields are not prerequisites but byproducts instead.1 I review the accounts in question, showing how Popper's issue from and how (...) they differ from Kolmogorov's and Rényi's, and I examine on closing Popper's notion of ‘autonomous independence’. So as not to interrupt the exposition, I allow myself in the main text but a few proofs, relegating others to the Appendix and indicating as I go along where in the literature the rest can be found. (shrink)