De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.

This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics (ergodic theory) is of independent interest, but also adds weight to the claim that it is possible to justify an (...) objective interpretation of probabilities in a theory having as a basis the paradigmatically deterministic theory of classical mechanics. (shrink)

De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.

This is an extensive review of recent work on the foundations of statistical mechanics.