Many points of contact between statistics and the philosophy of science are reviewed. Some of the topics mentioned are kinds of probability, weight of evidence (corroboration), tail probabilities ($p$-values), Bayes/non-Bayes compromises, "explicativity," induction and probabilistic causality.
"The Interface Between Statistics and Philosophy of Science." Statist. Sci. 3 (4) 386 - 397, November, 1988. https://doi.org/10.1214/ss/1177012754