The Bactra Review   Error and the Growth of Experimental Knowledge
Some frequentists, like Neyman and Mayo (see her pp. 165--8) want to add some qualifications to such statements. Mathematical probability is a property of some formal, abstract mathematical objects. It so happens, as an empirical fact, that these objects can be used, with a fair degree of accuracy, to represent various bits and pieces of the real world. The long-run limits invoked are to be understood as a way of speaking about what would happen if we repeated experiments indefinitely, about (as Neyman puts it) "imaginary random experiments." Rather than explore this topic in the depth it deserves, which would lead to discussing, on the one hand, the axioms of probability, measure theory, sigma-algebras and Kolmogorov complexity, and on the other hand the connection between mathematics and physical reality, I'll continue to speak in a simple, vulgar and somewhat inaccurate fashion.