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.