An Introduction to the Philosophy of Science

Introduction

In the last chapter, we explored that aspect of probability ideas concerned with “the degree of belief warranted by evidence.” Now we turn to the other aspect: “the tendency, displayed by some chance devices, to produce stable relative frequencies” (Hacking, 1975, 1). Our use of examples involving games of chance to introduce the mathematics of probability at the beginning of the previous chapter relied implicitly on this idea. But are dice games relevant to science? As we will see, thinking of scientific experiments or measuring procedures as chance mechanisms with tendencies “to produce stable relative frequencies” holds the key to the potential value of relative frequency ideas for philosophy of science.

Frequentism understands probability statements as statements about the relative frequency with which a certain outcome would occur under repeated execution of some process. Frequentist ideas have been central to the development of theoretical and applied statistics, and thus have had a significant influence on how scientists analyze data and report their results. Some of these statistical practices have been subjected to considerable criticism, however, and philosophers of science have tended to regard Bayesianism as based on a more coherent set of principles. Recently, the error-statistical philosophy has attempted to respond to philosophical criticisms of frequentist statistics, while remaining founded on the idea of experiments as chance mechanisms.