Abstract. After sketching the conflict between objectivists and subjectivists on the foundations of statistics, this chapter discusses an issue facing statisticians of both schools, namely, model validation. Statistical models originate in the study of games of chance and have been successfully applied in the physical and life sciences. However, there are basic problems in applying the models to social phenomena; some of the difficulties will be pointed out. Hooke's law will be contrasted with regression models for salary discrimination, the latter being a fairly typical application in the social sciences.

What is probability?

For a contemporary mathematician, probability is easy to define, as a countably additive set function on a σ-field, with a total mass of one. This definition, perhaps cryptic for non-mathematicians, was introduced by A. N. Kolmogorov around 1930, and has been extremely convenient for mathematical work; theorems can be stated with clarity, and proved with rigor.