This article develops an axiomatic theory for statistical hypothesis generation that is based on the ideas of Gauss’ Theoria Motus. At the core of the theory is Bernoulli’s fifth axiom: Between two, the one that seems more probable should always be chosen. Under supplementary assumptions well-known special cases appear, such as regression analysis and principal component analysis. Through rigor, the abstracted theory provides clarity as to how different statistical hypothesis generation methods are interrelated, how they differ, and which method that should be used in a given situation.