 These examples suggest that the \(\lt\) partial order corresponds to our intuitive simplicity judgements about empirical hypotheses; Genin and Kelly [2019] provide an extensive defense of this claim. It can be shown that the \(\lt\) ordering agrees with the simplicity ranks defined in the previous subsection, in the sense that if \(H_1 \lt H_2\) but not \(H_2 \lt H_1\), then the simplicity rank of \(H_1\) is less than the rank of \(H_2\). These observations motivate an Ockham principle: An inductive method satisfies the Ockham principle with respect to separability if it always conjectures a maximally simple hypothesis \(H\) consistent with the evidence. In our notation, if an Ockham method adopts a hypothesis \(H\) given a finite observation sequence, then there is no alternative simpler hypothesis \(H'\) such that \(H' \lt H\). That is, every alternative hypothesis \(H'\) will eventually be separated from \(H\) by the evidence if \(H'\) is true. In the raven example, the generalizing method satisfies the Ockham principle, but the contrary method does not, because it adopts \(H_2 =\) “some raven is not black”. The following theorem shows that the connection between the Ockham principle and regressive mind changes is general. 