 Hypotheses with higher simplicity rank are regarded as simpler than those with lower ranks. Simplicity ranks are defined in terms of logical entailment relations, hence are language-invariant. Simplicity ranks as defined can be seen as degrees of falsifiability in the following sense. Consider a hypothesis of simplicity rank 1. Such a hypothesis is falsifiable because an evidence sequence that verifies an alternative hypothesis of rank 0 falsifies it. Moreover, a hypothesis of simplicity rank 1 is persistently falsifiable in the sense that it remains falsifiable no matter what evidence sequence consistent with it is observed. A hypothesis of simplicity rank \(n+1\) is persistently falsifiable by hypotheses of rank \(n.\) Let us illustrate the definition in our running examples.