 Recall that when we have a finite collection of concrete alternative hypotheses available, \(\{h_1, h_2 , \ldots ,h_m\}\), but where this set of alternatives is not exhaustive (where additional, unarticulated, undiscovered alternative hypotheses may exist), the catch-all alternative hypothesis \(h_K\) is just the denial of each of the concrete alternatives, \(({\nsim}h_1\cdot{\nsim}h_2\cdot \ldots \cdot{\nsim}h_m)\). Generally, the likelihood of evidence claims relative to a catch-all hypothesis will not enjoy the same kind of objectivity possessed by the likelihoods for concrete alternative hypotheses. So, we leave the subscript \(\alpha\) attached to the likelihood for the catch-all hypothesis to indicate this lack of objectivity.