 Although the catch-all hypothesis may lack objective likelihoods, the influence of the catch-all term in Bayes’ Theorem diminishes as additional concrete hypotheses are articulated. That is, as new hypotheses are discovered they are “peeled off” of the catch-all. So, when a new hypothesis \(h_{m+1}\) is formulated and made explicit, the old catch-all hypothesis \(h_K\) is replaced by a new catch-all, \(h_{K*}\), of form \(({\nsim}h_1\cdot \cdot{\nsim}h_2\cdot \ldots \cdot{\nsim}h_{m}\cdot{\nsim}h_{m+1})\); and the prior probability for the new catch-all hypothesis is gotten by diminishing the prior of the old catch-all: \(P_{\alpha}[h_{K*} \pmid b] = P_{\alpha}[h_K \pmid b] - P_{\alpha}[h_{m+1} \pmid b]\). Thus, the influence of the catch-all term should diminish towards 0 as new alternative hypotheses are made  explicit.[10] 