 All proposals of this kind are vitiated by the following sort of example due to Korb (1992). Let \(A\) be any proposition with a degree of belief above threshold but short of certainty. Let \(L_i\) be the proposition that the \(i^{th}\) lottery ticket (of a large lottery with \(N\) tickets) will lose. Consider the set \({\bf S} = \{ \neg A \cup L_i | 1 \leq i \leq N \}.\) Each member of \({\bf S}\) is above threshold, since \(L_i\) is above threshold. Furthermore, the set \({\bf S} \cup \{ A\}\) meets Douven’s (as well as Pollock’s and Ryan’s) defeating conditions. Therefore, these proposals prohibit full belief in any proposition with degree of belief short of certainty. Douven and Williamson (2006) generalize this sort of example to trivialize an entire class of similar formal proposals.