 Several authors (Pollock (1995), Ryan (1996), Douven (2002)) attempt to revise the strong Lockean thesis by placing restrictions on when a high degree of belief warrants full belief. Broadly speaking, they propose that a high degree of belief is sufficient to warrant full belief unless some defeating condition holds. For example, Douven (2002) says that it is sufficient except when the proposition is a member of a  probabilistically self-undermining set. A set \({\bf S}\) is probabilistically self-undermining iff for all \(A \in {\bf S}, \Pr(A)&gt;s\) and \(\Pr(A | B)\leq s,\) where \(B=\cap( {\bf S} \setminus \{ A \}).\) It is clear that this proposal would prohibit full belief that a particular lottery ticket will lose.