 Logics of extreme probability (beginning with the work of Ernest Adams) did not permit the nesting of default conditionals for this reason: the conditionals were supposed to represent something like subjective conditional probabilities of the agent, to which the agent was supposed to have perfect introspective access. Consequently, it made no sense to nest this conditionals within disjunctions (as though the agent couldn’t tell which disjunct represented his actual probability assignment) or within other conditionals (since the subjective probability of a subjective probability is always trivial — either exactly 1 or exactly 0). However, there is no reason why the logic of extreme probabilities couldn’t be given a different interpretation, with \((p \Rightarrow q)\) representing something like the objective probability of \(q\), conditional on \(p\), is infinitely close to 1. In this case, it makes perfect sense to nest such statements of objective conditional probability within Boolean operators (either the probability of \(q\) on \(p\) is close to 1, or the probability of \(r\) on \(s\) is close to 1), or within operators of objective probability (the objective probability that the objective probability of \(p\) is close to 1 is itself close to 1). What is required in the latter case is a theory of higher-order probabilities.