We provide an axiomatic characterization of recursive Maxmin preferences that stem from (possibly) incomplete preferences representing choices that are justified by hard evidence. The decision-maker disposes of objective probabilistic information that may induce dynamically inconsistent behavior. To ensure that her choices be informed by objective information, dynamically consistent, and ambiguity averse, she constructs her subjective set of priors as the rectangular hull of the objective information set. The characterization builds upon two axioms that naturally combine these three requirements in a behavioral way. Moreover, our main result suggests a principled justification for the use of recursive Maxmin preferences in applications to dynamic choice problems.