Today, human-level machine intelligence is in the domain of futurism, but there is every reason to expect that it will be developed eventually. Once artiﬁcial agents become able to improve themselves further, they may far surpass human intelligence, making it vitally important to ensure that the result of an “intelligence explosion” is aligned with human interests. In this paper, we discuss one aspect of this challenge: ensuring that the initial agent’s reasoning about its future versions is reliable, even if these future versions are far more intelligent than the current reasoner. We refer to reasoning of this sort as Vingean reﬂection.