The prospect of cognitive enhancement well beyond current human capacities raises worries that the fundamental equality in moral status of human beings could be undermined. Cognitive enhancement might create beings with moral status higher than persons. Yet, there is an expressibility problem of spelling out what the higher threshold in cognitive capacity would be like. Nicholas Agar has put forward the bold claim that we can show by means of inductive reasoning that indefinite cognitive enhancement will probably mark a difference in moral status. The hope is that induction can determine the plausibility of post‐personhood existence in the absence of an account of what the higher status would be like. In this article, we argue that Agar's argument fails and, more generally, that inductive reasoning has little bearing on assessing the likelihood of post‐personhood in the absence of an account of higher status. We conclude that induction cannot bypass the expressibility problem about post‐persons.