In this essay, I evaluate the theory that leadership ought to be "paradoxical", meaning that leaders should embrace contradictions and incoherent norms. The idea of a paradoxical practice is trending in both education leadership and policy studies (as well as in business leadership studies), but in fact the literature on education (in Singapore and elsewhere) suggests that this is not helpful for arresting the terrors of performativity, and that there are examples of high performing education systems flourishing better through being consistent with core values. I detail how paradoxical leadership makes it difficult for defending ethical practice and how their rejection and shaming of the Aristotelian principle of non-contradiction risks effecting a woke culture that represses criticality. I argue that all this is part of an ongoing nominalist trend (the bifurcation between nature and thinking) in the history of ideas, only that we are at a philosophical tipping point. I explore the alternative, which takes contradictions seriously and irons out inconsistencies, and pre-empt objections internal to the Aristotelian tradition, and also offer an interpretation of James March's influential theory of leadership to show that if read carefully, the theory does not fit well with the paradoxes approach.