This first chapter probes the limits of Badiou’s “formalised inhumanism”. It argues that it is wrong to characterise the figure of the human that emerges in Badiou’s thought as radically new, and traces its similarities with other figures which Badiou rejects. For both Badiou and his antagonists, the human is irreducibly composite: it cannot be what it is without a constitutive relation to an instance of inhumanity or non-humanity outside itself. Badiou’s split anthropology of the “human animal” and the “immortal” faces one major structural and ethical problem, which arises from the way in which he seeks to understand the relation between the animal and immortal: he makes fidelity to a truth, and therefore humanity in its full sense, contingent upon an individual’s possession of what he calls “the one and only uniquely human capacity” (Métapolitique111/ Metapolitics 97-8), namely the capacity for affirmative thought. Such thought functions for Badiou as a “host capacity”, a boundary marker or a gatekeeper of the uniqueness of humanity among animal, organic and non-organic entities. Despite exploring several creative ways to overcome the problems caused by Badiou’s “host capacity” account of humanity, I conclude that it remains a thorn in the flesh of his claim that “several times in its brief existence, every human animal is granted the chance to incorporate itself into the subjective present of a truth” (Logiques des mondes 536 n11/Logics of Worlds 514 n11).