Ian Hacking’s wide-ranging and penetrating analysis of science contains two well-developed lines of thought. The first emphasizes the contingent history of our inquiries into nature, focusing on the various ways in which our concepts and styles of reasoning evolve through time, how their current application is constrained by the conditions under which they arose, and how they might have evolved differently. The second is the mistrust of the idea that the world contains mind-independent natural kinds, preferring nominalism to ‘inherent structurism’. These two pillars of thought seem at first to be mutually reinforcing: the lack of natural structure can help make sense of scientific variability and revision, while variability and revision provide reason to suspect that natural structure is little more than idealization. In what follows, I argue that these two pillars not only fail to support each other, but in fact conflict. One of them must fall, and it is clear which.