Existential risk research (X-risk) is usually advertised in terms of protecting long-term human flourishing, specifically from so-called extinction-level catastrophic threats. This framing opens up X-risk to legitimate criticism about the role of extant power structures in determining the operant notion of human flourishing in the foundations of the science. But an alternative foundations for the science of X-risk, which emphasizes its applied nature, shows that such criticism need not be a criticism of the science of X-risk, so much as it is a criticism of its usual applications. Toward this end, I argue that the science of X-risk is best construed as derivative of a wider science of iterative, rational deliberation, typically involving human agents: X-risk is focused on ambient existential risk to those agents, when considered as embedded in complex, deliberate systems. From this perspective, the foundations of X-risk represents a rich territory for investigation, implicating a variety of topics familiar in contemporary philosophical research, e.g. philosophy of modeling and applied mathematics, strategic reasoning and problems of collective action, values in science, and science in society.