What is the relationship between extinction and disability? As “we” face a future of resource-depletion, eco-system collapse, and runaway global warming, it might seem more urgent than ever to develop new forms of rationality and technology to allow us to survive. The conception of survival, or living-on, is at the heart of Derrida’s deconstruction, as is an inherently promissory account of time and experience. In the spirit of deconstruction, this chapter looks at the ways in which ability, capacity, and radically future promising are intertwined with an inflated and unsustainable mode of existence. Just as extinction threats pose necessary questions to the present regarding what life or lives will survive into the future, so the legacy of philosophy’s past and conditions pose questions as to the forms of life that have been granted a prima facie right to survival.