The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

For much of this century, philosophers hoped that Einstein’s general theory of relativity would play the role of physician to philosophy. Its development would positively influence the philosophy of methodology and confirmation, and its ontology would answer many traditional philosophical debates—for example, the issue of spacetime substantivalism. In physics, by contrast, the attitude is increasingly that GTR itself needs a physician. The more we learn about GTR the more we discover how odd are the spacetimes that it allows. Not only (...) does GTR permit singularities, naked and clothed, but it allows time travel, topology change, and event and particle horizons, to name but a few of these oddities. Rather than revel in the riches of the theory, however, many physicists seek to rule out one or more of the above “pathologies” on the grounds that they are “physically unreasonable.” Thus contemporary researchers hawk various “cures” for the “illnesses” of GTR: among them, Chronology Protection to ensure against time travel, Cosmic Censorship for naked singularities, Inflation for horizons, and so on. The physics of these illnesses and cures, and the problems they engender, are the source of much controversy in the physics literature. Philosophers have largely neglected it. But clearly the subject needs philosophers of physics to determine whether the patient is genuinely ailing, and if so, to sift the real antidotes from the snake oil. (shrink)