  The setting for the discussion is a general relativistic spacetime  \((\mathcal{M},g_{ab})\) where  \(\mathcal{M}\) is a differentiable manifold and \(g_{ab}\) is a Lorentz signature metric defined on all of \(\mathcal{M}\). The central issue addressed in the physics literature on time machines is whether in this general setting it is physically possible to operate a Thornian time machine. This issue is to be settled by proving theorems about the solutions to the equations that represent what are taken to be physical laws operating in the general relativistic setting—or at least this is so once the notion of a Thornian time machine has been explicated. Unfortunately, no adequate and generally accepted explication that lends itself to the required mathematical proofs is to be found in the literature. This is neither surprising nor deplorable. Mathematical physicists do not wait until some concept has received its final explication before trying to prove theorems about it; indeed, the process of theorem proving is often an essential part of conceptual clarification. The moral is well illustrated by the history of the concept of a spacetime singularity in general relativity where this concept received its now canonical definition only in the process of proving the Penrose-Hawking-Geroch singularity theorems, which came at the end of a decades long dispute over the issue of whether spacetime singularities are a generic feature of solutions to Einstein’s gravitational field   equations.[6] However, this is not to say that philosophers interested in time machines should simply wait until the dust has settled in the physics literature; indeed, the physics literature could benefit from deployment of the analytical skills that are the stock in trade of philosophy. For example, the paradoxes of time travel and the fate of time machines are not infrequently confused in the physics literature, and as will become evident below, subtler confusions abound as well.