Space and Time

Here, formal tools are used to pose and answer several philosophical questions concerning space and time. The questions involve the properties of possible worlds allowed by the general theory of relativity. In particular, attention is given to various causal properties such as "determinism" and "time travel"

On Feyerabend, General Relativity, and 'Unreasonable' Universes

I investigate the principle *anything goes* within the context of general relativity. After a few preliminaries, I show a sense in which the universe is unknowable from within this context; I suggest that we 'keep our options open' with respect to competing models of it. Given the state of affairs, proceeding counter-inductively seems to be especially appropriate; I use this method to blur some of the usual lines between 'reasonable' and 'unreasonable' models of the universe. Along the way, one is led to a useful collection of variant theories of general relativity -- each theory incompatible with the standard formulation. One may contrast one variant theory with another in order to understand foundational questions within 'general relativity' in a more nuanced way. I close by sketching some of the work ahead if we are to embrace such a pluralistic methodology

Some 'No Hole' Spacetime Properties Are Unstable

We show a sense in which the spacetime property of effective completeness -- a type of ``local hole-freeness'' or ``local inextendibility'' -- is not stable

Space and Time

Here, formal tools are used to pose and answer several philosophical questions concerning space and time. The questions involve the properties of possible worlds allowed by the general theory of relativity. In particular, attention is given to various causal properties such as "determinism" and "time travel"

Does the Curvature Structure of Spacetime Determine Its Topology?

We explore the title question. After some topological preliminaries, we define a "curvature isomorphism" between spacetimes. We introduce a hierarchy of curvature conditions and show that at a certain level, a curvature isomorphism must be a homeomorphism. The highest level of the hierarchy is satisfied by a spacetime if every smooth scalar function on its manifold is an invariant scalar curvature function. We show that such "maximally structured" spacetimes exist and that a curvature isomorphism between them must be a diffeomorphism. We highlight a number of connections between our project and the one in which the topology of spacetime is determined from a causal relation between spacetime points (Malament 1977). We emphasize that analogous results are obtained here by considering only invariant properties of spacetime points -- no relations needed