I discuss how modern cosmology illustrates under-determination of theoretical hypotheses by data, in ways that are different from most philosophical discussions. I emphasise cosmology's concern with what data could in principle be collected by a single observer ; and I give a broadly sceptical discussion of cosmology's appeal to the cosmological principle as a way of breaking the under-determination.I confine most of the discussion to the history of the observable universe from about one second after the Big Bang, as described (...) by the mainstream cosmological model: in effect, what cosmologists in the early 1970s dubbed the ‘standard model’, as elaborated since then. But in the closing Section 4, I broach some questions about times earlier than one second. (shrink)

In this note, we cast doubt on the requirement of spacetime inextendibility; it is not at all clear that our universe is “as large as it can be.”.

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

In my contribution to the Symposium ("On the Vagaries of Determinism and Indeterminism"), I will identify several issues that arise in trying to decide whether Newtonian particle mechanics qualifies as a deterministic theory. I'll also give a mini-tutorial on the geometry and dynamical properties of Norton's dome surface. The goal is to better understand how his example works, and better appreciate just how wonderfully strange it is.

Here we briefly review the concept of "prediction" within the context of classical relativity theory. We prove a theorem asserting that one may predict one's own future only in a closed universe. We then question whether prediction is possible at all (even in closed universes). We note that interest in prediction has stemmed from considering the epistemological predicament of the observer. We argue that the definitions of prediction found thus far in the literature do not fully appreciate this predicament. We (...) propose a more adequate alternative and show that, under this definition, prediction is essentially impossible in general relativity. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

The aim of this paper is to discuss some aspects of the nature gravitational energy within the general theory of relativity. Some aspects of the difficulties to ascribe the usual features of localization and conservation to gravitational energy are reviewed and considered in the light of the dual of role of the dynamical gravitational field, which encodes both inertio-gravitational effects and the chronogeometrical structures of spacetime. These considerations will lead us to discuss the fact that the very notion of energy (...) - gravitational or not - is actually well-defined in the theory only with respect to some background structure. (shrink)

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.

A number of models of general relativity seem to contain “holes” that are thought to be “physically unreasonable.” One seeks a condition to rule out these models. We examine a number of possibilities already in use. We then introduce a new condition: epistemic hole-freeness. Epistemic hole-freeness is not just a new condition—it is new in kind. In particular, it does not presuppose a distinction between space-times that are “physically reasonable” and those that are not.

There has been a long-standing debate about the relationship of predictability and determinism. Some have maintained that determinism implies predictability while others have maintained that predictability implies determinism. Many have maintained that there are no implication relations between determinism and predictability. This summary is, of course, somewhat oversimplified and quick at least in the sense that there are various notions of determinism and predictability at work in the philosophical literature. In this essay I will focus on what I take to (...) be the Laplacean vision for determinism and predictability. While many forms of predictability are inconsistent with this vision, I argue that a suitably restricted notion of predictability, consistent with the practice of physicists, is implied by the Laplacean notion of determinism. It is argued that limitations on predictability are of an in principle nature in the Appendix. (shrink)