Dispositions, Causes, Persistence As Is, and General Relativity

Abstract

I argue that, on a dispositionalist account of causation and indeed on any other view of causation according to which causation is a real relation, general relativity (GR) does not give causal principles a role in explaining phenomena. In doing so, I bring out a surprisingly substantial constraint on adequate views about the explanations and ontology of GR, namely the requirement that such views show how GR can explain motion that is free of disturbing influences.

Acknowledgements

Thanks to Joseph Berkovitch, Angelo Cei, and the journal's referees for their helpful comments.

Notes

See, among many others, Harré and Madden (1973), Fetzer (1977), Cartwright (1989, 1999), Bigelow, Ellis, and Lierse (1992), Chalmers (1999), Molnar (2003), Mumford (2004), Heil (2005), and Bird (2007).

Another important claim many friends of dispositions make is that one can reduce some or all laws of nature to d-causal principles. I do not elaborate on this claim here as I avoid drawing any conclusions about views of laws of nature from my discussion.

See Cartwright and Alexandrova (2005) for a brief summary of some of the ways in which the special sciences are often supposed to presuppose that d-causal principles are ultimate explanatory principles.

When I write of cases of absences of change or of instances of the absence of change, I refer to instances of the absence of change in some respect in some situation. Thus, that there is some instance of the absence of change does not mean that there is no change in general or in whatever situation the absence is found.

Insisting that candidate fundamental explanatory principles are not explanatory would not help either to identify the candidates with d-causal principles or to equate the candidates with some conjunction of d-causal and other principles. For d-causal principles are supposed to be explanatory. Further, as we will see, such insistence is not plausible in the case of GR.

See Psillos (1999, 171–172) for an overview of the considerations for thinking that explanatory strength is an epistemic virtue, i.e. a virtue that is a guide to truth. See van Fraassen (1983, 166–169) for a case for thinking that explanatory strength is just a pragmatic virtue, i.e. a virtue that is indicative of empirical adequacy.

This is a case in which d-causal principles would explain the absence of a certain caused change and hence the absence of explicable change. My focus is on the inability of d-causal principles to explain the absence of inexplicable change rather than just on explaining the absence of change precisely because d-causal principles can explain the absence of explicable change.

An even stronger conclusion can be drawn here and can be drawn without assuming that if d-conservation principles could explain i-conservation principles, d-conservation principles would also be able to explain instances of the absence of inexplicable change. Insofar as d-causal principles provide information about what will be the case, the information in question is about physical occurrences. It is not information about absences of inexplicable change. So there is no way of deriving, solely from d-causal principles, principles that do provide information about what absences of inexplicable change will be the case.

When I speak of mass-energy here, I exclude the mass-energy of the gravitational field itself.

Some, e.g. Brown (2005), prefer to say that GR explains by appealing to the coupling between the gravitational field and mass-energy in space-time. But that the explanations of general relativity are in terms of space-time geometry is not essential to my argument. What is essential to it is just that relativistic explanations are a single kind of explanation that explains what d-causal principles cannot explain.

A test particle is a particle with energy and momentum sufficiently small so that its effect on the curvature of space-time is negligible, and with a size that is such that the inhomogeneities of the gravitational field in its vicinity have a negligible effect on its motion.

The fact that Newtonian mechanics treats inertial motion as motion that is not subject to gravity allows one to argue that it offers no explanation for inertial motion. Since GR treats inertial and non-inertial motion as motion in a gravitational field, however, it does not allow such an argument. Indeed, the case for thinking that GR explains the principle of inertia and, with it, inertial motion is well established in the literature (Brown 2005).

The explanation would have to be partial, of course, because d-causal principles cannot explain instances of the absence of inexplicable change.

The reference to electromagnetic fields made here is needed because information about these fields sometimes goes into explanations that are based on Einstein's field equation. I am not, however, considering what types of explanations result when Einstein's field equation is combined with equations for non-gravitational phenomena.

Whether equation (4) really is a local conservation principle is unclear (Hoefer 2000). I, accordingly, do not assume that it is.

In other cases, equation (4) will have to be supplemented by additional relevant dynamical equations, e.g. by Maxwell's equations in the case of an electromagnetic field, if the dynamics are fully to be determined.

This argument is nicely put by Ciufolini and Wheeler (1995, 27–28).

Explanations derived from equation (3) will, even when they purport to be solely about gravitational phenomena, sometimes make use of auxiliary, (arguably) explanatory hypotheses that are not part of a theory of gravity as such. I make no claim about the explanations these hypotheses provide.