Geometrizing gravity and vice-versa: The force of a formulation

It is well-known that Newton’s theory of gravity, commonly held to describe a gravitational force, can be recast in a geometrical form: Newton- Cartan theory. It is less well-known that general relativity, an apparently geometrical theory, can be reformulated in such a way that it resembles a force theory; teleparallel gravity does just this. This raises questions. One of these concerns theoretical underdetermination. I argue that these theories do not, in fact, represent cases of worrying underdetermination. On close examination, the alternative formulations are best interpreted as postulating the same spacetime ontology. In accepting this, we see that the ontological commitments of these theories cannot be directly deduced from their mathematical form. The geometrical nature of a gravitational theory is not a straightforward consequence of anything internal to that theory as a theory of gravity. Rather, it essentially relies on the rest of nature (the nongravitational interactions) conspiring to choose the appropriate set of inertial frames.