The Hole Argument and Beyond, Part I: The Story so Far

Abstract

In this two-part paper, we review, and then develop, the assessment of the hole argument for general relativity. This first Part reviews the literature hitherto, focussing on the philosophical aspects. It also introduces two main ideas we will need in Part II: which will propose a framework for making comparisons of non-isomorphic spacetimes. In Section 1 of this paper, we recall Einstein's original argument. Section 2 recalls the argument's revival by philosophers in the 1980s and 1990s. This includes the first main idea we will need in Part II: namely, that two spacetime points in different possible situations are never strictly identical -- they are merely counterparts. In Section 3, we report -- and rebut -- more recent claims to "dissolve" the argument. Our rebuttal is based on the fact that in differential geometry, and its applications in physics such as general relativity, points are in some cases identified, or correspond with each other, between one context and another, by means other than isometry (or isomorphism). We call such a correspondence a threading of points. This is the second main idea we shall use in Part II.