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"The Hole Argument and Some Physical and Philosophical Implications"
John Stachel 
Abstract
1 Introduction
1.1 Why should we care?
1.2 Summary: Where we are headed
1.3 Outline of the article
2 Early History
2.1 From the special theory to the search for a theory of gravity
2.2 From the equivalence principle to the metric tensor
2.3 From the metric tensor to the hole argument
2.4 From the hole argument back to general covariance
2.5 The point coincidence argument
2.6 From general covariance to Kretschmann’s critique
2.7 The Cauchy problem for the Einstein equations: from Hilbert to Lichnerowicz
3 Modern Revival of the Argument
3.1 Did Einstein misunderstand coordinate transformations?
3.2 Einstein’s vision and fiber bundles
4 The Hole Argument and Some Extensions
4.1 Structures, algebraic and geometric, permutability and general permutability
4.2 Differentiable manifolds and diffeomorphisms, covariance and general covariance
4.3 Fiber bundles: principal bundles, associated bundles, frame bundles, natural and gauge-natural bundles
4.4 Covariance and general covariance for natural and gauge-natural bundles
5 Current Discussions: Philosophical Issues
5.1 Relationalism versus substantivalism: Is that all there is?
5.2 Evolution of Earman’s relationalism
5.3 Pooley’s position: sophisticated substantivalism
5.4 Stachel and dynamic structural realism
5.5 Relations, internal and external, quiddity and haecceity
5.6 Structures, algebraic and geometric
5.7 Does “general relativity” extend the principle of relativity?
6 Current Discussions: Physical Issues
6.1 Space-time symmetry groups and partially background-independent space-times
6.2 General relativity as a gauge theory
6.3 The hole argument for elementary particles
6.4 The problem of quantum gravity
7 Conclusion: The Hole Argument Redivivus
A Nijenhuis on the Formal Definition of Natural Bundles
B Appendix to Section 4: Some Philosophical Concepts
B.1 Things: Synchonic states and diachronic processes
B.2 Open versus closed systems: Determinism versus causality
B.3 Properties: Intrinsic and extrinsic
B.4 Relations: Internal and external
B.5 Quiddity and haecceity
References
Footnotes
To avoid future confusion, let me emphasize that the terminology introduced in Section 4 differs from that of Einstein, and indeed that of many contemporary accounts. In this review, the requirement that, if G(x) is a solution to the field equations, then ′ G (x) must also be a solution is called covariance. General covariance is the requirement that G(x) and ′ G (x) represent one and the same physical solution. Another difference is that Section 4 these conditions are formulated coordinate independently.