Earman and Norton's hole argument demonstrates that diffeomorphic equivalence classes, not individual spacetime models, are the proper locus of physical content in general relativity.

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Key Terms

Diffeomorphic equivalence classes(as describing what contains physical content): Groups of mathematical models that describe the same physical situation, even though they look different when you write out their equations; they're 'equivalent' in a deep mathematical sense.
Earman and Norton(as the authors being referenced): Two philosophers (John Earman and John D. Norton) who wrote influential papers about 'supertasks'—thought experiments involving infinite sequences of actions happening in finite time.
General relativity(as used in physics): Einstein's theory explaining how gravity works by describing space and time as flexible, bendable things affected by massive objects like stars and planets.
Physical content(philosophy of science): Meaning that comes from describing how things actually work in reality, rather than just being abstract ideas.

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The hole argument(as used in philosophy of physics and metaphysics)

A thought experiment in philosophy of physics (developed by John Earman and David Norton) that asks whether two physical situations that differ only in how we label points in spacetime are actually the same or different; it challenges whether our descriptions of reality are truly capturing what's real versus just how we're representing it.

Earman and Norton's hole argument demonstrates that diffeomorphic equivalence classes, not individual spacetime models, are the proper locus of physical content in general relativity.

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