Regarding ‘Leibniz Equivalence’

Leibniz Equivalence is a principle of applied mathematics that is widely assumed in both general relativity textbooks and in the philosophical literature on Einstein’s hole argument. In this article, I clarify an ambiguity in the statement of this Leibniz Equivalence, and argue that the relevant exp...

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Bibliographic Details
Published in:Foundations of physics 2020-04, Vol.50 (4), p.250-269
Main Author: Roberts, Bryan W.
Format: Article
Language:English
Subjects:
Applications of mathematics
Classical and Quantum Gravitation
Classical Mechanics
Equivalence
History and Philosophical Foundations of Physics
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativity
Relativity Theory
Special Issue : Hole Argument
Statistical Physics and Dynamical Systems
Textbooks
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Summary:Leibniz Equivalence is a principle of applied mathematics that is widely assumed in both general relativity textbooks and in the philosophical literature on Einstein’s hole argument. In this article, I clarify an ambiguity in the statement of this Leibniz Equivalence, and argue that the relevant expression of it for the hole argument is strictly false. I then show that the hole argument still succeeds as a refutation of manifold substantivalism; however, recent proposals that the hole argument is undermined by principles of representational equivalence do not fare so well.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-020-00325-9