Regarding ‘Leibniz Equivalence’
Bryan W. Roberts
Abstract
Abstract 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.
Topics & Concepts
Equivalence (formal languages)Argument (complex analysis)EinsteinAmbiguityPhilosophy of scienceGeneral relativityEpistemologyStatement (logic)MathematicsTheoretical physicsEquivalence principle (geometric)Theory of relativityCalculus (dental)PhilosophyPure mathematicsPhysicsMathematical physicsGeometryLinguisticsChemistryBiochemistryMedicineDentistryRelativity and Gravitational TheoryQuantum Mechanics and ApplicationsPhilosophy, Science, and History