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.

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关于“莱布尼茨等价”

莱布尼茨等价性是应用数学的一项原理，在广义相对论教科书和有关爱因斯坦空穴论证的哲学文献中都被广泛假定。在这篇文章中，我澄清了这个莱布尼茨等价的陈述中的一个歧义，并认为它对于洞论证的相关表达是严格错误的。然后我表明，洞论证仍然成功地驳斥了多种实体论；然而，最近提出的洞论点受到代表性等效原则的破坏的提议并不那么好。