The significance of Max Black’s indistinguishable spheres for the nature of particles in quantum mechanics is discussed, focusing in particular on the use of the idea of weak indiscernibility. It is argued that there can be four such Black spheres but that five are impossible. It follows from this that Black’s example cannot serve as a model for indistinguishability in physics. But Black’s discussion of his spheres gave rise to the idea of weak discernibility and it is argued that such predicates are unsatisfiable in the way intended. The underlying problem with weak discernibility spreads out to also undermine the whole notion that indistinguishability rests on a notion of the permutation invariance of particles. A better foundation is indicated.

中文翻译：

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五个无法区分的球体

讨论了 Max Black 的不可区分球体对量子力学中粒子性质的重要性，特别关注弱不可区分性概念的使用。有人认为可以有四个这样的黑色球体，但不可能有五个。因此，布莱克的例子不能作为物理学中不可区分性的模型。但是布莱克对他的领域的讨论引起了弱可辨别性的想法，并且有人认为这种谓词在预期的方式中是无法满足的。弱可辨别性的潜在问题扩展到也破坏了不可区分性基于粒子排列不变性概念的整个概念。表明了更好的基础。