I offer a variant of Putnam’s “permutation argument,” originally an argument against metaphysical realism. This variant is called the “natural permutation argument.” I explain how the natural permutation argument generates a form of referential inscrutability which is not resolvable by consideration of “natural properties” in the sense of Lewis’s response to Putnam. However, unlike the classical permutation argument (which is applicable to nearly all interpretations of all first-order theories), the natural permutation argument only applies to interpretations which have some special symmetries. I give an analysis of the interpretations to which the natural permutation argument does apply, and I explain how, when it fails to apply, the referential inscrutability generated by permutation arguments is resolvable by a Lewisian strategy. In order to demonstrate how these problems of referential inscrutability play out in an a priori setting relevant to philosophy, I discuss the applicability of the natural permutation argument in set-theoretic reasoning. I use the well-known Kunen inconsistency theorem to show that, in Zermelo–Fraenkel set theory, the Axiom of Choice is sufficient to resolve referential inscrutability. I then explain how, as a result of a recent theorem of Daghighi–Golshani–Hamkins–Jeřábek, in certain non-well-founded set theories the natural permutation argument does yield an intractable inscrutability of reference.

我提供普特南“排列论证”的一个变体，最初是反对形而上学实在论的论证。这种变体称为“自然排列论证”。我解释了自然排列论证如何产生一种指称的不可理解性形式，这种形式无法通过考虑刘易斯对普特南的回应中的“自然属性”来解决。然而，与经典排列论证（几乎适用于所有一阶理论的所有解释）不同，自然排列论证仅适用于具有某些特殊对称性的解释。我对自然排列论证确实适用的解释进行了分析，并解释了当它无法应用时，排列论证产生的指称的不可理解性如何可以通过刘易斯策略来解决。为了证明这些指称的不可理解性问题如何在与哲学相关的先验环境中发挥作用，我讨论了自然排列论证在集合论推理中的适用性。我使用著名的库南不一致性定理来证明，在策梅洛-弗兰克尔集合论中，选择公理足以解决指称的不可理解性。然后，我将解释，根据 Daghighi-Golshani-Hamkins-Jeřábek 最近的定理，在某些没有充分根据的集合论中，自然排列论证确实会产生难以理解的指称。