A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that, by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic.

中文翻译：

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Metalogic 和过度生成的论点

反对二阶逻辑逻辑性的一个突出反对意见是所谓的 Overgeneration Argument。然而，如何理解这一论点尚不清楚。在文章的第一部分，我们检查了这个论证并定位了它的主要来源，即所谓的二阶逻辑和数学的纠缠。然后，我们确定了纠缠被认为是有问题的各种原因。在文章的第二部分，我们从元理论的角度来看待这个问题。我们证明了一些结果，证明纠缠对用于二阶逻辑的语义类型很敏感。这些结果提供了证据，通过从二阶逻辑的标准集合论语义转移到利用高阶资源的语义，