By mimicking the standard definition for a formal language, we define what it is for a natural language to be compact. We set out a valid English argument none of whose finite subarguments is valid. We consider one by one objections to the argument's logical validity and then dismiss them. The conclusion is that English—and any other language with the capacity to express the argument—is not compact. This rules out a large class of logics as the correct foundational one, for example any sound and complete logic, and in particular first-order logic. The correct foundational logic is not compact.

中文翻译：

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英语后果紧凑吗？

通过模仿形式语言的标准定义，我们定义了自然语言的紧凑性。我们提出了一个有效的英语论证，其有限子论证都无效。我们一一考虑反对该论证的逻辑有效性，然后驳回它们。结论是英语——以及任何其他能够表达论点的语言——并不紧凑。这排除了一大类逻辑作为正确的基础逻辑，例如任何健全和完整的逻辑，尤其是一阶逻辑。正确的基础逻辑并不紧凑。