Why must incompatibility be symmetric? An odd question, but recent work in the semantics of non-classical logic, which appeals to the notion of incompatibility as a primitive and defines negation in terms of it, has brought this question to the fore. Francesco Berto proposes such a semantics for negation argues that, since incompatibility must be symmetric, double negation introduction must be a law of negation. However, he offers no argument for the claim that incompatibility really must be symmetric. Here, I provide such an argument, showing that, insofar as we think of incompatibility in normative pragmatic terms, it can play its basic pragmatic function only if it is symmetric. The upshot is that we can vindicate Berto’s claim about the symmetry of incompatibility but only if we, pace Berto, think about incompatibility, in the first instance, as a pragmatic relation between acts rather than a semantic relation between contents.

中文翻译：

---

为什么不相容必须是对称的？

为什么不相容必须是对称的？这是一个奇怪的问题，但最近非经典逻辑语义学的工作，将不相容性的概念作为一个原语，并用它来定义否定，使这个问题脱颖而出。Francesco Berto 提出了这样一种否定语义，认为由于不相容性必定是对称的，因此双重否定的引入必定是否定法则。然而，他没有为不兼容确实必须是对称的主张提供任何论据。在这里，我提出这样一个论点，表明我们用规范语用术语来思考不相容性，只有对称才能发挥其基本语用功能。结果是，我们可以证明贝尔托关于不相容性对称性的主张是正确的，但前提是我们首先考虑不相容性，