Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first reconstruct his argument and present its restriction to the case of quantum logic (QL). Then we show that there is no problematic tension between the applicability of classical mathematical models to quantum phenomena and the endorsement of QL in the reasoning about the latter. Once we identify the premise in Williamson’s argument that turns out to be false when restricted to QL, we argue that the same premise fails for a wider variety of non-classical logics. In the end, we use our discussion to draw some general lessons concerning the relationship between applied logic and applied mathematics.

中文翻译：

---

非经典逻辑与应用经典数学之间所谓的紧张关系

蒂莫西·威廉姆森 (Timothy Williamson) 最近认为，经典数学在自然科学和社会科学中的适用性引发了在非数学领域认可广泛的非经典逻辑的问题。我们首先重构他的论点，并提出其对量子逻辑（QL）情况的限制。然后我们表明，经典数学模型对量子现象的适用性与对后者的推理中 QL 的认可之间不存在有问题的紧张关系。一旦我们确定了威廉姆森论证中的前提，当限制于 QL 时，该前提被证明是错误的，我们认为相同的前提对于更广泛的非经典逻辑是失败的。最后，我们通过讨论得出一些关于应用逻辑和应用数学之间关系的一般教训。