Williamson argues for the contention that substructural logics are ‘ill-suited to acting as background logics for science’. That contention, if true, would be very important, but it is refutable, given what is already known about certain substructural logics. Classical Core Logic is a substructural logic, for it eschews the structural rules of Thinning and Cut and has Reflexivity as its only structural rule. Yet it suffices for classical mathematics, and it furnishes all the proofs and disproofs one needs for the hypothetico-deductive method in science. We explain exactly what Classical Core Logic is, why it is a substructural logic par excellence, and what the basic requirements would be for a logic to be ‘suited to acting as [a] background logic for science’. We also explain how Classical Core Logic meets all these requirements. We end by examining Williamson’s argument in order to expose where its error lies.

中文翻译：

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论数学和科学的子结构逻辑的充分性

威廉姆森认为，子结构逻辑“不适合充当科学的背景逻辑”。如果这个论点属实，那将是非常重要的，但鉴于对某些子结构逻辑的已知信息，它是可以反驳的。经典核心逻辑是一种子结构逻辑，因为它避开了细化和切割的结构规则，并将反射性作为其唯一的结构规则。然而，它对经典数学来说已经足够了，它为科学中的假设-演绎方法提供了所有需要的证明和反驳。我们准确地解释了经典核心逻辑是什么，为什么它是一种卓越的子结构逻辑，以及逻辑“适合充当科学的背景逻辑”的基本要求是什么。我们还解释了经典核心逻辑如何满足所有这些要求。