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Virtual Logic—Syllogisms

机译：虚拟逻辑—三段论

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摘要

Beneath all our formalisms, of ordinary language or of mathematics, there is the underpinning of human reason, more robust than the words. It is in the realm of reason that we achieve our certainty. Consider the following quotation from Charles Sanders Pierce (1839-1914) [2]: Mathematics, along with ethics and logic alone of the sciences, stands in no need of logic. Make of logic what the majority of treatises in the past have made of it — that is to say, mainly formal logic, and the formal logic represented as an art of reasoning — and in my opinion, this objection becomes more than sound, for such logic is a great hindrance to right reasoning. True mathematical reasoning is so much more evident than it is possible to render any doctrine of logic proper — without just such reasoning — that an appeal in mathematics to logic could only embroil a situation. On the contrary, such difficulties as may arise concerning necessary reasoning have to be solved by the logician by reducing them to questions of mathematics.
机译：在我们所有形式主义，普通语言或数学之下，存在着人类理性的基础，它比文字更坚固。我们在理性的范围内实现了确定性。考虑以下来自查尔斯·桑德斯·皮尔斯（1839-1914）[2]的语录：数学，以及仅涉及科学的伦理学和逻辑学，就不需要逻辑学。用逻辑来解释过去大多数论文所讲的内容（也就是说，主要是形式逻辑，而形式逻辑代表推理的艺术），在我看来，这种反对远非听起来合理，逻辑是正确推理的极大障碍。真正的数学推理远比提供任何合理的逻辑学说（而不仅仅是推理）要明显得多，以至于数学对逻辑的呼吁只会使情况陷入困境。相反，逻辑学家必须通过将其归结为数学问题来解决与必要推理相关的困难。

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