In this paper we use proof-theoretic methods, specifically sequent calculi, admissibility of cut within them and the resultant subformula property, to examine a range of philosophically-motivated deontic logics. We show that for all of those logics it is a (meta)theorem that the Special Hume Thesis holds, namely that no purely normative conclusion follows non-trivially from purely descriptive premises (nor vice versa). In addition to its interest on its own, this also illustrates one way in which proof theory sheds light on philosophically substantial questions.

中文翻译：

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是，应该，和削减

在本文中，我们使用证明理论方法，特别是后续演算、它们中的切割的可接受性以及由此产生的子公式属性，来检验一系列哲学动机的道义逻辑。我们表明，对于所有这些逻辑，它是特殊休谟论点所持有的（元）定理，即没有纯粹的规范性结论非平凡地从纯粹的描述性前提得出（反之亦然）。除了它本身的兴趣之外，这还说明了证明理论阐明哲学实质性问题的一种方式。