"In this talk we offer a case study of utilizing logic to obtain philosophical results. We examine a range of deontic logics and their philosophical motivations. We distinguish syntactically between normative and descriptive statements and show, using proof-theoretic methods, that for the entire range of 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, in fact, vice versa). In this way we identify a metanormative constraint which allows us to dismiss certain arguments as unconvincing based simply on their form. We finish up by laying out ways in which this project can be extended to further uses of logic in philosophy."