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.
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Gratzl, N., Pavlović, E. Is, Ought, and Cut. J Philos Logic (2023). https://doi.org/10.1007/s10992-023-09701-y
- Special Hume thesis
- Is-Ought argument
- Sequent calculus
- Subformula property
- Deontic logics