Quick recap: the paradox in question can be formulated like so (I think; look in the SEP article on deontic logic for a better recap if this doesn't work):
- If Jill kills Jane, she ought to kill Jane gently.
- Jill kills Jane gently if and only if Jill kills Jane at all.
- Jill kills Jane.
- Therefore, Jill ought to kill Jane gently.
My intuition is that this and some other paradoxes (or "problems"/"puzzles") in deontic logic, such as that of epistemic obligation (you end up obligated to make an evil fact real in order to fulfill your duty to know which evil facts to fight against), might be resolved by appealing to the distinction between sentence-types and sentence-tokens. In the Jill-kills-Jane case, for instance, the idea is that the hypothetical (1) holds only as a sentence-type, and that a token of its discharged consequent doesn't hold. An (I'll admit unclear) analogy would be with the following take on mathematical facts/truth, in the formalist umbrella/camp: Weir, by contrast, explicitly embraces formalism (1991; 1993; 2010; 2016), moreover formalism in the game formalism tradition. His position, if situated with respect to fictionalism, can be seen as one in which ‘consequence’ is read, in the formalist tradition, syntactically, in terms of formal derivability. As a first approximation, the position is that a mathematical sentence is true if there exists a concrete derivation of a token of it, false if there exists a concrete derivation of a token of its negation. Since truth and falsity conditions make no appeal to abstract proofs, this type of formalism is firmly anti-platonist [SEP, "Formalism in the Philosophy of Mathematics," sec. 8].