Because Arrhenius's formal impossibility results are axiology-neutral and apply across both transitive and non-transitive orderings, non-transitivity provides no principled escape from the paradoxes Arrhenius identifies.

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Arrhenius(The statement refers to his formal work on ethical paradoxes): Gustaf Arrhenius is a contemporary philosopher who studies ethics and population questions—particularly puzzles about whether it's better to have more people alive, and how to compare different possible futures.
Axiology-neutral(describing the scope of Arrhenius's findings across different ethical systems): Not favoring any particular view about what is good or valuable; the results work regardless of which ethics or values you believe in.
Formal impossibility results(Arrhenius proved certain ethical problems have no perfect answer): Mathematical or logical proofs showing that no solution can satisfy all the requirements we want at the same time—like proving it's impossible to create a system that meets every fairness condition we care about.
Non-transitive ordering(as a potential escape from Arrhenius's paradoxes)

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