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It's plausible that, at a suitably high level of abstraction, the different "paths" can be understood in such a way as will result in convergence. (This is especially so if we reinterpret the various procedural methods as building in that *independently true* moral beliefs are more ideal! That's not usually how they are intended, though.)

But there's a real question which (if any) higher-order property does genuine explanatory work. I'd be surprised if they *all* do. It would be interesting to read a sustained defense of that idea though. (Parfit's convergence-seeking project always seemed misguided to me for this reason. He didn't attend enough to the explanatory question to even bother defending the view that each side of the moral mountain was *equally* responsible for holding up the peak.)

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