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Xodarap comments on A Pure Math Argument for Total Utilitarianism - Less Wrong
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Comments (36)
Thanks for the feedback, I should've used clearer terminology.
This seems to be the consensus. It's very surprising to me that we get such a strong result from only the l-group axioms, and the fact that his result is so celebrated seems to indicate that other mathematicians find it surprising too, but the commenters here are rather blase.
Do you think giving examples of how many things completely unrelated to addition are groups (wallpaper groups, rubik's cube, functions under composition, etc.) would help show that the really restrictive axiom is the archimedean one?
It doesn't seem to me like the issue is one of terminology, but maybe I'm missing something.
I'm not convinced that it is. The examples you give aren't ordered groups, after all.
It's unclear to me whether your main purpose here is to exhibit a surprising fact about ethics (which happens to be proved by means of Hölder's theorem) or to exhibit an interesting mathematical theorem (which happens to have a nice illustration involving ethics). From the original posting it looked like the former but what you've now written seems to suggest the latter.
My impression is that the blasé-ness is aimed more at the alleged application to ethics rather than denying that the theorem, quite mathematical theorem, is interesting and surprising.