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Vladimir_Nesov comments on A Defense of Naive Metaethics - Less Wrong
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"3^^^^3 > 3^^^3", properties of higher cardinals, hyperreal numbers, facts about a GoL world, about universes with various oracles we don't have.
Things for which you can't build a trivial analogy out of physical objects, like a pile of 27 rocks (which are not themselves simple, but this is not easy to appreciate in the context of this comparison).
Certainly, one could reduce normative language into purely logical-mathematical facts, if that was how one was using normative language. But I haven't heard of people doing this. Have you? Would a reduction of 'ought' into purely mathematical statements ever connect up again to physics in a possible world? If so, could you give an example - even a silly one?
Since it's hard to convey tone through text, let me explicitly state that my tone is a genuinely curious and collaboratively truth-seeking one. I suspect you've done more and better thinking on metaethics than I have, so I'm trying to gain what contributions from you I can.
Why do you talk of "language" so much? Suppose we didn't have language (and there was only ever a single person), I don't think the problem changes.
Say, I would like to minimize ((X-2)*(X-2)+3)^^^3, where X is the number I'm going to observe on the screen. This is a pretty self-contained specification, and yet it refers to the world. The "logical" side of this can be regarded as a recipe, a symbolic representation of your goals. It also talks about a number that is too big to fit into the physical world.
Okay, sure. We agree about this, then.