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HalMorris comments on Morality Isn't Logical - Less Wrong Discussion
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Unless you turn "interesting" into something rigorously defined and precisely communicated to others, what it means is that all natural numbers are {some quality that is not rigorously defined and can't be precisely communicated to others}.
I guess I feel that even if I haven't defined "interesting" rigorously, I still have some intuitions for what "interesting" means, large parts of which will be shared by my intended audience.
For example, I could make the empirical prediction that if someone names a number I could talk about it for a bit and then they would agree it was interesting (I mean this as a toy example; I'm not sure I could do this.)
One could then take approximations of these conversations, or even the existence of these conversations, and define interesting* to be "I can say a unique few sentences about historic results surrounding this number and related mathematical factoids." Which then might be a strong empirical predictor of people claiming something is interesting.
So I feel like there's something beyond a useless logical fact being expressed by my intuitions here.