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army1987 comments on Natural Laws Are Descriptions, not Rules - Less Wrong
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I don't know too much about Tegmark, but I'm pretty sure he doesn't have your second meaning in mind.
That said, I'm not sure your first meaning is actually tautological, given that for Tegmark's idea to be an answer as WeiDai suggests, _whatever "exist" means it has to encompass the kind of thing that you are doing right now.
The idea that things which "exist in an abstract mathematical sense" can, solely by virtue of that, do what you're doing right now is perhaps tautological, but if so the tautology is not one that most humans will readily recognize as one.
Yes, I was unintentionally implicitly assuming that this universe is a mathematical structure. (OTOH, ISTM that this is a somewhat standard assumption on LW, e.g. Solomonoff induction wouldn't make that much sense without it.)
Perhaps. But the connotations of saying that something exists in an abstract, mathematical sense tend to run counter to that.