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Ishaan comments on Does the simulation argument even need simulations? - Less Wrong
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I think Tegmark's level 1-4 taxonomy is useful. Strip it of physics and put it to philosophy:
Lv 1) What we can observe directly (qualia)
Lv 2) What we can' t observe, but could be (Russel's teapot)
Lv 3) What we can't observe, but we know might have happened if chance played out differently. (many-worlds)
Lv 4) Mathematical universes.
These are distinct concepts. The question is, where and how do you draw a line and call it reality? (I say that we can't include 4, nor can we only include 1. We either include 1, 2 or 1, 2, 3...preferably the former.)
I took the portion of your comment I quoted to be about level 4 only. Anyway, that is where my comment is aimed, at agreeing that we can't include 4.