Considering all mathematical structures equally “real” makes the concept of “reality” lose all meaning.
I agree, and I’d like to offer additional argument. Mathematical objects exist. Almost no one would deny that, for example, there is a number between 7,534,345,617 and 7,534,345,619. Or that there is a Lie group with such-and-such properties. What distinguishes Tegmark’s claims from these unremarkable statements? Roughly this: Tegmark is saying that these mathematical objects are physically real. But on his own view, this just amounts to saying that mathematical objects are mathematical objects. Yeah yeah Tegmark, mathematical objects are mathematical objects, can’t dispute that, but don’t much care. Now I’ll turn my attention back to tangible matters.
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 agree, and I’d like to offer additional argument. Mathematical objects exist. Almost no one would deny that, for example, there is a number between 7,534,345,617 and 7,534,345,619. Or that there is a Lie group with such-and-such properties. What distinguishes Tegmark’s claims from these unremarkable statements? Roughly this: Tegmark is saying that these mathematical objects are physically real. But on his own view, this just amounts to saying that mathematical objects are mathematical objects. Yeah yeah Tegmark, mathematical objects are mathematical objects, can’t dispute that, but don’t much care. Now I’ll turn my attention back to tangible matters.
Tegmark steals his own thunder.
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.