I’m pretty sure Eliezer’s approach is the opposite of Tegmark’s. For Tegmark, the math is real and our physical world emerges from it, or is an image of part of it. For Eliezer, our world, in all its thick, visceral, spatiotemporal glory, is the Real, and logical, mathematical, counterfactual, moral, mentalizing, essentializing, and otherwise abstract reasoning is a human invention that happens to be useful because its rules are precisely and consistently defined. There’s much less urgency to producing a reductive account of mathematical reasoning when you’ve never reified ‘number’ in the first place.
Of course, that’s not to deny that something like Tegmark’s view (perhaps a simpler version, Game-of-Life-style or restricted to a very small subset of possibility-space that happens to be causally structured) could be true. But if such a view ends up being true, it will provide a reduction of everything we know to something else; it won’t be likely to help at all in reducing high-level human concepts like number or qualia or possibility directly to Something Else. For ordinary reductive purposes, it’s physics or bust.
I’m pretty sure Eliezer’s approach is the opposite of Tegmark’s. For Tegmark, the math is real and our physical world emerges from it, or is an image of part of it. For Eliezer, our world, in all its thick, visceral, spatiotemporal glory, is the Real, and logical, mathematical, counterfactual, moral, mentalizing, essentializing, and otherwise abstract reasoning is a human invention that happens to be useful because its rules are precisely and consistently defined. There’s much less urgency to producing a reductive account of mathematical reasoning when you’ve never reified ‘number’ in the first place.
Of course, that’s not to deny that something like Tegmark’s view (perhaps a simpler version, Game-of-Life-style or restricted to a very small subset of possibility-space that happens to be causally structured) could be true. But if such a view ends up being true, it will provide a reduction of everything we know to something else; it won’t be likely to help at all in reducing high-level human concepts like number or qualia or possibility directly to Something Else. For ordinary reductive purposes, it’s physics or bust.