Unfortunately, I do not find Tegmark's line of reasoning to be extremely compelling. The leap from the existence of an external reality {independent of humans} to the conclusion that, in Tegmark's words, "You must believe in what I call the mathematical universe hypothesis: that our physical reality is a mathematical structure," involves, in my opinion, a sleight of hand. When Tegmark attempts to characterize what mathematics really is, he says: "To a modern logician, a mathematical structure is precisely this: a set of abstract entities with relations between them." But this modern logician is human! In other words, Tegmark never really proves that our mathematics is not invented by humans; he simply assumes it. Furthermore, as the French neurobiologist Jean-Pierre Changeaux has pointed out in response to a similar assertion: "To claim physical reality for mathematical objects, on a level of the natural phenomena we study in biology, poses a worrisome epistemological problem it seems to me. How can a physical state, internal to our brain, represent another physical state external to it?
( Mario Livio )
[ Is God a Mathematician? ]
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