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torekp comments on Pluralistic Existence in Many Many-Worlds - Less Wrong
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It is less crazy than it sounds the more you study philosophy of physics I suppose. It basically depends on accepting or not that matter could be just relational properties, with nothing intrinsic.
It's a leap of faith to suppose that even our universe, never mind levels I-III, is exhausted by its mathematical properties, as opposed to simply mathematically describable. And I don't really see what it buys you. I suppose it's equally a leap of faith to suppose that our universe has more properties than that, but I just prefer not to leap at all.
What would it mean for our universe not to be exhausted by its mathematical properties? Isn't whether a property seems mathematical just a function of how precisely you've described it?
Let's start with an example: my length-in-meters, along the major axis, rounded to the nearest integer, is 2. In this statement "2", "rounded to nearest integer", and "major axis" are clearly mathematical; while "length-in-meters" and "my (me)" are not obviously mathematical. The question is how to cash out these terms or properties into mathematics.
We could try to find a mathematical feature that defines "length-in-meters", but how is that supposed to work? We could talk about the distance light travels in 1 / 299,792,458 seconds, but now we've introduced both "seconds" and "light". The problem (if you consider non-mathematical language a problem) just seems to be getting worse.
Additionally, if every apparently non-mathematical concept is just disguised mathematics, then for any given real world object, there is a mathematical structure that maps to that object and no other object. That seems implausible. Possibly analogous, in some way I can't put my finger on: the Ugly Duckling theorem.