Notice [David Lewis’s Possible Worlds] is distinct from the Mathematical/Ultimate in that there may be properties of non-mathematical kind.
I don’t see why Tegmark 4 excludes those properties. Such a universe is still mathematically possible, in a sense akin to logically possible: it violates none of the Peano Axioms, for instance.
So the reason is that Tegmarks claim is that the the mathematical properties not only define the Multiverse, but also that they constitute the entire extension of it.
If there were substances, properties, or objects, that behaved mathematically well, that would still falsify his claim.
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.
I don’t see why Tegmark 4 excludes those properties. Such a universe is still mathematically possible, in a sense akin to logically possible: it violates none of the Peano Axioms, for instance.
I think the trivial case is “the universe that exists but has no mathematical model”.
So the reason is that Tegmarks claim is that the the mathematical properties not only define the Multiverse, but also that they constitute the entire extension of it. If there were substances, properties, or objects, that behaved mathematically well, that would still falsify his claim.
Wow, thanks. I didn’t realize that Tegmark was so … crazy.
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.