I don’t know what it would look like, but that isn’t an argument that the universe is mathematical.
Frankly, I think there’s something confused about the way I’m/we’re talking about this, so I don’t fully endorse what I’m saying here. But I’m going to carry on.
I guess I’m confused because in my head “mathematical” means “describable by a formal system”, and I don’t know how a thing could fail to be so describable.
So, the kind of thing I have in mind is the claim that reality is precisely and completely described by some particular mathematical object.
In my head, the argument goes roughly like this, with ‘surely’ to be read as ‘c’mon I would be so confused if not’:
Surely there’s some precise way the universe is.
If there’s some precise way the universe is, surely one could describe that way using a precise system that supports logical inference.
I guess it could fail if the system isn’t ‘mathematical’, or something? Like I just realized that I needed to add ‘supports logical inference’ to make the argument support the conclusion.
So, let’s suppose for a moment that ZFC set theory is the one true foundation of mathematics, and it has a “standard model” that we can meaningfully point at, and the question is whether our universe is somewhere in the standard model (or, rather, “perfectly described” by some element of the standard model, whatever that means).
In this case it’s easy to imagine that the universe is actually some structure not in the standard model (such as the standard model itself, or the truth predicate for ZFC; something along those lines).
Now, granted, the whole point of moving from some particular system like that to the more general hypothesis “the universe is mathematical” is to capture such cases. However, the notion of “mathematics in general” or “described by some formal system” or whatever is sufficiently murky that there could still be an analogous problem—EG, suppose there’s a formal system which describes the entire activity of human mathematics. Then “the real universe” could be some object outside the domain of that formal system, EG, the truth predicate for that formal system, the intended ‘standard model’ of that system, etc.
I’m not confident that we should think that way, but it’s a salient possibility.
Agree, and would love to see a more detailed explicit discussion of what this means and whether it’s true. (Also, worth noting that there may be a precise way the universe is, but no “precise” way that “you” fit into the universe, because “you” aren’t precise.)
I don’t know what it would look like, but that isn’t an argument that the universe is mathematical.
Frankly, I think there’s something confused about the way I’m/we’re talking about this, so I don’t fully endorse what I’m saying here. But I’m going to carry on.
So, the kind of thing I have in mind is the claim that reality is precisely and completely described by some particular mathematical object.
In my head, the argument goes roughly like this, with ‘surely’ to be read as ‘c’mon I would be so confused if not’:
Surely there’s some precise way the universe is.
If there’s some precise way the universe is, surely one could describe that way using a precise system that supports logical inference.
I guess it could fail if the system isn’t ‘mathematical’, or something? Like I just realized that I needed to add ‘supports logical inference’ to make the argument support the conclusion.
So, let’s suppose for a moment that ZFC set theory is the one true foundation of mathematics, and it has a “standard model” that we can meaningfully point at, and the question is whether our universe is somewhere in the standard model (or, rather, “perfectly described” by some element of the standard model, whatever that means).
In this case it’s easy to imagine that the universe is actually some structure not in the standard model (such as the standard model itself, or the truth predicate for ZFC; something along those lines).
Now, granted, the whole point of moving from some particular system like that to the more general hypothesis “the universe is mathematical” is to capture such cases. However, the notion of “mathematics in general” or “described by some formal system” or whatever is sufficiently murky that there could still be an analogous problem—EG, suppose there’s a formal system which describes the entire activity of human mathematics. Then “the real universe” could be some object outside the domain of that formal system, EG, the truth predicate for that formal system, the intended ‘standard model’ of that system, etc.
I’m not confident that we should think that way, but it’s a salient possibility.
>Surely there’s some precise way the universe is.
Agree, and would love to see a more detailed explicit discussion of what this means and whether it’s true. (Also, worth noting that there may be a precise way the universe is, but no “precise” way that “you” fit into the universe, because “you” aren’t precise.)