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.
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.