Suppose we lived in a universe where the sum of two and two wasn’t any number in particular.
This doesn’t make much sense as stated. Math is a collection of tools for making useful maps of a territory (in the local parlance). The concept of numbers is one such tool. Numbers are not physical objects, they are a part of the model. You cannot add numbers in the physical universe, you can only manipulate physical objects in it. One way to rephrase your statement is “Suppose we lived in a universe where when you combine two peanuts with another two peanuts, you don’t get four peanuts”. This is how it works for many physical objects in our universe, as well: if you combine two blobs of ink, you get one blob of ink, if you combine one male rabbit and one female rabbit, the number of rabbits grows in time. If the universe you describe is somewhat predictable, it has some quantifiable laws, and the abstraction of these laws will be called “math” in that universe.
One way to rephrase your statement is “Suppose we lived in a universe where when you combine two peanuts with another two peanuts, you don’t get four peanuts”.
The intended meaning of that sentence was that adding two of one thing to two of another thing does not give consistent results, regardless of the things you’re adding. Adding two peanuts to two peanuts does not consistently result in any particular quantity of peanuts, and the same is true of any other objects you might attempt to add together.
If the universe you describe is somewhat predictable
For the sake of an argument, we shall suppose that it’s not. It’s nigh-impossible to even make sense of the hypothetical as proposed, but then, if there were alternate realities where math could exist or not exist, they would probably be mutually nonsensical.
Isn’t whether numbers are part of the territory or part of the map a debatable topic?
It is indeed. If you are a Platonist, numbers are real to you.
The universe is more than just a collection of physical objects. There are properties of objects, their relationships, their dynamics...
Well, current physical models suggest that the universe is some complicated wave function, parts of which can be factorized to produce objects, some of these objects (humans) run algorithms describing other objects and how they behave, and parts of these algorithms can be expressed as “properties of objects, their relationships, their dynamics...”
This doesn’t make much sense as stated. Math is a collection of tools for making useful maps of a territory (in the local parlance). The concept of numbers is one such tool. Numbers are not physical objects, they are a part of the model. You cannot add numbers in the physical universe, you can only manipulate physical objects in it. One way to rephrase your statement is “Suppose we lived in a universe where when you combine two peanuts with another two peanuts, you don’t get four peanuts”. This is how it works for many physical objects in our universe, as well: if you combine two blobs of ink, you get one blob of ink, if you combine one male rabbit and one female rabbit, the number of rabbits grows in time. If the universe you describe is somewhat predictable, it has some quantifiable laws, and the abstraction of these laws will be called “math” in that universe.
The intended meaning of that sentence was that adding two of one thing to two of another thing does not give consistent results, regardless of the things you’re adding. Adding two peanuts to two peanuts does not consistently result in any particular quantity of peanuts, and the same is true of any other objects you might attempt to add together.
For the sake of an argument, we shall suppose that it’s not. It’s nigh-impossible to even make sense of the hypothetical as proposed, but then, if there were alternate realities where math could exist or not exist, they would probably be mutually nonsensical.
Isn’t whether numbers are part of the territory or part of the map a debatable topic?
The universe is more than just a collection of physical objects. There are properties of objects, their relationships, their dynamics...
It is indeed. If you are a Platonist, numbers are real to you.
Well, current physical models suggest that the universe is some complicated wave function, parts of which can be factorized to produce objects, some of these objects (humans) run algorithms describing other objects and how they behave, and parts of these algorithms can be expressed as “properties of objects, their relationships, their dynamics...”
In the sense that the existence of God is. There is a lack of direct empirical evidence for the actual existence of numbers.