My [uninformed] interpretation of mathematics is that it is an abstraction which does exist in this world, which we have observed like we might observe gravity. We then go on to infer things about these abstract concepts using proofs.
So we would observe numbers in many places in nature, from which we would make a model of numbers (which would be an abstract model of all the things which we have observed following the rules of numbers), and from our model of numbers we could infer properties of numbers (much like we can infer things about a falling ball from our model of gravity), and these inferences would be “proofs” (and thankfully, because numbers are so much simpler than most things, we can list all our assumptions and have perfect information about them, so our inferences are indeed proofs in the sense that we can be certain of them).
But it seems like a common view that mathematics has some sort of special place in the universe, above the laws of physics, and I don’t really know what arguments people have for believing this. What are the arguments for this belief?
Edit: Reformulated my question to make it more specific.
My [uninformed] interpretation of mathematics is that it is an abstraction which does exist in this world, which we have observed like we might observe gravity. We then go on to infer things about these abstract concepts using proofs.
So we would observe numbers in many places in nature, from which we would make a model of numbers (which would be an abstract model of all the things which we have observed following the rules of numbers), and from our model of numbers we could infer properties of numbers (much like we can infer things about a falling ball from our model of gravity), and these inferences would be “proofs” (and thankfully, because numbers are so much simpler than most things, we can list all our assumptions and have perfect information about them, so our inferences are indeed proofs in the sense that we can be certain of them).
But it seems like a common view that mathematics has some sort of special place in the universe, above the laws of physics, and I don’t really know what arguments people have for believing this. What are the arguments for this belief?
Edit: Reformulated my question to make it more specific.
It’s more fun to think of the reverse relationship!