You can empirically prove math like you’d empirically prove other things - make predictions based on math and test these predictions. But it seems like you are expecting these proofs to be like mathematical proofs - uncompromising logic that leaves no room for getting false positives by chance. They won’t. They’ll be like all other empirical proofs - “mere” scientific theories that must forever live with the possibility - however improbable - that the universe somehow aligned to make all the predictions come true even though the hypothesis they were derived from is wrong.
But this is not a property of the math we were trying to prove. This is just the nature of the empirical proofs. Implying, based on that, that math is less verifiable than all the physical observable things (like frozen oxygen) is ridiculous - the proofs for these things suffer from the exact same problem!
The (poorly) argued point they are trying to make is the distinction between the empirically identified congruences between the math and the internally consistent tautological truth of the math itself.
The reason I bring this up is your point about math modeling empirical evidence is an important distinction. Where their argument truly breaks down is the idea that all internally consistent tautologies are of equal value to us as humans. This is obviously false.
And frankly, their other argument about this showing that true things exist without empirical proof is offensively stupid since we already have much better proofs demonstrating that true things exist without proof.
You can empirically prove math like you’d empirically prove other things - make predictions based on math and test these predictions. But it seems like you are expecting these proofs to be like mathematical proofs - uncompromising logic that leaves no room for getting false positives by chance. They won’t. They’ll be like all other empirical proofs - “mere” scientific theories that must forever live with the possibility - however improbable - that the universe somehow aligned to make all the predictions come true even though the hypothesis they were derived from is wrong.
But this is not a property of the math we were trying to prove. This is just the nature of the empirical proofs. Implying, based on that, that math is less verifiable than all the physical observable things (like frozen oxygen) is ridiculous - the proofs for these things suffer from the exact same problem!
The (poorly) argued point they are trying to make is the distinction between the empirically identified congruences between the math and the internally consistent tautological truth of the math itself.
The reason I bring this up is your point about math modeling empirical evidence is an important distinction. Where their argument truly breaks down is the idea that all internally consistent tautologies are of equal value to us as humans. This is obviously false.
And frankly, their other argument about this showing that true things exist without empirical proof is offensively stupid since we already have much better proofs demonstrating that true things exist without proof.