You end up with a tower of “universes” that each have some statements they can’t prove which are provable in a higher universe.
You might wonder about the limit… but axioms are only interesting when finite: if you have infinite axioms, just assume the true statements.
You might wonder which those are… but then you’re confronted with the fact it’s all made up and you can have consistent systems from contrary axioms, eg either allowing or disallowing choice.
Mathematics is useful because it gives us a language to tell stories where we can accurately guess questions like “what came before?” or “what happens next?” and where we can describe similarities between stories.
You might wonder about the limit… but axioms are only interesting when finite: if you have infinite axioms, just assume the true statements.
You might wonder which those are… but then you’re confronted with the fact it’s all made up and you can have consistent systems from contrary axioms, eg either allowing or disallowing choice.
Mathematics is useful because it gives us a language to tell stories where we can accurately guess questions like “what came before?” or “what happens next?” and where we can describe similarities between stories.
A modern ontology.