Mathematical structuralism was developed to explain the ontology of mathematical objects, and is often contrasted with Platonism, which is the position that numbers are real things like you or I.
A funny insight about Platonism (if it's not funny, treat this as a bad joke)
I think aka "∅"
therefore I know I thought aka "{∅}"
therefore I know I knew I have thought aka "{{∅}}"
and ...
boom! The entire Math system is imported. (BTW, limitations known as "computation theory" is also introduced)
So maybe we are actually mathematical being on a manifold named as "real world". To me it is more concise and profound than "philosophy". As we are real, so do all mathematical objects.
The problem is: do numbers exist? One group says, they don't. Another say, they do exist in the Platonic world, but this Platonic world is accessible from the world we inhabit in. Next time, look at the folks who looks for Platonic love:)
I think aka "∅" therefore I know I thought aka "{∅}" therefore I know I knew I have thought aka "{{∅}}"
and ...
boom! The entire Math system is imported. (BTW, limitations known as "computation theory" is also introduced)
So maybe we are actually mathematical being on a manifold named as "real world". To me it is more concise and profound than "philosophy". As we are real, so do all mathematical objects.