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:)
"Conceivably Strunk was trying to inculcate in everyone the habit of writing like Henry James and not like Mark Twain" was where I lost it. And I love Twain!
> So what is a brain other than a very complex non-linear function which takes inputs, iterates on them, integrates them with memory and eventually generates output?
A thing that processes and embodies sensory input, makes informed guesses about other people's intentions and values, grows tumors, worries about the dirty dishes.... How many other "complex non-linear functions" are made of meat?
