Comment by xanderlewis
5 days ago
Opposing view (that I happen to hold, at least if I had to choose one side or the other): not only is mathematics 'reality'; it is arguably the only thing that has a reasonable claim to being 'reality' itself.
After all, facts (whatever that means) about the physical world can only be obtained by proxy (through measurement), whereas mathematical facts are just... evident. They're nakedly apparent. Nothing is being modelled. What you call the 'model' is the object of study itself.
A denial of the 'reality' of pure mathematics would imply the claim that an alien civilisation given enough time would not discover the same facts or would even discover different – perhaps contradictory – facts. This seems implausible, excluding very technical foundational issues. And even then it's hard to believe.
> To the best of our knowledge, such cases are basically coincidence.
This couldn't be further from the truth. It's not coincidence at all. The reason that mathematics inevitably ends up being 'useful' (whatever that means; it heavily depends on who you ask!) is because it's very much real. It might be somewhat 'theoretical', but that doesn't mean it's made up. It really shouldn't surprise anyone that an understanding of the most basic principles of reality turns out to be somewhat useful.
I think you're not even disagreeing with me, we're just using different definitions of the word "reality". I meant it to use specifically "the physical world" - which you are treating as distinct from mathematics as well in your second paragraph.
But then you must agree that it's not a coincidence.
And yet another view:
Mathematics is an abstract game of symbols and rules invented by humans. It has nothing to do with reality. However it is quite useful for modelling our understanding of reality.