@clayote sorry, maybe that's unclear - what I mean is that it's not that everything artificial is uninteresting, but rather if we have just created maths out of nothing then we've done an extremely bad job, which makes it uninteresting
@cyberia I think this is what motivated Russel's Principia Mathematica
As I understand it, reinventing arithmetic from first principles turned out to be so much work that he just kinda gave up before he got to multiplication
@clayote I believe Russell was a logical positivist (although I haven't read the chapter about him in this book I'm reading), and therefore maybe agreed with Gödel that at least *something* about maths was externally real, but he wanted to be more logically rigorous about our understanding of its foundations, hence the Principia
@cyberia I tend to think of math much the same way I think of language
Ultimately, we make all these words up, but they still mean things, and there's value in making them mean the *right* thing for a given purpose
@clayote oh that looks interesting! what's your maths background if you don't mind my asking?
I just did it for my bachelor's and got interested in philosophy of maths in my free time