I think Gödel has to be right about mathematical Platonism, because the alternative is that maths is ugly purely due to errors in its construction.
We *have* to believe that maths is externally real, otherwise we've already lost.
maybe a weaker phrasing of this is with an if-statement:
if maths is to be interesting at all, something like Gödel's understanding has to be true - it has to be externally real
@cyberia I don't understand why something being artificial makes it uninteresting
@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 have all kinds of problems with the way actual computers work and still think they're interesting and we should make better ones that are user serviceable and understandable
@clayote sure, but computers have a purpose and a use other than just "being interesting", so it's worth something to keep them going
but pure maths on its own terms exists only to be interesting, and if it can't even do that, well...
@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
@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
@cyberia degree in compsci
and I didn't end up even working with formal methods...
@cyberia further reading https://arxiv.org/abs/math/9404236