Joel David Hamkins: belief

Transcript context

…How traumatic is that, that there’s statements that are independent from the theory? I mean, my view is that, yeah, this isn’t traumatic at all. This is rather completely eye-opening in terms of our understanding of the nature of mathematical reality. I mean, we’re not… we understand this profound fact about our situation with regard to mathematical truth. The incompleteness theorem tells us, look, we just can’t write down a list of axioms that is going to be consistent and it’s going to answer all the questions. It’s impossible. And so I don’t think of it as trauma. I just think, look, this is the nature of mathematical reality, and it’s good that we know it, and so now we need to move on from that and, you know, do what we can in light of that. Is it fair to say that in general it means if I give you a statement, you can’t know if your axiomatic system would be able to prove it?…

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