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I'm not either, but I think it depends on which system you're working from within. There's the ugly, beautiful thing from Godel's second incompleteness theorem
by manifestsilence 7y ago
I'm not either, but I think it depends on which system you're working from within. There's the ugly, beautiful thing from Godel's second incompleteness theorem saying a formal system cannot prove its own consistency from within.
With set theory, it looks like there was some reformulating of the fundamental terms to prevent paradox, but I'm not quite clear on whether that leaves us with a consistent formal system in the end:
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t...
- dwohnitmok 7y agoIt leaves us with a system that we strongly suspect is consistent, but which we cannot prove is such (at least not without resorting to a stronger system whose consistency is again unproven). Note that even were ZFC be proven to be inconsistent it would probably not be a huge issue practically speaking for most mathematicians. This Math Overflow answer describes it best: https://mathoverflow.net/a/41030 https://mathoverflow.net/a/41030
- manifestsilence 7y agoAwesome, thank you for clarifying!