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After considering the responses, I declare the analogue of Hofstadter's law: foundations of math are always weirder than you give them credit for, even after yo
by ikeboy 11y ago
After considering the responses, I declare the analogue of Hofstadter's law: foundations of math are always weirder than you give them credit for, even after you've taken Hofstadter's law into account.
- cousin_it 11y agoMost of the weirdness comes from Godel's and Lob's theorems, and they don't seem that strange to me anymore. Here's a little tidbit that might make you more at peace with what's happening. Imagine that you didn't know anything about Godel's results. If you found some theory that proved its own consistency, would that be a reason to trust that theory more? Not at all! Inconsistent theories also happily prove their own consistency (because they prove all sentences). So it seems like Godel's theorems are thwarting a desire that was wrong-headed to begin with.
- ikeboy 11y agoI'm not worried about the inconsistencies. I'm worried that we can't even define natural number and be sure that there's no infinite natural number.