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RE: The significance of mathematics - and why it can prove its own incompleteness
Self-reference and completeness are tricky to grasp and accept. I've had to explain the second incompleteness theorem many times to people who claim it can be used as an argument in favor if god's existence. Am always like:
😤 No, not at all! Let me get a dry erase marker...
Interestingly though, even Gödel himself did some work on ontological god evidence, but did not publish it during his lifetime. I'm unfamiliar with his actual idea of "proof" but I hear that it is also a little bit weird which is probably why he wasn't confident enough to publish it.