Most 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

Most 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.