Löb's Theorem
One of the top-5 most important things I've ever read: Löb's Theorem Cured My Social Anxiety. Teaser:
During the conversation in which I described my plan to him, we meandered to the topic of a meetup of professional hypnotists he’d recently attended. He told me they talked in passing about what it’s like to change their own behaviors. They all knew they could use a long, draw-out induction (or series of inductions and post-hypnotic suggestions) to self-modify if they wanted. But that takes time and energy, and it turns out that if you’re sufficiently confident it’ll work… you don’t have to bother with the hypnosis.
Think about that for a minute. They treated it as a perfectly normal, every-day occurrence. Basically they were saying, “Yeah, when I don’t like what System 1 is doing, I just tell it to do something else instead. No biggy.” They seem to have this available as a primitive action.
Initially, I said it sort of tongue-in-cheek: “Ha, well I guess we don’t really need that induction I described then!”
Pause.
System 2: Surely not. It can't be that simple. There’s just no way that will actually work. Nobody cures a life-long psychological disorder overnight. Don’t be ridiculous.
Background
What is it? Has to do with Peano arithmetic and logic… A Cartoon Guide to Löb's Theorem
The Santa Claus sentence
"If this sentence is true, then Santa Claus exists." (Clearly, if that sentence were really true, then Santa Claus would have to exist. But this is just what the sentence asserts, so it is true, and Santa Claus does exist.)