But that sentence isn’t self-contradictory like “This is a lie”, it is just self-referential, like “This sentence has five words”. It does have a well-defined meaning and is decidable for all hypothetical consistent people other than hypothetical consitentified Stuart Armstrong.
You’re right, I didn’t think that one through, thanks!
I still think the interesting thing is the potential for writing down a mathematical statement humanity can’t decide, not an English one that we can’t decide even though it is meaningful, but I’ll shut up about the question for now.
But that sentence isn’t self-contradictory like “This is a lie”, it is just self-referential, like “This sentence has five words”. It does have a well-defined meaning and is decidable for all hypothetical consistent people other than hypothetical consitentified Stuart Armstrong.
You’re right, I didn’t think that one through, thanks!
I still think the interesting thing is the potential for writing down a mathematical statement humanity can’t decide, not an English one that we can’t decide even though it is meaningful, but I’ll shut up about the question for now.