Why not do make the function that outputs answers also feed itself "is this actually right/are you sure/is this not wrong"? Too expensive? Giant loop?
It can't tell it's wrong, it just reacts in a plausible well to you telling it it's wrong (acknowledging it and giving another explanation). Since ChatGPT is an expansion of GPT-3, those things won't be really solved since being somewhat of a knowledge base is a nice side effect, not the main goal of the model.
So you are saying the order of events if:
1. you ask it a question
2. it gives you an answer (in this case, it's wrong)
3. you ask it "are you sure? i think that's wrong"
4. it answers again "you are right, i think the answer i just gave you was wrong, here is what i think is the right answer this time" (and again, it's wrong)
and repeat forever?
Then you reset your session, you ask the same question and you get the wrong answer again.
They do this, with humans. Both during training (they use supervised and reinforcement learning), and now at a much greater scale: it's what the free public access period is for and why there's a thumbs up/down button next to the output.
Mansplained by a robot...
> AI: Answer that's clearly factually wrong (e.g. a function that doesn't exist or a completely wrong numerical figure).
> Me: that's not right, the function doesn't exist (etc.)
> AI: you are right, that function doesn't exist. The answer is blah
And repeat, since if it didn't get it right first time, it seems unlikely to be able to get there at all (and you'd not know when it did unless you already know the answer).
It's very like a specific person I know in a PR-marketing type job that will just glide across a noticed outright falsehood and instantly reshape what they're saying in real time and carry on as if nothing happened, leaving you wondering if you're taking crazy pills.