A emotional tone or hostility detector, on the other hand, is ModernBERT + BiLSTM for the win. I'd argue the problem with fake news is not that it is fake but that it works on peoples emotions and that people prefer it to the real thing.
You can detect common established bullshit patterns and probably new ones that are like the old ones. 30 years from now there will be new bullshit patterns your model doesn't see.
Though, Gödel's completeness theorem I suppose does relate provability to truth in that it shows that (for systems with the right kind of rules of inference) provability is equivalent to something being true in all models...
Still, are you sure Tarski's undefinability theorem isn't more relevant to your point?