Comment by lmm

Non-empirical statements are meaningless in the same sense that fairies don't exist. It's not a priori impossible that a non-empirical but constructive/valuable/useful statement could exist - a black swan - just as it's not impossible that a fairy could exist - but it seems very unlikely and I'd put a very low weight on someone's claim to have seen one, given how often such claims have turned out to be false. When I dismiss something as non-empirical, that's the same kind of dismissal as saying something's a conspiracy theory - formally I'm not claiming that it's outright impossible, just unlikely (though in everyday language I might say "impossible", just as we do for conspiracy theories or fairies).