Each person has a citadel of beliefs, of ideas and thoughts that they hold dear. It is different for each person but the common element is that all have this citadel. It could include thoughts like the love they feel, that their parents loved them, religious beliefs, conviction in the work they do, their knowledge about science or the disbelief in it...and sometimes even the AI slop they watch on social media. What puts a belief in the citadel is not its subject but its stake. Nobody defends the claim that the earth is old, because nothing of theirs rides on it. The beliefs that get walls are the ones where being wrong would cost more than accuracy. It would cost standing, or belonging, or a story about their own life that would have to be rewritten. And so any time these beliefs are challenged, no matter how rational the argument may be, they will do all they can to resist dropping these ideas. This is not stupidity. They have estimated the cost correctly and decided not to pay it.
All that we really need to live an examined life is to hold just one rule in the citadel...that it must remain empty at all times. The paradox is obvious and it is the point. A rule held in the citadel is a resident of the citadel, so the rule must in the end empty itself along with everything else. It is not a belief but an operation. Something done rather than something held, and when it has finished its work there is nothing left of it to keep. We need to drop all our priors, all knowledge, all things borrowed from others...and then examine life. This is not free. The citadel is shelter, and to empty it is to agree to be cold. And the only thing that remains at the end, must be the truth. And the truth does not need to be defended in a citadel. It can be argued for, and the argument can fail, which is a different thing from being protected. And if the argument fails, we hold a new truth...and leave it in the open...for the truth needs no citadel.