What if it's out of reach even for the best among us? To me it looks like many of our core beliefs cannot be shaped through reason, and are not the product of reason in the first place. Our convictions have simply been copied from our environment through osmosis.
I'm sure you can't help but notice the amount of groupthink that takes place in any community, whether in real life or right here. How does this groupthink come to be? People don't really change their minds in long discussion threads like these; it certainly doesn't feel like they do. And yet minds get changed or there wouldn't be groupthink. By reading, responding, and reading some more, we slowly change over time; like water carves its way through rock. We shape HN by our responses and in turn HN shapes us: the relation is symbiotic.
We can, sometimes, if we try really hard, and then only for a moment, apply real reason. I see no evidence that this has a big impact on what people believe and how they act, though. People who are good at formal reasoning are good at arriving at the correct answer in reasoning puzzles, but there is no matching improvement when it comes to the decisions they make in their life. It's pretty clear that even really smart people can't reason themselves out of their problems. This is a big problem for the view that convictions are the product of reason.
In contrast, the friends you keep and the media you consume does make a tremendous impact on what you believe and how you act. Change who your friends are and, through repeated exposure, your convictions will change subliminally.