My friend Steven Savage has a longish, but highly worthwhile, post where he talks about truth as being a matter of connection.
Something is True (or at least “truer” than other things) because it can be explained in multiple ways, because its validity is confirmed multiple ways, and the “true thing” relates to other data, concepts, and experiences. ... Truth is a web of connections. Truth does not exist outside of context.
One thing I would add to this picture (although by no means the only thing, I'm sure) is the concept of falsifiability, which stems from all that Steven is talking about but has dimensions of its own. If I can talk about the truth of something, I also need to be able to say, "What would prove this false?"
Software developers have the concept of "test-driven development," where you write unit tests that go hand-in-hand with the functionality you're creating. Whatever it is you're trying to do, you need to make sure that's what is actually happening, or your efforts will be in vain.
One theory as to how we've arrived in a "post-truth" society is that we've put too much emphasis on trusting "experts" and not enough emphasis on equipping people with the tools to perform their own tests of the truth. I agree with this up to a point, because I think veneration of authority is always detrimental to thought.
Many of the people I see who are most hostile in their rejection of the truth and expertise have no skill in identifying truth or recognizing falsifiability. As Steven pointed out, they have become their own cult leaders — they look for what confirms their existing prejudices, even (and especially) those that they are not fully aware of, and they select in favor of that. As someone else put it: "Their arguments are reverse-engineered from the answers they want."
Such people never become aware of their own incompetence, and modern life equips them with all sorts of failsafes for never having to break their shins against such a hard truth. People who call themselves "skeptics" and simply swap one source of bias for another aren't skeptics; they're solipsists.
My own feeling is that this is a problem because of the way people are conditioned to think about themselves, and identify with static images of themselves.
To wit: If I think of myself as a skeptical person, therefore I am one — even if my actual skepticism is indiscernible from just snarling at people telling me something I don't really want to hear. I don't actually have to practice skepticism or critical thinking; I just have to assume the label, if only in my own eyes and not anyone else's.
But practicing critical thinking would mean admitting that you're wrong and having to correct course, and for some people such a demand amounts to an attack on their sacred person. Because, let's face it — that amounts to becoming a different person. More profound horrors are scarcely possible for those who think of themselves as being perfect just as they are.
Maybe that's the real problem — that people think of themselves as immutable wholes, not processes subject to constant re-evaluation. We don't teach people to look at themselves that way to begin with, so maybe we shouldn't be surprised when they don't show much interest in doing it generally.