> that doesn't mean that the concept of "fact checking" is inherently problematicPerhaps not, but I think there are wrinkles in it that you might not be considering.
First, if "fact checking" just means "consulting other sources of information to see if they say the same thing", then you have to deal with the question of the credibility of those other sources of information. No source of information is always right. Nor is any "fact checker" always right in judging the relative credibility of sources of information. Ultimately, unless you have your own personal knowledge of some fact, any "fact checking" is going to come down to which sources you trust and which sources you don't. Those are always judgment calls and there will always be some degree of residual skepticism, so citing "fact checks" as if they were authoritative is problematic.
Second, if you try to go beyond that and actually do things like independent experiments to check claims (for example, when scientists try to replicate experiments or studies), then you're not really checking on previous facts, you're creating new facts, which you are then going to use to judge the validity of previous claims. But those previous claims were not factual claims but theoretical ones (for example, doing study B to help in judging the claim "study A shows that treatment X is effective against illness Y"). And again, these kinds of comparisons are judgment calls (sure, sometimes you uncover strong evidence that, for example, the data in study A was fabricated, but study B alone won't tell you that).
> t could be that there is no way in our current culture of doing anything remotely like what "fact checking" probably needs to be.
The critical problem I see with the Facebook case is that their "fact checking" results in something more than just publishing whatever Facebook's ultimate judgment is on some website (as, for example, Snopes and other "fact checking" sites do). Facebook's "fact checking" has other consequences, such as blocking access to things people have posted. And since our current culture seems to be fixated on using "fact checking" in this way, not just to arrive at judgments which are then published as speech, for the reader to take or leave, but to take actions that amount to filtering, restricting, or blocking other speech, yes, I think our current culture is not really capable of doing the limited kind of things that "fact checking" properly done would consist of.