So the situation is bad enough when I am encountering a new source. But if I'm already familiar with a source, and it's consistently wrong about the things I know, then I can only be even more suspicious of everything else they say; and sadly, an awful lot of publications do fall into that category. Finding a mistake in a book does make it more likely that it contains other mistakes, and it does make any given fact in the book more likely to be wrong.
If you can only check one thing and it's wrong, then it is entirely and clearly irrational to assume that everything else is correct.
It's not fully defensible to assume that it's 100% wrong either. Just by plain statistics you may assume almost anything must have some correct portion.
What's rational is to make as few assumptions as possible, and where guessing or informed guessing is necessary, use only the information you actually have. That means back to the beginning, if you can only evaluate one part, and it has a many errors, then that is the only thing you can use to make any assumptions about the rest, unless and until you get actual credible assertions about the rest from someone else who are themselves credible in that domain.
(If you want to read more about this then google "single observation unbiased estimator")
That's exactly the wrong kind of extrapolation I'm pointing out. If you found a flaw in one chapter, the book can be trash, and the chance of it being trash is definitely higher than without any other data, but whether the absolute chance of it being trash is sufficiently high enough can only be determined based on the nature of the flaw, and even then, the confidence for that conclusion can't be really that high.
Determining whether a source is trustworthy is an ongoing process: you're seeing one portion where you have some expertise or evidence and then another portion where you don't. You have to extrapolate from what you can validate to whether what you can't is valid.
The complaint behind Gell-Mann amnesia is that we're too quick to dismiss clear evidence that a source is untrustworthy, that we have a bias towards trust.
To put it in perspective, let's imagine the opposite, call it Crank Awareness. If you see a document and it's laid out poorly, uses weird boldface, all caps, colors and blinking text, you'll, at the very least, get the impression it's written by a crank before you even start reading.
> But believing they are always bad is the same logical fallacy as believing they are always good.
Again, this comes back to the problem of strict logical reasoning vs. treating trust as a larger process. We have limited resources to evaluate sources, so we're stuck making fallacious generalizations when we need to make a decision based on our sources. What we want in the long run is to incentivize authors to exercise care and diligence.
That would indicate we should punish known bad information by deprecating the authors. So another way of reading Gell-Mann amnesia is that readers aren't doing this. They're seeing stuff that they know is wrong and continuing to patronize the publications regardless, thus authors can be untrustworthy and still collect a paycheck.
Well then why did you write about liking the book and whether it's good as the cause of disagreement? That's a very very different thing from whether the book is an accurate source!
Even a specific section you prove to be wrong can still be good.
You can't simply extrapolate from finding one mistake in a book to declaring the whole book wrong. Likewise, you can't extrapolate from finding few bad publications to "everything is crap". I'm not trying to claim journalists are all good or even consistently good. But believing they are always bad is the same logical fallacy as believing they are always good.