For each of the believers in the two stories, there seems to have been a prior state in which there was an inferential structure:
The pictures on a tv screen move and change because there are little men in there.
We could add a bunch of steps (something needs to move them; little men could move them) and make it a
modus ponens and so on, but that's the start and finish.
Similarly:
If I'm a space ranger, then I spent years at the Space Ranger Academy training to be one.
It looks to me like the consequent in each of these cases gets detached -- in one case because there's an alternative explanation that doesn't need little men, so the necessity of the inference is denied, and in the other because the premise is denied.
That leaves each of these conclusions not falsified but floating free, unsupported. There are little men in there, but not for any particular reason (and then you could rationalize that -- they make sure everything works smoothly); I went to Space Ranger Academy but for no reason, or only to become a toy not a Space Ranger.
This is a funny thing, because it's not exactly illogical not to deny the conclusion of an inference, just because the inference or premises were defective. It could still be true, and in neither case was the particular conclusion that is still affirmed challenged.
The engineer could have just opened up a tv and said, "See, no little men," but you might have to do that with a bunch of tvs, and even then maybe our guy would think, surely some tvs have little men in them. How would you convince Buzz that he never went to Space Ranger Academy? Maybe showing him the Space Ranger Academy playset at the toy store (Buzz Lightyear figure sold separately).
All that to one side -- consequent cut free, still possibly true, never specifically challenged -- we might want to say there is a standard of evidential support that these beliefs no longer meet. We still have grounds to criticize, if we want, but these grounds are a little shakier. "Don't believe anything you don't have strong evidence for" is a rule begging to be selectively enforced.
But what do we say about the persistent or vestigial credence accorded these free-floating beliefs? Is that just habit, doxastic inertia? Will these beliefs maybe just fade away over time now that there's no obvious way to continually reinforce them?
Or do we think that we can see here that
belief is not really a product of inference at all? Maybe it's more like Hume might describe it, just a sort of emotional accompaniment to a thought, because you can undercut the inference and leave the feeling of belief intact.
Btw, can anyone provide a case from real life instead of these stories? Or if not from real life then from philosophy?