I'm asking this question in the scenario where you do not go out of your way to find out whether you're right or wrong. That is, based only on the regular experience and data that you would collect while doing nothing out of the ordinary, how would you know if you were wrong about what you ordinarily believe.
The point of the question is to highlight cases where you can't trust a belief. I have, ordinarily, too many beliefs to be skeptical about and to prove, if I truly want certainty. Fortunately, the world provides us with plenty of data through our ordinary experience, and it allows us to form pretty trustworthy beliefs, most of the time.
It's good to question at least some of our beliefs, though, especially in cases where you maybe shouldn't trust a belief, without first having gone out of your way to gather data to refute or verify it.
A simple example: suppose I believe I can walk through walls. Well, how would I know I was wrong? Without going out of my way, I can recall all the times I've accidentally backed into, or bumped into, a wall. The ordinary course of experience provides me data to the contrary of that belief. It's easy to be disabused of beliefs like being able to walk through walls or being able to fly.
You may have heard of the "statistic" that 99 Out Of 100 Programmers Can’t Program. Maybe you believe it. Maybe you don't. But now, just suppose it's wrong. How would you know without going out of your way to gather data?
I would know because based on my experience, I can recall all the times I've met or talked to programmers who can program. In fact, I might recall that the vast majority of programmers I know of can program just fine. That's how I would know if the statistic is wrong.
Well, in fact, based on my experience, that is true of all the people I consider programmers of interest (so I'll exclude programmers who are just starting to learn, for example). So without going out of my way, I would believe that statistic is wrong.
Notice that this is basically gathering data through a convenience sampling. It's convenient because the sample has already been gathered through the course of ordinary experience!
Now that doesn't mean the statistic is wrong on the whole. Perhaps a random sample would prove the statistic. But I'll be lazy for a moment, and instead, try to understand the context where that original "statistic" was proposed. That statistic was proposed by people doing hiring, but I have never had the experience of hiring someone. So what might be a better explanation for both my experience-created convenience sample, and the proposed "statistic"?
Perhaps the statistic should be qualified as: 19 out of 20 programmers who apply to this position at my company can't pass the FizzBuzz test. Okay, that's probably true given how specific it is, and it explains why the statistic doesn't seem to hold based on my own experience. In fact, based on my own experience freezing up during an interview when asked programming questions (despite my ability to program just fine in multiple languages), it even seems likely that this statistic would appear.
By Occam's razor, I'd suggest the statistic applies only to job applicants, and isn't necessarily true of non-job-applicants (whether the non-job-applicants currently have a job or not). Is this right? Has anyone done a randomized study?
A friend of mine has accounting qualifications to do accounting work. He has never done any such work, however, because from what he's heard, he wouldn't enjoy doing that kind of work. Whether he's right or wrong doesn't matter right now. Just suppose, for the moment, that he's wrong. How would he even know without going out of his way to gather data?
Obviously, he's went through some education to gain that qualification, so he's done some of the work involved through course work. But how closely does course work mirror real work in industry? From my experience in software development, the relation isn't extremely close, so I'd tend to discount using course work experience as very strong data for how one would enjoy that line of work in industry.
Accounting involves a lot of "paper and pencil", rote calculation work, at least at the lowest levels. Everyone has done that kind of work, even if it's not accounting related. So I suppose one may extrapolate from that experience. On the other hand, the really "low level grunt work" in accounting might be left behind rather quickly, as others I know in accounting have found by staying in accounting, and rising to other accounting roles.
Without having put in good-faith effort into industry accounting work, I can't imagine what ordinary experiential data can be used as a base for a believable extrapolation to what it would be like to actually do accounting in industry. So how would my friend there know if his belief is in fact wrong? I guess he just wouldn't.
Not that he's actually wrong, though. I'm just suggesting he hasn't gathered any strong evidence to try to falsify the belief, which makes the belief suspect.
In western philosophy, it's pretty well standard to assume that being alive is better than being dead. We can "pretty up" that statement with talk of utilities, the greater good, platonic perfections, etc, but that doesn't matter right now. Just suppose that's wrong, for the moment. How would you know?
You might try thinking back to the time you talked about the experience of death with someone who's actually tried being warm and dead. Oh wait, I guess they are, by hypothesis, too dead to have talked to you. You might try thinking back to the time you've yourself been dead. But then it would be too late to change your mind if you were wrong about it being better dead.
So what have you got to try extrapolating from? Well, being physically hurt, even a little bit, seems bad from experience. Being hurt a lot is even worse. So extrapolating to being so hurt that you're dead, it must be really, really bad! But some die quietly in their sleep, apparently peacefully and without hurting at all. What about them? Have you, as you went about your business in the past, tried that?
How would you know if it's really better one way or another, without having tried to prove it, one way or another, and without having gone out of your way to gather data? In fact, in this case, is it even in principle possible to gather any high quality data? hmm...
What beliefs do you have? Which ones are you relying on to make that important decision you've been thinking about?