That's the hard thing, looking inside ourselves to realize that, even when we're very sincere, we're rarely honest, in the sense that we're not being very careful to be accurate. But is sure feels sincere to us....Do we all pretty much know what the requirements of honesty are? Just to be sure, let's spell a few of them out:
Honesty is when you're really trying hard to be accurate. To be honest, you have to think about possible criticisms and take them seriously. You have to ask what the evidence on the other side would be. You have to wonder who has supported which sides of a position. If you're going to be honest about something, there's a set of considerations you're supposed to look at. We all pretty much know what they are. But when we're sincere, that doesn't mean we've done those sorts of things.
1) If there are "opponents" that ostensibly hold beliefs inconsistent to yours, you should seek them out and see where they falter. Be sure to "pick on people your own size"--don't focus on the weak arguments of the opposition or invent straw men. If you can't identify exactly how they falter but still have an intuition that they're wrong, then OK (see #11): admit that. Don't rationalize more complicated explanations. But if you can't point to the exact reason why your opponents are wrong and back up your claim, then be extra wary of your own unconscious biases.
2) At any given point, your honest beliefs all should be consistent with one another. This holds for analogous situations to an extent. For example, if you honestly believe that most people behave a certain way, then you need a good reason to argue that you yourself don't follow that trend too. Reversal: This doesn't mean that you can't change your mind on beliefs from one moment to the next! In fact that's the appropriate response when your knowledge of the facts change. What it means is that at any one moment your honest beliefs must be consistent.
3) In order to be honest, you should consider what predictions your belief implies. If there is any way you can test those predictions at low cost, you should do so. If this is a belief that you profess to really care about, then you should be actively trying to test those predictions even at moderate cost (of your own time, for instance). And if there are no predictions of your belief, then you should admit that maybe your belief doesn't really matter.
4) ... ?