In addition, as Eliezer’s earlier post about the math proof shows, if the original reason that led you to believe you could do something was shown to be false, you should almost certainly give up. It’s very unlikely you were right for the wrong reasons. If, knowing what you know now, you would never have tried, then you should probably stop.
This ignores the case where your “original reason” was an attempt to formalize some informal reason. If your error is in the formalization process and not in the reason itself, being right for the wrong reason is a plausible scenario.
You’re ignoring the probability of succeeding at something else. If you’re still doing this, it’s zero. If you give up, it’s not.
Of course, that can also be considered a cost of failure, in which case you didn’t ignore it.
Edit: This is equivalent to counting opportunity cost as a cost of failure that’s not a cost of giving up, so maybe you weren’t ignoring it.
In addition, as Eliezer’s earlier post about the math proof shows, if the original reason that led you to believe you could do something was shown to be false, you should almost certainly give up. It’s very unlikely you were right for the wrong reasons. If, knowing what you know now, you would never have tried, then you should probably stop.
This ignores the case where your “original reason” was an attempt to formalize some informal reason. If your error is in the formalization process and not in the reason itself, being right for the wrong reason is a plausible scenario.