The column discusses a different issue—different conclusions, not different premises.

There is no difference at all. Different conclusions mean different premises. Unless there is a mistake in the logical inference, in which case no problem arises in the first place.

There is a difference, because one of the ways—and more precisely the only way—to check that the other person is locked in is to point out that his conclusion does not follow from the premises and see that he does not retract.
Otherwise, you wrote that there is a lot of room for uncertainty, like a comparison between two truthometers.

But with basic premises, there is no issue of being locked in.

?

I don’t see any point in going over this again. If you find a logical contradiction in the other person’s position and he does not retract, then he is just an idiot or dishonest. That is not what we are discussing here.

Come on now, what I said is exactly what you wrote in the column—that this is the way to characterize that the other person is mistaken and therefore locked in.
But when you cannot see that he is locked in, you wrote that there is no reason not to remain in doubt.
In my opinion, you should definitely write a new column 637, because in my humble opinion you have not forgotten what you wrote in column 247. And it may be that since then you have developed a new view in the area of disagreement.

Either poor reading comprehension or plain stubbornness (or both). In any case, there is no point in continuing this discussion.

Hey, that’s not nice 🙂
I’ll prove to you that you’re mistaken. I copied the relevant parts from the article; decide what you say about them.
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“After I reconsidered my position and my colleague’s arguments, and reached the conclusion that I am still right and he is mistaken, I am permitted to maintain my position if in my opinion my colleague did not do what I did. That is, in my estimation he did not seriously consider my position and my arguments after hearing them (he was ‘locked in’).”

“This is a relevant consideration only if that really is the case in my opinion, and not when I merely raise this suspicion as an ad hoc justification for my stubbornness in holding onto my position. In such a situation, I myself suffer from the same flaw of which I accuse him (since I myself am not seriously considering the position of the disagreeing colleague).”

“One of the indications that the other person is not seriously considering my position is when I raise a strong logical argument and he does not accept it without showing where it fails, or when I point out a logical refutation in his arguments and he still does not retreat. We are speaking about a case where it is clear to me that if he had seriously considered my arguments, he certainly should have accepted them.”
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That is, the reason to give priority to your own basic premises is only when you have good reason to assume that the other person is locked in. The way to check this (and you gave no other way) is to point to a logical failure.
Isn’t that exactly what I said 👊?

And therefore all this is relevant only for arguments that are not basic premises, because regarding basic premises you have no reason at all to assume the other person is locked in! (Unless you show him that his conclusion is absurd, which usually does not happen.)

Checking validity is only the extreme case; someone who fails there is really an idiot. A sensible examination mainly includes examining the premises.