I read it, thanks. Bottom line, there is no good solution to this problem. If you explain to yourself what the psychological problem of your disputant is (locked in, rigid, etc.), that doesn’t break the symmetry when he thinks the same thing about you.

Why is the fact that he is mistaken supposed to impress me? Anyone can make any claim. So what? Why does the claim that there are others who say otherwise than I do prove anything? So they’re wrong. And if they think I’m wrong, that’s obvious. It’s a logical derivative of their mistake.

Not the mere fact of their claim, but their authentic perception that you are wrong and they are right. When I step outside myself and zoom out, there is me versus another person, and I can’t break the symmetry by means of arguments that don’t depend subjectively on my personal perception. Peer disagreement is a tangle with no real way out, even though it obviously leads to absurd skeptical results.

But why do you need to step outside yourself? Is that even possible? You are you and not somebody else. Think about a religious court hearing the claims of both sides. The judges themselves do not know what the truth is, while the sides do. There the religious court really is supposed to relate to the situation from the outside, because it has no direct access to the factual truth. But in an argument between the sides, am I supposed to step into my fellow’s shoes and judge the situation from the outside? If I am right, then he is lying or mistaken, and that’s that.
This reminds me of Mahar”i Basan’s question: why do we allow the current possessor to keep the money without proof? After all, there is a possible prohibition of theft hanging over him. The question is self-evidently absurd, because he himself knows that he is right; the doubt exists only for the judges, not for him. Is he supposed to shift to some objective perspective and declare himself in doubt because the judges do not know the truth? Therefore there it is clear that the question is not difficult, except in the case of certainty versus uncertainty when seeking to extract property, where the current possessor himself really is in doubt.

The examples you gave are irrelevant דווקא because of the subjective asymmetry in them. The current possessor knows what the religious court does not know. I’m talking about a factual dispute where my colleague and I have the same knowledge. I’m not telling him anything new. He simply inferred differently. I can even explain to myself that he’s rigid, too proud to admit a mistake, etc., but if I have a real indication that he also thinks the exact same thing about me in his heart of hearts, I have no reason to prefer my opinion over his.

As for whether this is possible: that’s a good question. But that’s a psychological question, not a philosophical one. I’m talking about what is appropriate.

Even in the current argument between us, I’m forced to admit that I need to remain in doubt regarding the claim that peer disagreement is a problem with no solution; after all, you think otherwise.

Let me preface by saying that this was not only a psychological claim but also a substantive one. I cannot step outside because I do not need to step outside. When I am dealing with the question of what I think, that is by definition my own view and not the view of someone from the UN. Even in the question of whether I am right (the peer question), the one who decides is me. I claim that the demand to step into an objective perspective on this particular question is not well-defined.
I claim that we do not have the same knowledge. My cognitive observation (of the ideas) gives me information that, in my estimation, he has not reached. He is blind to certain aspects of the ideal world.
Your loopish remark at the end is very charming.

“I claim that the demand to step into an objective perspective on this particular question is not well-defined”
Are you claiming that the peer problem does not even get off the ground? Have so many pens been broken for nothing?

First of all, not a few pens are broken over ill-defined questions. Far too many, unfortunately. Second, absolutely not. The question is a good one within the framework of my discussion with myself: should I be concerned that the other person is right? And my answer is that within the framework of my own thought, it is neither correct nor well-defined to demand stepping outside, and if we are dealing with my perspective, then it is indeed justified to rely on my own conclusions.