Seems like these "critical arguments" do a lot of heavy lifting.

Suppose you make a critical argument against my hypothesis, and the arguments feels smart to you, but silly to me. I make a counter-argument, which to me feels like it completely demolished your position, but in your opinion it just shows how stupid I am. Suppose the following rounds of arguments are similarly fruitless.

Now what?

In a situation between a smart scientist who happens to be right, and a crackpot that refuses admitting the smallest mistake, how would you distinguish which is which? The situation seems symmetrical; both sides are yelling at each other, no progress on either side.

Would you decide by which argument seems more plausible to you? Then you are just another person in a 3-people ring, and the current balance of powers happens to be 2:1. Is this about having a majority?

Or would you decide that "there is no answer" is the right answer? In that case, as long as there remains a single crackpot on this planet, we have a scientific controversy. (You can't even say that the crackpot is probably wrong, because that would be probabilistic reasoning.)

You must accept your fallibility, perpetually work to find and correct errors, and still be aware that you are making some mistakes without realizing it.

Seems to me you kinda admit that knowledge is ultimately uncertain (i.e. probabilistic), but you refuse to talk about probabilities. (Related LW concept: "Fallacy of gray ".) We are fallible, but it is wrong to make a guess how much. We resolve experimentally uncertain hypotheses by verbal fights, which we pretend to have exactly one of three outcomes: "side A lost", "side B lost", "neither side lost"; nothing in between, such as "side A seems 3x more convincing than side B". I mean, if you start making too many points on a line, it would start to resemble a continuum, and your argument seems to be that there is no quantitative certainty, only qualitative; that only 0, 1, and 0.5 (or perhaps NaN) are valid probabilities of a hypothesis.

Okay, I feel like am already repeating myself.