A type of level 2 disagreement

I want to elaborate on my reductio against level 4 disagreements, mentioned earlier this morning. It may be that a person cannot form cogent arguments for his own claim but will not admit defeat of his view. In order for this to be a level 2 defeat, his argument must really be rationally indefensible in principle--meaning that, somewhere at least, he must be contradicting some assumptions that have been made. These assumptions can be either exclusively his own, or some level 1 assumptions, or both. If he really is this irrational, he might well not admit this defeat of his position, but because the cogency must therefore exist on the side of the negation of his view, his claim is still a level 2 falsehood. In other words, a dispute can exist at level 2 independently of whether both sides are willing to admit that a proper resolution has been made. This is simply part of the nature of rational discourse, and part of why it can be so difficult to resolve disputes. We don't always know when a dispute has been resolved at level 2, but it seems hard to deny that it is an objective, factual matter that exists independently of whether either side will recognise or admit it.

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