Putting aside the obvious question of why a subjectivist would be trying to convince some one of some thing, how is it possible to rely on the laws of logic to prove that the laws of logic do not exist? It is absurd. Still, the one who claims that he cannot know anything, (even though he cannot know that he cannot know anything) cannot defend his claim to epestimological incompetence without invoking some objective standard that of necessity requires that he can say something rational about knowledge of the unknowable, which is inherently self-vitiating.
Not that they don't exist, but that they lead to a paradox.
It is absurd.
Absurdity of course being a "logical" construct whose validity is entirely measured against its own yardstick, a tautology if ever there was one. "This is illogical because it is absurd, and is absurd because it defies logic."
Still, the one who claims that he cannot know anything, (even though he cannot know that he cannot know anything) cannot defend his claim to epestimological incompetence without invoking some objective standard
Yes, the "objective standard" that my counterpart embraces, not necessarily one to which I subscribe. It is you who are bound by those rules, not I. One cannot impose "logical" rules on a universe that creates the kinds of paradoxes of which you speak.