Radical Scepticism is the philosophical position that knowledge is impossible. It leads to a paradox of knowledge - we cannot really know everything.
I first learned about this concept in Duncan Pritchard's Scepticism: A Very Short Introduction. This paradox of knowledge felt extremely infuriating to me. It highlights scepticism of two kinds - healthy scepticism and radical scepticism.
A healthy sceptic believes that in principle all knowledge is falsifiable, no matter how faint the possibility. This is only a concern when one has a strong reason to feel that their current beliefs are build on the wrong foundations. As long as it works, it works.
A radical sceptic, however, blows this tiny possibility of falsifying everything to raise the paradox of knowledge - if all knowledge has the tiniest possibility of being falsified, can we really be sure? I find this argument frustrating because it put knowledge to an extremely harsh global standard and isn't meaningful at all. Often, I find politicians relying on seemingly innocuous realizations of this paradox in real life and that makes me cringe. This also then leads to arguments around truth relativism and no basis for rationality.
I don't think I ever want to argue with a radical sceptic because it is meaningless. It doesn't get anything done. Of course, for your armchair philosopher, questioning the nature of reality and things like the simulation hypothesis may be intellectually stimulating. I find Ludwig Wittgenstein's quote for the basis of rationality most well-intentioned for the world as it is.
If I want the door to turn, the hinges must stay put.
In the context of probability theory, it reminds me of Cox's Axioms. In geometry, it reminds me of Euclid's postulates. In number theory, it reminds me of Peano postulates. I am certain every field of scientific inquiry relies on such unquestionable "hinges" that form the basis of rational thought and progress.