The Dogmatism Paradox begins with the claim that I know some proposition p and uses apparently good reasoning to draw a seemingly irrational dogmatic conclusion: that I should therefore dismiss any new evidence against p. A standard solution to this paradox is to note that when I acquire new evidence against p, that evidence defeats my justification for believing p. As a result, I no longer know that p, and so the reasoning used to generate the paradox begins with a false premise.

By appealing to recent work in social epistemology by Endre Begby and C. Thi Nguyen, I develop a new, stronger version of the Dogmatism Paradox that is immune to this standard solution. This version of the Dogmatism Paradox has significant consequences for contemporary polarized political disagreements, in which subjects on both sides of the disagreement have reason to distrust new evidence against their beliefs. So, unless the paradox can be solved, many political disagreements in sufficiently polarized communities will turn out to be rationally intractable in the sense that agreement can only be reached by one side irrationally revising their beliefs.