It's generally harmless for philosophers to believe stuff, since they don't drive buses, and they generally get their vaccinations regardless of the epistemological status of their effectiveness. For that matter, they continue to eat food, despite the uncertainty whether they're really holding a peanut butter sandwich and not, say, the average temperature of the asteroid Ceres.

They get to be anarchic, as long as you can't prove otherwise -- and "prove" in the mathematical sense, not the scientific one. All it costs you is paper, pencils, and the price of a trash can. (Which they never use.) If you shut down the line of reasoning just because other people are incredibly, dangerously stupid, you're going to have to shut down pretty much everything.