Watching philosophers debate was one of the ways a budding politician could pick up tips on how to be a convincing speaker.
If multiple philosophers can debate, or lone philosophers can give lectures, anyone hanging out in the meeting hall at the time should be able to pick up some minor pointers on persuasion and judging intent.
Perhaps a philosopher could acquire disciples, some of which he is paid to instruct by a noble, and some he just adopts, who grow up to be new philosophers. Some sort of hard limit on the percentage of the populace that can become philosophers might be necessary, to prevent situations where you have a city full of dwarves who are too well educated to work.
Perhaps only orphan commoners are adopted, and only by compassionate philosophers.
To balance things out, philosophers of a steelier mindset could take on insane dwarves. Maybe a healthy dose of stoicism could keep a dwarf from acting on his madness or melencholy until his biorhythm goes back into an up-cycle and his bad memories have faded a bit.
It doesn't have the raw emotional potency, or the historical accuracy of them being locked up and poked with sticks by tourists, though. Cops might need more options than "talk him down" and "lethal force" though, as capture rates for Ax Murderers seem to be nil.
I figure, if caged madmen are naturally vulnerable to being influenced by the Outside, and the things that exist there, the gods are going to know that, and instruct their followers in the path of not listening to crazy people.
Gods of chaos and murder probably wouldn't give a rip, one way or the other, so long as the Outside only destroys all mortal life.
Dwarves need to be smarter about fire, before they can be permitted to burn books, but chucking the thing in a chasm or lava pit should do for now.