A good teacher as a guide to ambiguity, not certainty.
"How to keep sane in spiral types of space."- Nabokov, Pale Fire

“One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.” 

“To teach how to live without certainty, and yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy, in our age, can still do for those who study it.”- Bertrand Russell