As I learned from my dear teacher and mentor, the late AU philosophy professor Andrea Tschemplik, knowledge of ignorance is one of the marks of a great philosopher. In Plato’s Apology, Socrates explains: “I am wiser than this man; it is likely that neither of us knows anything worthwhile, but he thinks he knows something when he does not, whereas when I do not know, neither do I think I know; so I am likely to be wiser than he to a small extent, that I do not think I know what I do not know.”
Socratic knowledge of ignorance is better than arrogance insofar as the person who is ignorant recognizes this ignorance and actively seeks the truth. The recognition of ignorance and pursuit of the truth are crucial here, though. It is cowardly to remain ignorant when one knows they are ignorant for the purpose of being able to avoid confronting difficult realities. Here I have in mind willful and stubborn ignorance born of a desire to use ignorance as an excuse for future mistakes or harms.
So, which is worse—arrogance or ignorance? Arrogance is worse, I think, for the arrogant person and for those who engage with the arrogant person. Arrogance leaves little room for growth, whereas ignorance—if we are brave enough to recognize and name it—invites us to search for the truth and become better versions of ourselves.