Updated: Jun 10, 2020
It is said that Socrates was considered the wisest by the Athenians, following the words of Apollo's famous oracle in Delphi. Socrates, on his part, would go on to test this statement, realizing that it is only correct insofar as he does not entertain truths of which he has no knowledge; that, basically, he is the wisest because he knows he doesn't know, unlike many of the pompous characters he enjoys deflating throughout his dialogues.
I would like to contribute here a small distinction: the difference between knowing what you don’t know, knowing that you don’t know, and knowing when you don’t know.
The first is contradictory and needs a justification for this fact (you can't know what you don't know, at best guess or trace rough contours to). The second is properly Socratic, but it treats of this state of knowledge/non-knowledge as self-same and constant in time. If you know that you don't know then why keep trying to disprove it? After all, you know that already!
The third construction is where I see the most phenomenological insight and philosophical hope. If you only know that you don't know as a function of time - your experiences, life events, age... - then this knowledge (of not knowing) remains, itself, insecure. if you don't insist on this here you are forced to either see Socrates as a dogmatist, or to accept the moralizing bore that western-Christian readings have made of him.
[Picture origin: https://www.thorvaldsensmuseum.dk/en/collections/work/N261,38]