Quick question...
 

Does anyone know the name of the paradox that says "The more you know, the more you know that you DON'T know."

I think that's a Socrates quote.

Try Tilted Knowledge.

I don't think that's a direct Socrates quote is it? I know his idea was very similar. He knew that he didn't know, which was something all the other supposedly wise men didn't know. It all revolved around his central questions "what is piety? what is justice..." There is a new book called "6 questions of Socrates" that looked really interesting. The author basically took the same line that Socrates did and asked supposed experts the same questions Socrates asked of the experts in his time. I guess that's a bit off topic though.

Not a socrates quote...
 

I believe that comes from a story that began with a trip to the Oracle of Delphi taken by a friend of Socrates. The friend returned and told Socrates that the Oracle anounced that there was no one wiser than Socrates. Socrates scoffed at this and could not understand how this was so. To disprove the Oracle, Socrates began to travel the land asking questions of various politicians, leaders, religious persons. He was searching for someone wiser and more knowledgable; instead he found that most of these people relied on suppositions, myths and fallacies. He eventually reconciled the Oracle's words with his own perceptions by realizing that since he knew he knew so little, he actually knew more than others who claimed they knew so much. Thus, "true knowledge consists of knowing that you know nothing." -Ted "Theodore" Logan.

Part of this story comes from Plato's "Apology" and part of it is apocryphal.