What did Socrates mean when he said "I know that I know nothing"? (Quora)

It would have been most unlike Socrates, whose analytical technique (called elenchus) was based upon exposing contradictions in the statements of other people, to express himself in a contradiction. Obviously anything that I know is something, therefore if I claim that I know I know nothing, I am contradicting myself.

If, however, I start from the assumption that I know nothing, I may ask anyone who claims knowledge to explain a particular aspect of what it is that they know. Usually Socrates would invite his interlocutors to state a generally-applicable principle, and then he would offer a specific instance of the principle’s non-applicability. This would lead to the interlocutor redefining the principle more narrowly. The process would be repeated until it could be repeated no further, at which point Socrates would deem that they had arrived at a truth.

The process has considerable merit, but is inevitably limited in scope. Ironically, Donald Rumsfeld’s much-derided, but actually important, categorisation of knowledge into known knowns, known unknowns and unknown unknowns helps us to understand this.

Most people are aware that there are limitations to their knowledge (or known knowns); for them there exist known unknowns. So, for example, I am aware that there is a field of human knowledge called quantum mechanics, but I have no detailed understanding of what that field encompasses.

Unknown unknowns have been usefully defined as “phenomena which cannot be expected because there has been no prior experience or theoretical basis for expecting the phenomena”.

But in later life Rumsfeld came to acknowledge the existence of a further category, possibly the most problematical of all, that of unknown knowns. These he defined as "the things you think you know, that it turns out you did not".

Like Rick in Casablanca, we can be misinformed. Sadly, we may act upon mistaken beliefs with all the intensity that would ideally be reserved for genuine certainties.

So, if we return to Socrates, we find that even the little that we think we know may be just waiting for some counter-argument or evidence to turn up.