Socrates never wrote a single word. That we know of. We know about Socrates through his student Plato, whose writings (in part) have survived. Plato is supposed to have copied down conversations Socrates had. Plato called these dialogues. This dialogue attempts to demonstrate that one may have belief but still not have knowledge.
Socrates: Now take this point. You would agree that there is such a thing as ‘knowing.’
Socrates: And such a thing as ‘believing.’
Socrates: Well, do you think that knowing and believing are the same, or is there a difference between knowledge and belief?
Gorgias: I should say that there is a difference.
Socrates: Quite right, and you can prove it like this. If you were asked whether there are such things as true and false beliefs, you would say that there are, no doubt.
Socrates: But are there such things as true and false knowledge?
Gorgias: Certainly not.
Socrates: Then knowledge and belief are clearly not the same thing.
Socrates: Yet men who believe may just as properly be called convinced as men who know?
Socrates: May we then posit the existence of two kinds of conviction, one which gives knowledge and one which gives belief without knowledge?