Over the entrance to the temple at Delphi are the words "Know Thyself." Defend the statement that Oedipus doesn't know himself in Oedipus Rex.
Throughout the majority of the play, Oedipus does not realize he is responsible for the plague. Oedipus also rejects Tiresias's account that he is his father's murderer and is married to his mother. Despite his initial belief and confidence that he is not responsible for King Laius's death, Oedipus continues to search for the truth. Oedipus is not willing to accept Tiresias's account and banishes Creon under the pretense that he is in alliance with the blind seer. After Jocasta tells Oedipus her husband was killed where three roads meet at Phocis, he becomes suspicious. Oedipus recalls killing an unknown man on his journey to Thebes and suspects the man may have been King Laius. Oedipus then remembers a drunk man at his family's banquet once mentioned that he was not really Polybus’s son. Oedipus was so disturbed at the comment that he consulted the oracle of Apollo, who told him that he would sire children by his own mother and kill his father.
As the play progresses, Oedipus receives the news that King Polybus has recently died, which gives him and Jocasta momentary peace. However, the messenger then reveals that Polybus was not Oedipus's real father and explains that he brought Oedipus into the king's home as an infant. This information perturbs Oedipus and Jocasta realizes the dreadful truth. Oedipus continues to summon individuals with knowledge about his past until he discovers he is responsible for killing his father and marrying his mother. Oedipus's ignorance of his origins and denial of prophesied information prompt him to begin a search for truth, only to discover the unfortunate prophecy of his childhood came true.
You are right in identifying Oedipus as the classic example of this statement. One of the reasons that this play is so famous is that Sophocles creates a situation where both the audience and quite a few of the characters know who committed the murder of the former king of Thebes but Oedipus, ironically the man who committed that murder, does not. What makes this irony more acute is the way in which he pledges himself to find that murderer and see him punished for the tragedy that has befallen Thebes. As the evidence stacks up against him, we see more and more how he is doing his best to ignore the truth, helped by characters such as Jocasta. However, note how he expresses himself when he is forced to truly know himself as the man who is the murderer he is looking for:
All come true, all burst to light!
O light--now let me look my last on you!
I stand revealed at last-
Cursed in my birth, cursed in my marriage,
Cursed in the lives I cut down with these hands.
Oedipus does his best to subconsciously ignore his true identity for most of the play, but when incontrovertible evidence forces him to see himself for who he is, he has no choice but to yield to the inevitable and finally accept self-knowledge. This is what makes him a perfect example who does everything he can to prevent knowing himself.