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When Sophocles' Oedipus the King opens, Oedipus has sent Creon to Delphi to ask Apollo's oracle what to do about the plague that is destroying Thebes. Creon returns and declares that the plague is a result of Laius' killer still being present in the city.
Given this, Oedipus begins trying to discover who killed Laius, who was king of Thebes before Oedipus. Of course, early on in the play Oedipus does not realize that he himself is Laius' killer. When the prophet Teiresias reluctantly names Oedipus as Laius' killer, Oedipus immediately moves into a state of denial and claims that Teiresias and Creon are conspiring to overthrow him.
When Creon learns that he has been accused of treason, he defends himself against Oedipus' accusations. The ensuring argument between the two men reveals that Oedipus is acting in a stubborn and irrational way. Creon, on the other hand, gives sound reasons why he has no desire to be king instead of Oedipus. Creon gets Oedipus to admit that he is already virtually equal in power to Oedipus. Creon also argues that he enjoys all the privileges of being a king "without the fear" and declares that he has "royal power without anxiety".
Thus, in this argument, Oedipus, famous for his mental prowess in solving the riddle of the Sphinx, shows himself irrational, whereas Creon makes cogent arguments as to why he should not be suspected of treason.
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