What purposes are served by the appearance of Antigone and Ismene in the Exodos of "Oedipus Rex?"
The children are a connection for Oedipus to what is valuable.
Antigone and Ismene are a result of Oedipus' union with Jocasta, his own mother. The prophecy, which Oedipus tried to desperately to avoid, had been fulfilled. Ashamed and horrified, and metaphorically "blind" his entire life, Oedipus literally blinds himself. Despite his condition and the revelation, Oedipus still feels a great love for the girls, who, unlike his sons, are still small children. He begs Creon,
...Take care of them,
I beg you. Wait, better -- permit me, would you?
Just to touch them with my hands and take
our fill of tears. Please...my noble king.
Grant it, with all your noble heart.
If I could hold them, just once, I'd think
I had them with me, like the early days
when I could see their eyes (1605-11).
Robert Fagles, the noted scholar and critic, says that "the connection to reality, to touch and feel his children, gives Oedipus a new strength which sustains him in misery and gives him the courage he needed to go on living, though he is now and outcast."
The girls, too, love their father; they, too, will be marked as outcasts. Too young to understand the full import of their new status or their father's acts, they embrace him. Oedipus knows they too will suffer; "Such a disgrace, and you must bear it all!" he cries. Though blind, he is now able to see.