The defining aspect of Edmund is probably his love of poetry and philosophy. The bookshelf is lined with his favorite authors: Nietzsche, Swinburne, Wilde, and Marx among others. The group of writers that Edmund has studied is by no means philosophically uniform. Overall, however, they speak to Edmund's general rationality, distaste for the status quo, and desire to penetrate beyond the appearances of things.
We can see echoes of these authors' thinking in Edmund's huge poetic speech, in which he describes his love of the sea. This speech is really the central moment of the play for Edmund and deserves special attention.
Übermensch can be translated as "superman" or "overman." Basically, it means an ideal form of man, who dictates his own will and transcends regular human existence. By striking out to sea alone, Edmund cuts himself off from the safe world he knows. He's dictated his own life. By communing with nature, Edmund has becoming one with a higher godlike consciousness. In that sense, Edmund has transcended normal human experience and found a deeper understanding of existence.
poetry and philosophy are Edmund's best tools for survival. Waxing poetic about death and despair is his way to cope. Unlike the rest of his family, Edmund has actually found something productive to do with all his anguish – create art. Edmund's talent with words and his philosophical nature are the keys through which he can escape the cycle that's trapped the rest of the Tyrones.