In order to understand some of the philosophical ideas behind the script, one needs to be familiar with existentialist philosophy and the ideas of German philosopher Friedrich Nietzsche who pioneered existentialist philosophy. Nietzsche believed that pain is essential to human experience. People should not numb their pain. Instead people should use their pain to cultivate their character. He likened the pain to the roots of a plant; the deeper they go, stronger the plant will be. In short, pain builds character.
The other concept of Nietszche that stood out to me in the screenplay is the eternal recurrence of events. Nietzsche suggested that events in the universe could be repeating themselves in endless cycle which he called "eternal recurrence". Charlie Kaufman probably named the title of the screenplay after this concept. We all know that he knows about Nietzsche as he is quoted a couple of times in the movie (the lines from "Beyond Good and Evil).
The other existentialist concept is the world is what you make of it. It is how you see it and it matters more how you see it than it being an independent reality. If someone erases you from their memory, that doesn't take anything away from the goodness of memories themselves. If they mean so much to you and still a part of you then that's all it matters. Well enough with the philosophy...
This is the story of romantic couple, Clementine (Kate Winslet) and Joel (Jim Carrey), who go through a breakup. Joel finds out that Clementine had a procedure done to erase all memories of him and their relationship. He decides to go through the same procedure and remove her from his memory. However, during the procedure he comes to a realization. This realization is the wisdom of the movie. It offers a great message inspired by the aforementioned philosophical ideas.
I think Eternal Sunshine is a great movie and a rare cinematic art. If you love literature, philosophy and intelligent film-making, the chances are you will like Eternal Sunshine.