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To me, Gatsby is the best example of a character dedicated to a formal ideal.
This is implied above, but I just want to be clear that Daisy is not the "Platonist" here, but Gatsby is in his pursuit of a formal idea, a dream, a perfection.
This dream survives the passage of time almost incredibly for Jay Gatsby and does not fade nor does it diminish. Perhaps there is some insanity in this fact...but if it is insane it is in the same way that "The Allegory of the Cave" is expressive of a whimsical vision of the world that purposefully separates the dream (existing on the formal plane)from reality.
What a great question! My first thought was, of course, that they aren't related at all—no one consciously thinking of Platonic matters or philosophy. However, almost as quickly I realized that there is indeed a strong Platonic thread throughout the novel. Daisy is Gatsby's ideal; it is as if she were an embodied Form of Beauty. Any details of her actual ethics or life are like the shadows on the walls of Plato's cave.
Because of this, her beauty and nature is timeless. It is independent of time. That's what leads Gatsby to say the following:
“Can't repeat the past,” Gatsby replies, “Why of course you can!”
Since the forms never change, you could of course repeat the past.
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