Jay Gatsby has a philosophy, or way of thinking, directed by his belief in two things: one can repeat the past, and one can re-create himself.
Gatsby has a mansion modeled after a French hôtel de ville built in West Egg near the home of Daisy Buchanan so that he can reintroduce himself into her life and renew the love that they once had. With Nick as his intermediary, he has Daisy meet him at Nick's cottage. Prior to this meeting, Nick warns Gatsby that the past cannot be revived. "Can't repeat the past? Why of course you can!" Gatsby replies with indignation. Further, in their conversation, Nick comes to realize that Gatsby is looking for
...something, some idea of himself perhaps, that had gone into loving Daisy. (Ch. 5)
Jay Gatsby embraces the ideal of the American Dream in his attempt to re-create himself:
Each night he added to the pattern of his fantasies....For a while these reveries provided an outlet for his imagination; they were a satisfactory hint of the unreality of reality, a promise that the rock of the world was founded securely on a fairy's wing. (Ch. 6)
With this ideal, Gatsby fashions himself. He holds parties, inviting hundreds of people, he smiles and smiles, he surrounds himself with material possessions to lure the materialistic Daisy who sold herself into a marriage for $350,000 pearls, and he purchases an automobile with "fenders spread like wings" and "a labyrinth of windshields that mirrored a dozen suns."
Gatsby, the "great Gatsby," works magic upon himself, perhaps not with mirrors and smoke, but with his imagination and his romantic heart that embraces the ideals of love and the American Dream.