What evidence is there to suggest the ghost of Hamlet's father is a projection of Hamlet's feelings about his mother's marriage to her brother-in-law?

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There is little hard evidence from the text that the Ghost is a projection of Hamlet's feelings, since, after all, Horatio, Marcellus, and Bernardo have already seen it (Marcellus and Bernardo more than once) when it appears for Hamlet. After he reveals his displeasure with his mother's marriage to Claudius, though, he does say, cryptically, to Horatio that "My father—methinks I see my father." When Horatio asks him where, he says that he sees him in his "mind's eye." Only at this point (in Act I, Scene 2) does Horatio reveal what he and the other sentries have seen, but it is worth noting that Hamlet says he suspects "foul play," and that when the ghost informs him of his murder, Hamlet exclaims "O my prophetic soul! My uncle!" Given what is in the text, though, it is hard to see how this is anything more than a statement that Hamlet has never really liked, and has been suspicious of his uncle/stepfather. The Ghost seems to be more than just a psychological phenomenon—it is a supernatural being.