I am glad to see you well:
Horatio,--or I do forget myself.
Horatio is Hamlet’s fellow student at Wittenberg. At that time a university education was a high privilege that distinguished gentlemen from commoners. Horatio is not royal, but he’s not a mere servant, either.
Hamlet is not simply saying “I didn’t recognize you at first.” What he is saying might be understood by reference to Hamlet’s declaration to Horatio in 3.2:
Since my dear soul was mistress of her choice
And could of men distinguish, her election
Hath seal’d thee for herself…
There is, in other words, an intimate one-to-one correspondence between Hamlet’s inner identity, his soul, and recognition of Horatio.
So Hamlet is jocularly saying: either you’re Horatio or I’ve forgotten who I am. Place the emphasis on “myself,” and the statement takes on a second meaning. Hence the arrival of Horatio means here a sudden change in Hamlet’s behavior and way of speaking. In this scene we see both his bitter pain and his friendliness.
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