HAMLET STUDY GUIDE QUESTION
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The ghost is certainly a strange omen. They know the ghost of Hamlet Sr. shows up all melencholy but refuses to speak to them. The surmise Hamlet's father (ghost) wishes to peak with Hamlet. Marcellus thinks "Something is rotten in the state of Denmark" so Hamlet would be well advised to find out what it is from the ghost.
Just to add, initially Marcellus thinks the ghost should speak with Horatio as he is Hamlet's closest confidant. The soldiers like Marcellus probably do not have access to Hamlet but Horatio certainly does.
WHy does Marcellus ask Horatio to speak to the ghost
Hamlet Act 1
Marcellus ask horatio to speak to the ghost because "as a Scholar who kows latin, Horatio is considiered better able to deal to the ghost"