What does Hamlet reveal about himself that in believing the Ghost, he suddenly decides the play can prove Claudius' guilt?In Shakespeare's Hamlet,...

When Old Hamlet first appears to his son in Shakespeare's
Hamlet, the Prince of Denmark is not sure if the ghost is a "good
ghost" or an evil spirit trying to lure him to his eternal damnation by killing a
king.

Elizabethans believed it was a mortal sin to kill a
king, for only God could ordain who would be king. If Claudius has, therefore, killed
his brother Old King Hamlet, then it was a mortal sin. However, if the Ghost is an evil
apparition, then Hamlet feels he needs more proof. Hamlet is accused of being
indecisive: this is his tragic flaw. However, it is easy to be more sympathetic to his
cause when we remember that this young man doesn't want to forfeit his
soul.

The Ghost's biggest complaint is that his brother
killed him with sins on his soul, without the benefit of time to confess his
wrong-doings. Because of this, Old Hamlet must wander somewhere between heaven and hell
(purgatory?). It is this reason only that causes Hamlet to pause when, after the King's
guilty reaction to the play, Claudius seems to be praying—Hamlet will not kill him then,
even with his proof, because he doesn't want Claudius to be able to go straight to
heaven, having just confessed his sins. (Ironically, Claudius
cannot pray in this scene, though he
tries.)

The quote that ends Hamlet's "O, what a rogue and
peasant slave am I" soliloquy in Act II, scene ii, turns his attention from his failure
to act, to his conviction that now is the time to act. He has been
watching the players. He compares his reactions to those of the actors. They play their
parts, only reading lines but without real feeling. He sees that he has been this way
until now: having the information that his father was murdered, but unable to say or do
anything, making his feelings useless because without action, they are
meaningless.

With this in mind, Hamlet decides to get the
proof or information he needs by having the actors play out a specific scene. He has
heard that sometimes, when the guilty party sees his crime acted out in a play, he will
react with such passion as to give away his guilt. Hamlet will have the actors reenact
the murder of Old Hamlet, and Claudius' part in it. Based on Claudius' reaction, Hamlet
will finally have proof to support or refute the Ghost's claim. If Claudius acts
guiltily, then Hamlet will know the Ghost has spoken the truth, and then Hamlet can
proceed without worry of losing his immortal soul.

At the
end of the soliloquy, Hamlet announces that the play will be the tool he uses to stab
Claudius' conscience into exposing this new King's
guilt:

The
play's the thing
Wherein I’ll see the conscience of the king.
(599-600)