| Quote #1
From his very first scene, Hamlet sets himself up as someone who hates deception and values inner truth above all. Here, he insists that outward appearances (like his "inky" black clothing, sighs, and tears – all the common markers of grief) can't possibly "denote" what's truly inside him. In other words, Hamlet's saying that his anguish and grief over his father's death are far more intense that they appear to the outside world. He's also implying that Gertrude, Claudius, and the rest of the court are totally fake and disingenuous because they don't care about him or his feelings at all and are far too concerned with keeping up appearances.
| Quote #2
Polonius likes to dish advice, as when he says that if you are true to yourself, you cannot deceive anyone else. Given Polonius's penchant for spying on his children and Hamlet in order to curry favor with King Claudius, he's not in any position to be talking about truth. We're reminded that when these kinds of cliché sayings are carelessly bandied about, they don't seem to carry any meaning at all.
| Quote #3
Like Hamlet, the ghost dwells on Gertrude's "seeming" virtue. Critics are a bit divided over what this means. Is the ghost saying Gertrude cheated on him when they were married? Or, does the ghost merely see her remarriage as a betrayal. The debate comes down to the meaning of "adulterate," which, in Elizabethan England could refer to a cheating spouse or any sexual sin in general (like incest). Either way, the ghost implies that his marriage to Gertrude was a sham. Like young Hamlet, the ghost sees Gertrude as an unfaithful woman with a serious sexual appetite.