Gertrude, Claudius, Rosencrantz, and Guildenstern are gathered in the hall. Claudius asks Gertrude what’s bothering her—she asks Rosencrantz and Guildenstern to leave, and they do. Gertrude tells Claudius that he wouldn’t believe what she’s seen tonight: Hamlet is entirely mad, and has slain Polonius in a hallucinatory rage. Claudius remarks that Hamlet’s “liberty is full of threats to all”—but he cared for the boy so much that he has put off doing what needed to be done. Hamlet, Claudius says, is like a “foul disease” that has begun to “feed even on the pith of life.” Claudius promises Gertrude that by the time the sun comes up, Hamlet will be “ship[ped]” away from Elsinore.
Claudius compares Hamlet to a “foul disease,” but while Gertrude takes Claudius’s words to implicate Hamlet’s madness, Claudius is actually referring to Hamlet as a liability because the young prince knows the truth about Claudius’s murderous ascent to the throne.
Claudius calls Rosencrantz and Guildenstern back in, and orders them to go find Hamlet and bring Polonius’s body to the chapel. They hurry off. Claudius tells Gertrude it’s time to “call up [their] wisest friends,” tell them all the truth about Hamlet, and ask advice as to what should be done about the boy.
Claudius knows that something must be done to stop Hamlet—but also is in the precarious position of being married to Hamlet’s mother, who loves her son very dearly and will not let Claudius simply kill him. Hamlet can’t kill Claudius, and Claudius can’t kill Hamlet.