As the actors are acting out the play, Claudius asks Hamlet what the play is about. Hamlet responds, “We that have free souls, it touches / us not: let the galled jade wince, our withers are / unwrung.” What does Hamlet mean by this? How are Hamlet’s comments ironic?
Hamlet is saying that, since those present are blameless, they can't be troubled by the action of the play. The audience is aware of the irony of these lines, since they know that Claudius had actually killed Hamlet's father.
The quote cited in the question is taken from act 3, scene 2 of Hamlet:
Your Majesty and we that have free
souls, it touches us not. Let the galled jade wince;
our withers are unwrung. (265-267)
Hamlet has arranged for a troupe of travelling players to enact a play called "The Mousetrap" or "The Murder of Gonzago" to be played for members of the court, including Claudius. The action of the scene shown from that play depicts a man murdering a King by pouring poison in his ear as he is sleeping. The murderer then woos the Queen with gifts, and, we can assume, eventually becomes her lover.
In this way, Hamlet, unwilling to rely only on the account of the ghost of his father concerning his death, intends to test the response of Claudius to an enactment of murder that very closely replicates the version of the spectral king.
In the relevant quote, Hamlet is saying to Claudius that only those with a guilty conscience can be upset by the play-within-a-play, and that blameless "free souls" like themselves can watch and be entertained by the action of the play as detached observers.
Of course, the audience knows that these lines are ironic, since Claudius is anything but a man with unrung withers, and is, in fact, guilty of the murder of Hamlet's father.
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