All but Gerald and Sheila leave the room. Sheila notices that Gerald was shocked at the name “Daisy Renton,” and she asks whether Eva/Daisy was the girl he was seeing in the spring and summer when he claimed to have been occupied at work. Gerald admits to an affair with a girl he thought was named Daisy. He asks Sheila to conceal this from the Inspector, but Sheila tells Gerald that the Inspector must already be aware of this information.
The Inspector is the play’s great unexplained presence, perhaps even stranger a character than Eva/Daisy, whose “real” identity is never defined. The Inspector is notable because his motivations are not clear to the audience, nor to the Birling family. He says he is a part of the police department, but Gerald’s and Arthur’s later investigation will show this is not the case. The Inspector seems aware of some police protocol, but no one on the force knows him, and it is not even evident if he is a resident of the town of Brumley. His political sympathies appear roughly socialist, but he does not identify them as such, nor does he say that his mission in the Birling home is a political one.
Instead, the Inspector begins by stating that he is there to ask questions. It becomes evident that these questions are designed to relate the characters, one by one, to the life of Eva Smith/Daisy Renton. As Sheila goes on to realize later, the Inspector has arrived to ask these questions just as Arthur has finished telling Gerald and Eric that men do not have heavy obligations to their fellow men. The Inspector thus offers, over the course of the play, a rebuke to this idea. He seems to argue that, because each family member can be connected to one girl, or to the idea of one girl, named either Eva or Daisy, then perhaps all people can be connected to all others by bonds of trust, betrayal, love, or anger.
Once the Inspector gets Arthur and Sheila to acknowledge that they recognize Eva/Daisy, he then wants them to admit the part they have played in her downfall. Arthur is unwilling to do this, because his personal beliefs do not allow for these kinds of causation. That is, Arthur thinks that people should look out for themselves, or, at most, for their families. He does not think that all people owe obligations to all other people. Thus the concerns of the workers in his factory are utterly abstract to Arthur. The workers will want higher wages, but that is because, in Arthur’s mind, workers are lazy and accustomed to “handouts.” Arthur accuses his own son Eric of this laziness.
Sheila is more willing to acknowledge and come to terms with her guilt. She realizes that her anger, directed toward the Eva/Daisy at Milward’s, was unjustified. Further, that anger derived from a feeling of resentment that other young women might look better in the outfit she wore than she did. Sheila realizes that she got Eva/Daisy fired because she, Sheila, was not comfortable with herself in her own skin. She begins, in this section of the play, to come to terms with that personal failing, and to imagine what it would mean to make amends for her actions.
The stage directions say that the Inspector is a large and imposing presence, and one can imagine in reading the play that the other characters more or less cower around him. The Inspector thus destabilizes the order that the family had achieved up until this point. In that old order, Arthur was the head of the household, and whatever Arthur commanded at a given moment was considered the truth. Sybil, then, was to carry out Arthur’s orders and make sure the family was comfortable. And Eric and Sheila were to go along with whatever their parents demanded of them. With Sheila’s engagement to Gerald, Arthur implies that he is handing off concern for his daughter to another man whom he trusts, and who himself works in manufacturing and is of a good family. This economy of marriage might seem, to a contemporary audience, at best outdated, and at worst offensive. And it is exactly this structure of the nuclear family that the Inspector’s presence upsets.