Still in the café, Berenger laments that Daisy holds little interest in him as a low-level employee, and believes she prefers Dudard, a rising star in his office. Jean berates him for surrendering so easily while the Logician beseeches the Old Gentleman to try and solve a logic problem. Both Jean and the Logician tutor their respective students. Jean recommends will-power and cultural self-improvement to garner Daisy's affections, and to improve his life in general. Berenger agrees to do so, and asks Jean to accompany him to the museum and theater. Jean says he has to take a nap and meet a friend for a drink. Berenger says that Jean is now the one who has little will-power, but Jean defends himself, calling his lapses the exception and Berenger's the rule.
Another rhino rushes by as the townspeople try to speak above the din, not yet recognizing the sound. The rhino's path of destruction prompts another round of choruses ("Oh, a rhinoceros!" "Well, of all things!"). The Housewife reveals that the rhino has trampled her cat. The townspeople (except for the Logician) sympathize with her. They all debate whether or not it was the same rhino or a different one, and if it was an "Asiatic" or "African" breed (dependent on the number of horns). Jean claims he counted the horns on the rhinos and can differentiate between the two of them. Berenger accuses him of talking nonsense, that Jean had no time to count the horns and that his distinctions between the two breeds are erroneous. The townspeople argue about horns and "Asiatic" people. Berenger and Jean fight and insult each other, and Jean storms off after calling Berenger a drunkard.
Daisy convinces Berenger to make up with Jean. The townspeople pose the rhino- problem to the Logician: how many rhinos were there, and how many horns did it/they have? The Logician only muddies the picture, arriving at the original question after a long disquisition. The Housewife leads a small funeral procession for her dead cat. The townspeople vow to stop the blight of the rhinos. Berenger expresses remorse for fighting with Jean and then says he's too upset to culture himself as planned. Instead, he drinks some brandy.
The foundation of logic is parodied as the Logician's efforts do nothing to clarify the absurd world. Berenger unleashes a key word to trigger his fight with Jean: "nonsense." The world does not merely lack sense; it is nonsensical, illogical in every way. Yet, as the Logician's ridiculous inversions show (especially in his use of reductio ad absurdum, or pushing logic to absurd or contradictory limits), total illogic does not provide meaning either, as some readers might assume existentialist authors propose. Rather, Ionesco shows that even the most conventional use of logic can be flawed. Instead of trying to figure out what has caused (and what can remedy) the presence of the rhinos, the supposedly logical citizens are more concerned with how many horns the rhinos have.
The strength of Berenger's and Jean's respective wills are shaded here for ironic and foreshadowing purposes. As Jean points out, Berenger does care about at least one thing: Daisy. His love of her makes his decision to save humanity at the end of the play seem believable. Jean's slur about Berenger's willingness to surrender, then, is a tremendous irony, since by the end of the play it is Jean who has given-in to the rhinos. Nevertheless, for now Berenger remains a passive individual, eschewing his prior cultural development plan in favor of another escapist drink.
The escalation of violence and its relationship to fascism is also explored in greater depth. In the first part of the scene, the Logician and Jean bump into each other, and both men say "No harm done." In this section, a cat is trampled. Ionesco subtly examines John Stuart Mill's proposition of the "harm principle" in On Liberty. According to Mill, individual freedom should be preserved at all costs unless it harms someone else. While the first rhino caused no harm to anyone else (mirrored in the polite dialogue between Jean and the Logician), the second one does. Ionesco suggests that any mentality, fascism included, should be permitted so long as it does not violate the harm principle (the first rhino), but such mentalities inevitably do harm others (the second rhino).