Describing the Archbishop's leadership style (or lack thereof), Wilder satirizes both this individual priest and the Catholic church he serves. Introducing this character, Wilder remarks:
The Archbishop knew that most of the priests of Peru were scoundrels. It required all his delicate Epicurean education to prevent his doing something about it; he had to repeat over to himself his favorite notions: that the injustice and unhappiness in the world is a constant [...] Like all the rich he could not bring himself to believe that the poor (look at their houses, look at their clothes) could really suffer.
As the highest-ranking priest in Lima, the Archbishop is supposed to be a serious and selfless leader, devoted to the people under his care. Instead, he strives to ignore the condition of the poor and the corruption within his own church as much as possible. Instead of describing this explicitly as a great moral failure, the book seemingly praises the archbishop's neglect as an accomplishment and a testament to his "delicate Epicurean education." This line alludes to the Greek philosopher Epicurus, who taught that people should try to live happy and tranquil lives on earth rather than worry about the afterlife. While Epicurus advocated for a relatively humble lifestyle, his name has become a shorthand for hedonistic, pleasure-seeking behavior, and the book is using it in this sense.
This passage also derives humor from the lofty tone used to convey beliefs that are obviously untrue, such as the Archbishop's assertion that the poor cannot "really suffer." In this way, the novel uses satire to communicate that the Archbishop lives extravagantly at the expense of the people he's supposed to serve.
Importantly, this satire implicates not only the Archbishop but the entire Catholic Church and the ruling class that supports it. Noting that the archbishop's "education" has taught him to ignore the poor, the book implies that the problem is here is systemic. Likewise, by noting that "all the rich" share the Archbishop's beliefs about the poor, and showing elsewhere that the Archbishop maintains close ties with Lima's leaders, Wilder uses satire to argue that the Spanish Empire's upper classes are aligned with the Catholic Church in their lack of care for others.
Describing the Perichole's attempts to escape her past as an actress and become a "virtuous" woman, Wilder makes a satirical allusion to Descartes:
In society she cultivated a delicate and languid magdelinism, as a great lady might, and she carried a candle in the penitential parades, side by side with ladies who had nothing to regret but an outburst of temper and a furtive glance into Descartes.
Now considered one of the foremost thinkers in the Western intellectual tradition, Rene Descartes was a 17th-century mathematician and philosopher whose supposedly heretical work aroused the ire of the Catholic Church. In colonial Lima, a society dominated by Catholic authorities and the ongoing Spanish inquisition, espousing Descartes' ideas would have been unorthodox and perhaps politically dangerous. But for women, who were considered incapable of higher learning or political action, a "furtive glance" into the philosopher's books would have been far less scandalous than working as an actress, a profession stigmatized as akin to sex work in many early modern societies.
In this passage, Wilder satirizes the close-minded nature of Spanish colonial society. Especially for his 20th-century readers, who would have recognized Descartes' enormous contributions to mathematics and philosophy, it's funny to imagine people deliberately turning away from his works. Through the tongue-in-cheek phrase "a furtive glance," Wilder also dramatizes the difference between the hypothetical woman's opinion of Descartes and that of the modern reader.
Importantly, Wilder also satirizes the Perichole's aspirations to ascend to the local aristocracy. In a society that is both fixated on hierarchy and repressive of women, her quest is most likely doomed. And if reading Descartes isn't really a sin, then the criteria for respectability in Peruvian society are largely meaningless—and so is the Perichole's desire to fit in.