The irony of competing world views
One common guess for what to do in the present pluralistic Western culture is to just "get along" and tolerate differences, but MacIntyre points out the irony schism between world views. It isn't just that people believe the same basic ethic in different ways, it's that people actually believe different virtues entirely. For instance, letting a child date might seem ethical to one person and it might seem like a terrible sin to someone else.
In other words, as much as it feels like everyone is pretty much the same, coexistence is not a tenable option if you take people's world views seriously. Only watered down versions of different societies are compatible, and then the basic problem remains of determining what is good, ethical behavior.
The irony of sophistry
One ironic problem with logic is that people who think they understand the world logically are very easy to manipulate, and MacIntyre uses the Greek sophists as an analogue for this paradox. Instead of reason inspiring more reason, reason quickly devolved into a tool that smart people could use to extort stupid people through the market. This is very similar to the irony of hubris.
The irony of science and philosophy
Ironically, the same philosophical problem that undermines religion and other dogmatic approaches to ethics also undermines science. By focusing the attention to the terrifying prospect of a world without science, one of the ironic implications is that actually, most people don't understand their own technology very much, meaning that his hypothetical from the first chapter—although technically just an analogy for understanding the plight of modern philosophy—might also be literally true. Perhaps the culture of the West has already outrun the influence of the modernist approach to science.
The irony of meaning
This is the irony of ironies. To the people who agree with the existentialists, meaning is imported on an experience the same way we ascribe meaning to abstract paintings. But to the essentialist, the meaning is already there, either in the object or in the human soul, and meaningful moments are the discovery of a higher, transcendent order to the universe.
The irony is that no one can know for sure, and once you decide one way, it's mind-bending to even attempt to understand the other side. It's way more likely that a modern person will just dig their heels in and continue on in ignorance, since after all, these things are very confusing.
The irony of pluralism
Ironically, the same diversity that we herald as essential to the capitalist intentions of the West (like the melting pot analogy) also carry with them a negative aspect. Namely, it means that pluralism can be used to dismantle world views and break down a person to their limited, individualized opinion of the world—without a community to keep them accountable to a specific world view. So yes, pluralism is wonderful, but in Europe and America, it also looks a little like the fall of Rome.
