The following morning, the narrator and Chris say farewell to the DeWeeses and leave Bozeman. The narrator begins a new Chautauqua about the thought of the French polymath Jules Henri Poincaré. Poincaré was, like Phaedrus, very interested in testing the limits of scientific reasoning. During Poincaré’s lifetime, different mathematical systems were invented, which demonstrated an uncertainty in a supposedly rational discipline. Poincaré addressed this predicament as well as the problematic possibility of infinite hypotheses that bothered Phaedrus, by proposing an attribute of facts that made some better than others. This melding of art and science brought tears to the narrator’s eyes when he read about it, because it was so reminiscent of Phaedrus’s thesis about Quality.
Like the references to Hume and Kant, this Chautauqua is designed to portray Phaedrus as a committed intellectual innovator, rather than as a crazy person. When his thought is compared with that of earlier intellectual pioneers, Phaedrus’s conclusions seem like logical continuations of these thinkers’ theses.
The narrator and Chris head through Missoula and continue westward. They pause to camp by the side of the road and Chris confesses sheepishly that he has diarrhea. After walking around a logging road, the narrator feels inexplicably wistful, and the two travelers go to sleep.
Because the narrator’s identity is so conflicted and connected to Phaedrus, his departure from Phaedrus’s longtime home evokes mixed feelings.