As if it wasn't complicated enough to follow one philosophical plot in the book, there are actually two separate plots cleverly interwoven throughout. The first is the story of the actual motorcycle journey that the narrator and his son are taking across several continents; the second tells of the life and the thoughts of a man named Phaedrus. Phaedrus is a solitary man, an intellectual who is consumed by the philosophical notion of Quality.
The narrator and Chris leave Minneapolis on a motorcycle trip with their friends, Sylvia and John Sutherland. The narrator then brings up the first of his Chautauquas, which are philosophical discourses. John and Sylvia do not like technology at all, and the narrator attributes this to their romantic view of life, valueing the superficial over the rational. The narrator, on the other hand, is a more analytical kind of person. As they travel he experiences several deja vu moments which make him feel he has been on this journey before. He calls these the ghosts in his thoughts. He extrapolates from these thoughts the feeling that Phaedrus is the past version of himself and that these ghost memories are actually recollections from his own incarnation as Phaedrus.
The group ride on through Montana and it is during this part of the journey that we learn about Phaedrus' life. He was a prodigious child, excelling at science, but lost faith in science and reason and felt that it could not explain the primary questions in the world. He dropped out of school as a result. He eventually took a job as an English professor at Montana State University, in Bozeman, Montana, coincidentally the destination of the four motorcycle riders. They stay with Robert and Gennie De Weese, who were Phaedrus' friends.
Chris and the narrator leave the group to hike a mountain, and the narrator continues to explain Phaedrus' quest to isolate the principles of Quality, the intangible "thing" that makes something good. Is Quality a subjective or an objective thing? Phaedrus cannot decide but realizes some time later that it is neither. Quality precedes subjectivity and objectivity but is in fact the "thing" that makes both subjectivity and objectivity possible. The two hikers camp out overnight and the narrator has a terrible nightmare in which a glass door separates him from his family. He can still see them but he cannot get to them. He is worried that the dream is in some way a warning and does not want to continue to hike to the summit, cutting the hike short and heading back to Bozeman.
After they leave Bozeman the group travel west, and the narrator begins to talk about the way in Quality can be seen in the art of motorcycle maintenance. He introduces several ideas; "gumption traps" prevent a person from developing an awareness of Quality. Gumption is the fuel that sustains the act of striving for Quality. Thinking inside the box is the main obstacle that stands between someone who doesn't understand Quality and that person beginning to fully understand it.
The narrator has the glass door dream again, which he now realizes is not a foreboding or warning dream at all, but rather is a symbol of his dual identities of himself and Phaedrus. He recalls spending time with his son whilst assuming the persona of Phaedrus and realizes that this complex mental state will need to be carefully explained to his son. He describes Phaedrus' continuing educational studies; he studies Ancient Greek and Philosophy at the University of Chicago and has a stand-up confrontation with the Chariman of the board of studies whom he considers to be unacceptably Aristotelian, the very opposite of himself and in direct opposition to his beliefs about Quality. The confrontation is the climax of Phaedrus' mental breakdown and he is hospitalized where he receives electroshock therapy.
Father and son continue to travel, riding ever closer to San Francisco, but their relationship is becoming increasingly strained. The narrator plans to send Chris home, and also plans to check himself into a hospital, confessing to his son that he suffers from mental illness, and also suggesting that this might be hereditary. He also tells Chris about his glass door dream, which distresses his son far more than the news of his father's declining mental state. Chris wants to know why his father did not just open the glass door that separated them. The narrator explains he was not allowed to. At the same time both Chris and his father realize that Phaedrus was not insane at all, and the narrator begins to reconcile both facets of his split identity. This joint realization and probing together actually brings father and son closer together; they ride towards San Francisco with a new respect for each other and a renewed air of friendship. Their mood has changed completely and they are now both in extremely high spirits.
