“What my brain doesn’t quite get,” Owen persisted, elevating himself to Cantor’s class of mental fragility, “is why it was such a big deal when Russell and Gödel found these internal contradictions or paradoxes—as Klein points out, the confusion is basically semantic. I don’t see what undecidability has to do with the history of the computer.”

“You don’t?” said Phyllis, unable to quite conceal her disappointed surprise, as if her own clarity of mind had been conferred upon Owen by her regal act of accepting him as her boyfriend. The two of them met before class and rejoined afterwards; they shared mid-morning coffee and a dragged-out late lunch at the Student Center across Mass. Ave.; they went to movies together in Harvard Square or on Washington Street in Boston; sardonic Jake and menacing Ralph had been banished to the rim of the circle at whose quiet center Owen found himself. In the evenings, unable to be away from each other for more than four hours, the two reunited amid the smoke and misted mirrors of the little restaurants where students huddled in overheated symposia.

“I mean,” he said, insisting on his own obtuseness, thrusting it upon her, “so what if there exists a set of sets that are not members of themselves, which makes it a set that both is and isn’t a member of itself?”

“But, Owen dear,” Phyllis said, “the antinomies—the paradoxes—undermine classical logic, but the way they have to be phrased brings us to symbolic logic, which brings in Boolean math and the Turing machine and algorithms. Undecidability is like knowing you have a swamp and having to invent methods to build on it anyway. It’s like the Back Bay on all its pilings,” she said, so pleased with her own analogy that her face for the moment was more a Bird’s than a Muffin’s.

Phyllis inhabited an attenuated realm where he longed to join her. Her very air of absence pulled him up, led him on; at times he had the sensation that the void which the rigors of post-Aristotelian logic discovered at the very roots of arithmetic existed also in her—a refusal to be obvious, an implacable denial beneath the diffident, compliant surface. “You know I don’t love you yet,” she said after they had been going together for a year and were already considered a couple by their peers.

Owen was shocked, especially since they were lying stretched out together somewhere, on a bed or floor—it must have been in her senior year, when she moved back to her parents’ house, giving them some sneaky privacy. They didn’t shed their hot clothes but were, in those inhibited, swaddled times, “making out.” Owen had assumed he was lovable, though beneath the regard of the Ginger Bittings of the world. His mother and Elsie had loved him.