The Information - James Gleick [84]
He was painfully thin, almost gaunt. His ears stuck out a little from his close-trimmed wavy hair. In the fall of 1939, at a party in the Garden Street apartment he shared with two roommates, he was standing shyly in his own doorway, a jazz record playing on the phonograph, when a young woman started throwing popcorn at him. She was Norma Levor, an adventurous nineteen-year-old Radcliffe student from New York. She had left school to live in Paris that summer but returned when Nazi Germany invaded Poland; even at home, the looming war had begun to unsettle people’s lives. Claude struck her as dark in temperament and sparkling in intellect. They began to see each other every day; he wrote sonnets for her, uncapitalized in the style of E. E. Cummings. She loved the way he loved words, the way he said Boooooooolean algebra. By January they were married (Boston judge, no ceremony), and she followed him to Princeton, where he had received a postdoctoral fellowship.
The invention of writing had catalyzed logic, by making it possible to reason about reasoning—to hold a train of thought up before the eyes for examination—and now, all these centuries later, logic was reanimated with the invention of machinery that could work upon symbols. In logic and mathematics, the highest forms of reasoning, everything seemed to be coming together.
By melding logic and mathematics in a system of axioms, signs, formulas, and proofs, philosophers seemed within reach of a kind of perfection—a rigorous, formal certainty. This was the goal of Bertrand Russell and Alfred North Whitehead, the giants of English rationalism, who published their great work in three volumes from 1910 to 1913. Their title, Principia Mathematica, grandly echoed Isaac Newton; their ambition was nothing less than the perfection of all mathematics. This was finally possible, they claimed, through the instrument of symbolic logic, with its obsidian signs and implacable rules. Their mission was to prove every mathematical fact. The process of proof, when carried out properly, should be mechanical. In contrast to words, symbolism (they declared) enables “perfectly precise expression.” This elusive quarry had been pursued by Boole, and before him, Babbage, and long before either of them, Leibniz, all believing that the perfection of reasoning could come with the perfect encoding of thought. Leibniz could only imagine it: “a certain script of language,” he wrote in 1678, “that perfectly represents the relationships between our thoughts.”♦ With such encoding, logical falsehoods would be instantly exposed.
The characters would be quite different from what has been imagined up to now.… The characters of this script should serve invention and judgment as in algebra and arithmetic.… It will be impossible to write, using these characters, chimerical notions [chimères].
Russell and Whitehead explained that symbolism suits the “highly abstract processes and ideas”♦ used in logic, with its trains of reasoning. Ordinary language works better for the muck and mire of the ordinary world. A statement like a whale is big uses simple words to express “a complicated fact,” they observed, whereas one is a number “leads, in language, to an intolerable prolixity.” Understanding whales, and bigness, requires knowledge and experience of real things, but to manage 1, and number, and all their associated arithmetical operations, when properly expressed in desiccated symbols, should be automatic.
They had noticed some bumps along the way, though—some of the chimères that should have been impossible. “A very large part of the labour,” they said in their preface, “has been expended on the contradictions and paradoxes which have infected logic.” “Infected” was a strong word but barely adequate to express the agony of the paradoxes. They were a cancer.
Some had been known since ancient times:
Epimenides the Cretan said