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Russell

Bertrand Russell · Born 1872 AD · Analytic · Principia Mathematica, History of Western Philosophy
Born 1872 ADlogical atomismtheory of descriptionsprincipia mathematicaneutral monismparadox7 min readView in network
The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.
The Philosophy of Logical Atomism, Lecture I

Bertrand Russell

There were, in a sense, two Bertrand Russells, and the marvel is that they were the same man. One was the most rigorous logician of his age, who spent ten years and hundreds of pages of dense symbols proving, from the bare laws of logic, that one plus one equals two. The other was a fearless public troublemaker who went to prison for opposing a war, was hounded out of a university for writing frankly about sex and marriage, campaigned into his nineties against nuclear weapons, and wrote so many lucid, witty, humane books for ordinary readers that he won the Nobel Prize in Literature. The textbooks tend to keep these two Russells in separate rooms, the austere logician in one and the celebrity gadfly in the other. But Russell himself knew they were a single enterprise, driven by one passionate conviction: that clear, honest, fearless thinking is the best hope our species has, and that most of human cruelty and misery flows from the opposite, from believing things on bad evidence, from dogma, from the refusal to doubt. The logic and the activism were the same weapon, aimed at the same enemy. Russell gave a long life to a single proposition, that reason, applied without fear to mathematics and to murder alike, can set us free.

Bertrand Russell. There were, in a sense, two of him, the most rigorous logician of his age and a fearless public troublemaker, and he knew they were one project: the faith that clear, fearless thinking is humanity's best hope.Unknown photographer, Bertrand Russell (1916), McMaster University Bertrand Russell Archives. Public domain (published before 1929) via Wikimedia Commons.

The surface and the logic beneath. The clearest glimpse of what Russell meant by clarity is a small, famous puzzle he solved in 1905, in a paper that founded a way of doing philosophy. Consider the sentence: "The present King of France is bald." There is no King of France. So is the sentence true? Obviously not. False, then? But if it is false, its opposite, "The present King of France is not bald," ought to be true, and that is no better, since there is still no king to be either bald or hairy. The sentence seems to be about something that does not exist, and philosophers had tied themselves in knots trying to say what. Russell cut the knot with a single, beautiful move. The grammatical surface of the sentence fools us, he showed, into treating "the present King of France" as a name, as if it pointed at some shadowy object. But unfold its real logical form, and it says three plain things at once: there is a King of France, there is only one, and he is bald. Put that way, the sentence is simply false, false because its very first claim is false, there being no such king, and the whole puzzle evaporates. This was Russell's great methodological lesson, the founding move of analytic philosophy: that the grammar of our sentences systematically misleads us about their real logical structure, and that a great many philosophical problems are not deep mysteries but tricks of surface grammar, which careful logical analysis can dissolve. Translate the confusion into precise logical form, and watch it disappear.

G.E. Moore, Russell's Cambridge ally. Together they insisted that philosophy advance by patient logical analysis, dissolving puzzles one at a time rather than spinning grand systems, the founding temper of analytic philosophy.Unknown photographer, George Edward Moore (c. 1903). Public domain (published before 1929) via Wikimedia Commons.

Three hundred pages to reach two. Russell's grandest project aimed the same passion for rigor at the foundations of mathematics itself. Where does mathematical truth come from? Why is two plus two necessarily four, with an iron certainty no fact about the physical world can match? Russell's answer, which he called logicism, was breathtaking in ambition: that mathematics is nothing other than logic, that every mathematical truth can be derived, step by rigorous step, from a handful of purely logical principles, with nothing smuggled in. With Alfred North Whitehead he set out to prove it, building the whole edifice from the ground up in the three enormous volumes of Principia Mathematica, a work so meticulous that the proof that one plus one equals two arrives only after several hundred pages. But the project carried a worm in its core, and it was Russell himself who found it. Imagine, he realized, the set of all sets that are not members of themselves; now ask whether that set is a member of itself. If it is, it is not; if it is not, it is, a clean and vicious contradiction sitting at the very foundation of logic. "Russell's Paradox" wrecked an earlier version of the project and forced him into elaborate repairs. And the deepest blow was still to come: a young logician named Gödel would soon prove that no system like Principia could ever be both complete and certain of its own consistency, that the dream of a perfectly secured mathematics was, in principle, unreachable. Russell's heroic failure taught the twentieth century something profound about the limits of logic itself, and that, too, is a kind of success.

The page of Principia Mathematica where, after several hundred pages, Russell and Whitehead reach a proof that 1+1=2. The heroic attempt to derive all of mathematics from pure logic, undone in part by a paradox Russell found himself.Alfred North Whitehead and Bertrand Russell, Principia Mathematica (1910), Volume I, page 379, theorem ✸54·43. Public domain via Wikimedia Commons.

The will to doubt. For most thinkers the rigor would have stayed in the study. Russell's deepest conviction was that it must not, that the same honesty we demand in mathematics we should demand everywhere, above all where it is least welcome: in religion, in politics, in our certainties about how to live. The great enemy of a decent world, he came to believe, is dogma, the refusal to doubt, the deadly human craving for absolute certainty that makes people cruel in the name of their convictions. The trouble with the world, he observed in a much-quoted remark, is that the stupid are cocksure while the intelligent are full of doubt. Against this he preached not cynicism but what he called the "will to doubt," the discipline of believing things only in proportion to the evidence, holding even your firmest opinions open to revision, and refusing to kill or oppress for a certainty you cannot actually justify. He thought a trained skepticism was not the enemy of conviction but the only honest foundation for it, and that a person who could say "I might be wrong" and mean it was worth a hundred zealots. Russell's doubt was never cold or idle; it was the working tool of a passionate humanity, a faith that if people could only learn to think clearly and to doubt honestly, they might stop doing one another quite so much needless harm. In an age, like his and like ours, loud with confident nonsense, the will to doubt is not weakness. It is the rarest kind of courage.

Reason that would not stay in the study. And Russell did the thing most philosophers never dare: he carried his reason out of the study and into the streets, at real and repeated cost. When the First World War swept his country into what he saw as a frenzy of organized madness, he opposed it in public, lost his position at Cambridge, and was thrown into prison, where he calmly wrote a book on mathematical philosophy in his cell. Decades later, well into his eighties and nineties, he turned the same fearless clarity on the gravest danger our species had ever built for itself, the nuclear bomb, which for the first time gave humanity the power to end itself in an afternoon. With Albert Einstein he drafted a famous manifesto begging the world's leaders to remember their humanity and find another way; he marched, organized, and was arrested again, an old man on the pavement, for protesting weapons that could incinerate millions. To Russell this was not a distraction from philosophy but its fulfillment. What is the use of learning to think clearly, he asked, if you will not use that clarity where it matters most, against cruelty, against war, against the comfortable lies that grease them? The same honesty that refused to let a sloppy proof pass refused to let a murderous certainty pass unchallenged. He believed, to the end, that reason is not a spectator sport, that a thinker who sees clearly has a duty to speak, and that the calm voice of evidence, raised against the roar of dogma and fear, is one of the few things that has ever made the world less brutal.

Russell presenting the Russell-Einstein Manifesto, 1955. Well into his eighties, he turned his fearless clarity on the nuclear bomb, begging the world to remember its humanity. Reason, he held, must not stay in the study.Unknown photographer, Bertrand Russell presenting the Russell-Einstein Manifesto, London (9 July 1955). Public Domain Mark 1.0 via Wikimedia Commons.

Clear thinking as a survival skill. The room holds many of Russell's works in his crisp, luminous English, cited by chapter; he wrote, across a long life, on nearly everything, logic and physics and history and education and happiness and power, always with the same clarity, and the prose alone is an education in how to think on paper. His technical work founded a tradition: modern logic is largely his and Frege's invention, and the whole vast enterprise of analytic philosophy, which still dominates the English-speaking world, began with the insistence he shared with Moore that philosophy should proceed by patient logical analysis rather than grand system-building. His brilliant, difficult student Wittgenstein both extended and turned against him; the Vienna Circle built on him; and his popular History of Western Philosophy introduced more people to the subject than any book of its century. But the figure worth remembering is the whole one, not the logician alone and not the activist alone, but the man who knew they were one thing, who brought the precision of the mathematician to the question of how to live and the passion of the reformer to the foundations of logic. He thought that clear thinking was not a dry academic virtue but a moral and even a political force, perhaps the only one that could save us from ourselves. In an age awash in confident nonsense, his union of ruthless logical honesty and fearless human decency is not a relic. It is something close to a survival skill.

Ludwig Wittgenstein, Russell's brilliant, difficult student, who both extended and turned against him. Russell's logical analysis founded the tradition, analytic philosophy, that still dominates the English-speaking world.Moritz Nähr, Ludwig Wittgenstein (1929), portrait for the conferment of the Trinity College scholarship. Public domain via Wikimedia Commons (work over 95 years old).

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