Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, was one of the founders of analytic philosophy (Analytic Philosophy) and, by the breadth of his work and the length of his public life, the most famous philosopher of the twentieth century. With A. N. Whitehead he wrote Principia Mathematica (1910–13), the monumental attempt to derive all of mathematics from logic. His paper “On Denoting” (1905) introduced the theory of descriptions, a model of philosophical analysis. He discovered the paradox that bears his name, which broke Frege‘s system; taught and was overtaken by Wittgenstein; and wrote books on knowledge, mind, matter, religion, marriage, education, happiness, politics and the history of philosophy that were read by millions. He was imprisoned for opposing the First World War, dismissed from academic posts for his views on sex and religion, won the Nobel Prize in Literature in 1950, and in his late eighties led the movement for nuclear disarmament.

Life

Russell was born on 18 May 1872 at Trellech, Monmouthshire, into one of Britain’s great Whig families; his grandfather, Lord John Russell, had twice been prime minister. His parents, freethinkers, both died before he was four, and he was raised by his grandmother at Pembroke Lodge in Richmond Park, a lonely, pious childhood from which he later said mathematics saved him: at eleven, his brother taught him Euclid, “one of the great events of my life, as dazzling as first love”. At sixteen he kept a secret diary in Greek letters recording his loss of faith.

At Trinity College, Cambridge (1890–94) he studied mathematics and philosophy, joined the Apostles, and was briefly a Hegelian idealist. With his friend G. E. Moore he broke with idealism around 1898. His Principles of Mathematics (1903) set out logicism; in writing it he discovered his paradox (1901) and, in 1902, wrote to Frege. With Whitehead he worked for a decade on Principia Mathematica, an effort that he said left his intellect permanently weakened. He was a lecturer at Trinity from 1910; in 1911 the young Wittgenstein appeared in his rooms.

When the First World War broke out, Russell became a leading pacifist. He was fined, dismissed from Trinity (1916), and in 1918 imprisoned for six months in Brixton, where he wrote Introduction to Mathematical Philosophy. He visited Soviet Russia in 1920, met Lenin, and came back disillusioned; he taught in China in 1920–21. With his second wife, Dora Black, he founded the progressive Beacon Hill School (1927). He earned his living by journalism, lecturing and popular books. In 1940 a New York court annulled his appointment to City College on the grounds of his moral views; he was rescued by a post at the Barnes Foundation, which then dismissed him, and he wrote A History of Western Philosophy (1945), a best-seller that supported him for the rest of his life. Back in Trinity in 1944, he won the Order of Merit (1949) and the Nobel Prize (1950).

In 1955 he issued the Russell–Einstein Manifesto against nuclear war, which led to the Pugwash Conferences; in 1958 he became the first president of the Campaign for Nuclear Disarmament; in 1961, aged eighty-nine, he was jailed for a week for civil disobedience. He opposed the Vietnam War and organised the Russell Tribunal (1967). He died at his home in Penrhyndeudraeth, Wales, on 2 February 1970, aged ninety-seven.

Logic and the foundations of mathematics

Russell’s central early aim was to show that mathematics is logic: that all mathematical concepts can be defined in purely logical terms and all mathematical truths derived from logical axioms. In 1901, while working on Cantor’s theory of infinite sets, he found the contradiction now called Russell’s paradox: consider the class of all classes that are not members of themselves; if it is a member of itself, then it is not; if it is not, then it is. The paradox showed that the natural assumption that every condition defines a class leads to contradiction — and it destroyed Frege’s system.

Russell’s answer was the theory of types, which arranges entities into a hierarchy (individuals, classes of individuals, classes of classes…) and forbids a class to contain members of its own type, so that “the class of all classes not members of themselves” cannot be formed. Principia Mathematica, written with Whitehead, built mathematics on this basis with enormous labour. It succeeded in deriving large parts of arithmetic and analysis, but only with axioms (infinity, reducibility) that were hard to call purely logical; and in 1931 Kurt Gödel showed that no such formal system can prove all arithmetical truths. Yet Principia made symbolic logic the common language of mathematics, philosophy and, later, computer science.

The theory of descriptions

Russell’s most influential single idea was set out in “On Denoting” (1905). Consider “The present King of France is bald”. There is no present King of France; so what is the sentence about? The Austrian philosopher Alexius Meinong had said that it is about a non-existent but somehow “subsisting” object. Russell, who had “a robust sense of reality”, refused. He analysed the sentence as a combination of three claims: there is at least one present King of France; there is at most one; and whoever is the present King of France is bald. The sentence is not about any king; it is a general claim, and it is simply false. “The present King of France is not bald” is ambiguous: false if it means there is a king who is not bald, true if it means it is not the case that there is a bald king.

The theory showed that the grammatical form of a sentence can disguise its logical form, and that philosophical puzzles about existence, reference and identity can be solved by revealing the logical structure beneath. It became, in Ramsey’s phrase, “a paradigm of philosophy”, and the template of analysis.

Knowledge and the world

In The Problems of Philosophy (1912), one of the best introductions to philosophy ever written, Russell distinguished knowledge by acquaintance — direct awareness of sense-data, of universals, of our own present states — from knowledge by description, our knowledge of everything else, including physical objects and other minds, which we know only as “the cause of these sense-data” and so on. The table we see is inferred, not given. The book ends with the famous claim that philosophy is to be studied for its questions rather than its answers, “because these questions enlarge our conception of what is possible, enrich our intellectual imagination, and diminish the dogmatic assurance which closes the mind against speculation”.

In lectures of 1918, The Philosophy of Logical Atomism, influenced by Wittgenstein, he held that the world consists of atomic facts — simple particulars having simple qualities or standing in simple relations — and that a logically perfect language would mirror them. Later, in The Analysis of Mind (1921) and The Analysis of Matter (1927), he adopted neutral monism: mind and matter are both constructions out of a neutral stuff of events. His last major work, Human Knowledge: Its Scope and Limits (1948), admitted that empiricism cannot justify its own principles of inference.

Religion, ethics and society

Russell was a lifelong agnostic — technically, he said, though for practical purposes an atheist. His lecture “Why I Am Not a Christian” (1927) rejected the arguments for God’s existence, criticised Christ’s teaching on hell, and argued that religion is based primarily on fear. In a 1952 essay he proposed his teapot: if he claimed that a china teapot orbits the sun between Earth and Mars, too small to be seen by any telescope, no one could disprove it, but no one would therefore be obliged to believe it; the burden of proof lies on those who make unfalsifiable claims.

In ethics he moved from Moore’s intuitionism toward the view that moral judgments express desires. His popular writings — Marriage and Morals (1929), which defended sexual freedom; The Conquest of Happiness (1930); In Praise of Idleness (1935), which argued for a four-hour working day; Power (1938) — made him a hero of liberals and a target of conservatives. His prologue to his autobiography named “three passions, simple but overwhelmingly strong”, that governed his life: “the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind”.

A History of Western Philosophy

Written in America during the war and published in 1945, Russell’s History surveys philosophy from the Presocratics to John Dewey, setting each thinker in social and political context. It is witty, opinionated and often unfair — dismissive of Georg Wilhelm Friedrich Hegel, Friedrich Nietzsche and the medievals — but it introduced generations of readers to the subject and remains in print.

Legacy

Russell’s technical work founded modern logic and analytic philosophy; his popular work made philosophy a public conversation. His critics complained that he changed his views too often; his answer was that he changed them when he found he was wrong. Through the Pugwash movement and the anti-nuclear campaign he became the conscience of the atomic age.

In conversation

• The present King of France — the theory of descriptions and the logic of existence.
• Russell’s teapot — the burden of proof in religious argument.
• “The longing for love, the search for knowledge, and unbearable pity” — the three passions of his life.