Russell's paradox
Does the set of all sets that are not members of themselves belong to itself? Either answer yields a contradiction. Naive set theory collapsed and the theory of types was born.
The Twentieth Century to Today · 1872 – 1970
Bertrand Russell
罗素 · Bertrand Arthur William Russell
A founder of analytic philosophy: co-author of Principia Mathematica, inventor of the theory of descriptions, lifelong campaigner for peace, reason and liberty, Nobel laureate in literature, leader of the anti-nuclear movement in old age.
Analytic PhilosophyBirthplace: Trellech, Monmouthshire
The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.
Source: attributed; cf. 'The Triumph of Stupidity' (1933)
Russell was descended from Whig aristocracy; his grandfather Lord John Russell was twice prime minister. Orphaned before four, he was raised by a severe Victorian grandmother and educated at home, lonely and precocious; at eleven, learning Euclid from his brother, he was dismayed that the axioms could not be proved. He read mathematics and philosophy at Trinity College, Cambridge, became a fellow in 1895, was a Hegelian in youth, and in 1898 turned with Moore to realism.
At the international congress of philosophy in Paris in 1900 he met Peano and grasped the power of symbolic logic; in 1901 he discovered the paradox that bears his name; in 1903 he published The Principles of Mathematics, then spent ten years with Whitehead on the three-volume Principia Mathematica, which lost money for the press and to whose printing costs the authors contributed. The theory of types, the theory of descriptions (how 'the present king of France is bald' can be meaningful) and logical atomism belong to these years. He said the decade's labour damaged his intellect permanently.
During the First World War his anti-war campaigning cost him his Trinity lectureship, and in 1918 he served six months in prison, writing the Introduction to Mathematical Philosophy there. He then lived by writing and lecturing, producing popular books on relativity, marriage, education, happiness and China, married four times, ran an experimental school, and in 1940 was barred by a New York court from a teaching post because of his views on morals. A History of Western Philosophy (1945) became a best-seller, and in 1950 he received the Nobel Prize for Literature.
In 1955 he and Einstein issued a manifesto warning against nuclear war; in 1958 he founded the Campaign for Nuclear Disarmament; in 1961, at eighty-nine, a sit-down protest put him in prison for a week; and in his last years he organised a tribunal on American conduct in Vietnam. He died at ninety-seven. His philosophical positions changed many times, but the demand for clarity and the distrust of authority never did. Three passions, he said, governed his life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.
Key Ideas
The theory of descriptions
'The present king of France is bald' is not about a non-existent object but asserts that there is exactly one king of France and he is bald, and is therefore false. Grammatical form disguises logical form.
Logical atomism
The world consists of atomic facts, and each atomic proposition of an ideal language corresponds to one. Philosophical analysis breaks complex propositions down to that level.
Knowledge by acquaintance and by description
We know sense-data and universals directly, everything else by description. The foundation of his empiricist epistemology.
Free thought
Never believe a thing because it is useful, only on the evidence. Most human misery comes from people who are certain they are right.
Influenced by
- Gottlob Frege
He was Frege's first important reader and the one whose paradox wrecked the system; the theory of types was his repair of Frege's logicism.
- Gottfried Wilhelm Leibniz
- John Stuart Mill
Mill was his godfather; he inherited Mill's liberalism and empiricism but replaced Mill's inductive logic with modern logic.
- David Hume
- Charles Sanders Peirce
- G. E. Moore
In 1898 Moore led him in revolt against British Hegelianism, 'the external world is real, grass is green'; he called it a liberation.
- Alfred North Whitehead
- Ludwig Wittgenstein
His student, later his critic. He wrote the introduction to the Tractatus; Wittgenstein said he had not understood a word.
Influenced
- Alfred North Whitehead
First teacher, then collaborator: the three volumes of Principia Mathematica were ten years of joint labour, with Whitehead responsible for most of the notation.
- Ludwig Wittgenstein
Russell was his teacher and within a year his pupil, saying 'the next big step in philosophy will be taken by him'. The atomist frame of the Tractatus was hammered out in argument with Russell.
- Rudolf Carnap
Having read Principia he wrote asking for a copy; Russell, unable to afford one, copied out the main definitions by hand and sent them. The Aufbau carried out Russell's programme of 'logical construction'.
- W. V. O. Quine
Principia Mathematica was his boyhood initiation; his doctoral thesis was a simplification of its logical system.
- Saul Kripke