Bertrand Russell

Key ideas

1. Logicism. Russell championed the view that mathematics can be derived from logic. With Alfred North Whitehead he pursued it in Principia Mathematica (1910–13), deriving large parts of set theory and arithmetic; whether the programme succeeded is still disputed.
2. Russell's paradox. Consider the set of all sets that are not members of themselves: it is a member of itself if and only if it is not. Russell found the contradiction in 1901, and it undermined Frege’s logic and every theory with unrestricted set formation.
3. The theory of types. To avoid the paradox Russell arranged sentences in a hierarchy of levels, with sentences about individuals first, then about sets of individuals, then about sets of sets, so that a set such as the paradoxical one is excluded.
4. The theory of descriptions. “On Denoting” (1905) treats phrases such as “the author of Waverley” not as names but as incomplete symbols. “The King of France is bald” says that exactly one thing is King of France and that it is bald, so it is false, not meaningless.
5. Acquaintance and description. We know some things directly, by acquaintance, such as our own sense-data, and everything else by description. Russell used the distinction to explain how knowledge of the external world can be built from what we are immediately aware of.
6. Logical atomism and neutral monism. Russell held that the world consists of facts built from simple particulars. After Wittgenstein’s criticism of his 1913 manuscript on knowledge he came to hold that mind and matter are two arrangements of one neutral stuff.
7. The burden of proof. Whoever asserts an empirically unfalsifiable claim must support it, Russell argued, and the sceptic need not disprove it. His example was a china teapot orbiting the Sun between Earth and Mars, too small for any telescope to see.

Bertrand Russell (1872–1970) was a British philosopher, logician and public intellectual, and one of the founders of analytic philosophy. He found the paradox that bears his name, wrote Principia Mathematica with Alfred North Whitehead, gave the theory of descriptions in “On Denoting” (1905), and wrote The Problems of Philosophy (1912) for general readers. He was also a pacifist and freethinker who campaigned against nuclear weapons, and he won the Nobel Prize in Literature in 1950.

Who was Russell?

He was born in 1872 at Trellech, Monmouthshire, orphaned young and raised mainly by his grandmother. His grandfather, Lord John Russell, had twice been prime minister, and John Stuart Mill was his secular godfather. He studied mathematics at Trinity College, Cambridge, graduating with first-class honours in 1893. Starting as an idealist, he and G. E. Moore rebelled against idealism around the end of 1898, and he spent the rest of his career defending logical analysis and pluralism.

His life was as public as his work. He was fined and dismissed from Trinity in 1916 for anti-war writing and imprisoned in 1918. His appointment at the City College of New York was annulled in 1940 after a court found him “morally unfit”. He was awarded the Order of Merit in 1949 and the Nobel Prize in 1950, helped to launch the Pugwash conferences through the Russell–Einstein Manifesto of 1955, and chaired the India League in England. He died in Wales on 2 February 1970, aged 97.

What did he do in logic?

Logicism is the view that mathematics can be derived from logic. Frege had attempted this. In 1901 Russell found a paradox, and he showed that a version of it could be derived in Frege’s system. Consider the set of all sets that are not members of themselves: it is a member of itself if and only if it is not. Russell’s remedy was the theory of types, which arranges sentences in a hierarchy of levels.

Principia Mathematica (1910–13), written with Whitehead, derived large parts of set theory and arithmetic from logical axioms. Whether it vindicated logicism remained controversial, and Gödel’s first incompleteness theorem later showed that no recursive extension of Principia could be both consistent and complete for arithmetic. Frege’s predicate calculus, which Russell refined, remains the basis of most modern logic.

What is the theory of descriptions?

“The author of Waverley” and “the present King of France” look like names, but are descriptions. Russell argued in “On Denoting” that such phrases are incomplete symbols. “The King of France is bald” says that exactly one thing is King of France and that it is bald; since nothing is, the sentence is false, not meaningless, and we need not admit non-existent objects into the world. Strawson later replied that such a sentence is neither true nor false. This is the theory of definite descriptions; in it Russell rejected Frege’s notion of sense (see sense and reference).

What did Russell say about knowledge?

In The Problems of Philosophy he distinguishes knowledge by acquaintance, direct awareness of sense-data and of one’s own experience, from knowledge by description, by which we know physical objects and other minds. Expectations based on experience, he notes, can mislead: “The man who has fed the chicken every day throughout its life at last wrings its neck instead”. On the problem of induction he argues that the principle of induction is needed for every argument from experience but cannot itself be proved by experience. The book ends with a defence of philosophy: it is to be studied “not for the sake of any definite answers to its questions” but for the questions themselves.

Later he moved to logical atomism and, after Wittgenstein criticised a 1913 manuscript, to neutral monism. Wittgenstein, his most famous pupil, wrote the Tractatus as a continuation of and reaction to Russell and Frege, and Russell supplied its introduction. When they met again in 1944 there was little warmth.

What did he say about religion and war?

In 1927 Russell gave the talk published as Why I Am Not a Christian. In an article written in 1952 and unpublished in his lifetime he gave the teapot analogy: the burden of proof lies on whoever asserts what cannot be tested. See Russell’s teapot. He opposed the First World War, changed his view of war against Hitler in 1943, and later opposed nuclear weapons and the Vietnam War, organising a tribunal with Sartre.

How to start reading Russell

The Problems of Philosophy is free on Project Gutenberg. Then try the essays in Mysticism and Logic, which include “A Free Man’s Worship” and “Mathematics and the Metaphysicians”, and Introduction to Mathematical Philosophy, written in prison. His later books are in copyright. For the UGC NET, the syllabus lists “Russell: Logical Atomism, Definite Descriptions, Refutation of Idealism”; see the UGC NET guide, and how to read philosophy for advice on first books.