Bertrand Russell

Bertrand Russell (1872–1970) was a British philosopher, logician, and social critic whose work helped establish analytic philosophy and reshape the foundations of mathematics.

Analytic philosophy: A philosophical tradition that uses logical analysis and attention to language to clarify problems. Russell helped establish this tradition through his emphasis on logical analysis.
Russell's paradox: A contradiction arising from the set of all sets that do not contain themselves. Russell’s discovery exposed a contradiction in unrestricted set formation.
Alfred North Whitehead: A British mathematician and philosopher who coauthored Principia Mathematica with Bertrand Russell. Their collaboration carried Russell’s logicist project into a massive formal system.
Beacon Hill School: An experimental school founded by Bertrand and Dora Russell in England in 1927. The school put Russell’s ideas about education and child freedom into practice.
Gödel's incompleteness theorems: Two theorems showing that sufficiently powerful consistent formal systems cannot prove every arithmetic truth or their own consistency. Gödel’s results limited the ambitions of the kind of formal foundations Russell pursued.
Mathematical logic: The formal study of mathematical reasoning using symbolic languages and rules of inference. Russell used symbolic logic to investigate mathematics’ foundations.
Theory of descriptions: Russell’s account of definite descriptions as quantified expressions rather than names of objects. It shows how logical analysis can dissolve apparent puzzles about nonexistent things.
Gottlob Frege: A German logician and philosopher who helped found modern logic and analytic philosophy. Russell’s paradox revealed a contradiction in Frege’s foundational system.
Russell–Einstein Manifesto: A 1955 statement by scientists warning of nuclear war and urging peaceful resolution of international conflicts. Russell helped initiate this appeal against the threat of nuclear weapons.
Vienna Circle: A group of philosophers and scientists who developed logical positivism in Vienna in the early twentieth century. Its members drew on Russell’s logic and analysis while developing their own philosophical program.

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