Bertrand Russell
Mathematics can be derived from logic, and philosophical confusions dissolve once we analyse the logical form hidden beneath ordinary sentences.
Placement
Logicism, the theory of descriptions and logical atomism – and a combative public enlightener, opponent of the First World War and later of nuclear weapons.
Key ideas
- Russell's paradox
- Theory of descriptions
- Logical atomism
Teachers: Alfred North Whitehead
Students: Ludwig Wittgenstein
Influence
Influenced by 10
Plato
influenced by
Russell defended universals that subsist independently of minds, calling Plato’s theory of ideas one of the most successful attempts at the problem (The Problems of Philosophy, 1912). B. Russell, The Problems of Philosophy (1912), ch. 9 (“The World of Universals”)
Evidence: also in InPhO · InPhO
Plato › 428–348 BCE
Gottfried Wilhelm Leibniz
influenced by ✓
Russell argued that Leibniz’s metaphysics follows from a few logical premises, above all the subject–predicate doctrine of propositions (A Critical Exposition of the Philosophy of Leibniz, 1900). B. Russell, A Critical Exposition of the Philosophy of Leibniz (1900); SEP “Bertrand Russell”; SEP “Gottfried Wilhelm Leibniz”
Gottfried Wilhelm Leibniz › 1646–1716
David Hume
influenced by ✓
Russell restated Hume’s problem of induction, holding that the inductive principle can be neither proved nor disproved by experience (The Problems of Philosophy, 1912). B. Russell, The Problems of Philosophy (1912), “On Induction”; A History of Western Philosophy (1945); SEP “Bertrand Russell”
David Hume › 1711–1776
John Stuart Mill
influenced by ✓
Russell, Mill’s lay godson, gave up the first-cause argument on reading Mill’s Autobiography, as he recalled in 1927, and honoured him in a British Academy lecture (1955). B. Russell, “Why I Am Not a Christian” (1927); “John Stuart Mill”, Proceedings of the British Academy 41 (1955); J. S. Mill, Autobiography (1873); SEP “Bertrand Russell”
John Stuart Mill › 1806–1873
Georg Cantor
influenced by ✓
Russell read Cantor intensively in his youth, and his paradox arose from a study of Cantor’s theorem. SEP “Bertrand Russell” (A. D. Irvine), on the Autobiography; SEP “The Early Development of Set Theory” (J. Ferreirós)
Evidence: also in Wikidata · Wikidata
Georg Cantor › 1845–1918
G. E. Moore
influenced by ✓
Russell followed Moore’s revolt against idealism, adopting his realism of propositions and concepts (‘The Nature of Judgment’, 1899), as the preface to The Principles of Mathematics (1903) acknowledges. G. E. Moore, “The Nature of Judgment”, Mind 8 (1899); B. Russell, The Principles of Mathematics (1903), preface; My Philosophical Development (1959); SEP “Bertrand Russell”
G. E. Moore › 1873–1958
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Laozi
influenced by
In The Problem of China (1922) Russell took Laozi’s “production without possession, action without self-assertion, development without domination” as the Chinese conception of the ends of life, set against Western possession, self-assertion and domination. B. Russell, The Problem of China (1922), ch. XI “Chinese and Western Civilization Contrasted”
Evidence: AI draft
Laozi › legendary figure
Hermann Lotze
influenced by
Early Russell, like early Moore, was shaped by British idealists who had taken over Lotze’s logic and metaphysics. SEP “Hermann Lotze” (D. Sullivan), §2
Evidence: AI draft
Hermann Lotze › 1817–1881
Giuseppe Peano
influenced by ✓
Russell met Peano at the Paris congress of 1900, and Principia Mathematica adopts Peano’s logical notation. SEP “Bertrand Russell” (A. D. Irvine), chronology; SEP “The Algebra of Logic Tradition” (S. Burris, J. Legris)
Evidence: also in Wikidata · Wikidata
Giuseppe Peano › 1858–1932
Alfred North Whitehead studied with
studied with ✓
Whitehead examined Russell for his entrance scholarship to Trinity College, Cambridge, in 1890 and taught him there; the former pupil became his co-author of Principia Mathematica (1910–13). B. Russell, Autobiography I (1967), ch. 3
Evidence: AI draft
Alfred North Whitehead › 1861–1947
Influenced 7
Susan Stebbing
influenced
Stebbing presented the logic of Principia Mathematica and Russell’s theory of descriptions in A Modern Introduction to Logic (1930), treating Russell as a reference point of Cambridge analysis. L. S. Stebbing, A Modern Introduction to Logic (1930); SEP “Susan Stebbing”
Evidence: AI draft
Susan Stebbing › 1885–1943
Stanisław Leśniewski
influenced
Leśniewski traced Russell’s paradox to a confusion of distributive and collective classes and built mereology, a theory of collective classes, in response (Podstawy ogólnej teoryi mnogości, 1916). S. Leśniewski, Podstawy ogólnej teoryi mnogości I (1916); SEP “Stanisław Leśniewski”; SEP “Mereology”
Evidence: AI draft
Stanisław Leśniewski › 1886–1939
Rudolf Carnap
influenced
Carnap set Russell’s maxim to replace inferred entities by logical constructions as motto of the Aufbau (1928); reading Our Knowledge of the External World (1914) had launched it. R. Carnap, Der logische Aufbau der Welt (1928); “Intellectual Autobiography”, in P. A. Schilpp (ed.), The Philosophy of Rudolf Carnap (1963); B. Russell, Our Knowledge of the External World (1914); SEP “Rudolf Carnap”
Evidence: also in InPhO · InPhO
Rudolf Carnap › 1891–1970
W. V. O. Quine
influenced
Quine generalised Principia Mathematica in his dissertation (1932) and used Russell’s theory of descriptions to dissolve the riddle of non-being (‘On What There Is’, 1948). W. V. Quine, The Logic of Sequences: A Generalization of Principia Mathematica (dissertation 1932; publ. 1990); “On What There Is”, Review of Metaphysics 2 (1948); SEP “Willard Van Orman Quine”
Evidence: also in InPhO · InPhO
W. V. O. Quine › 1908–2000
A. J. Ayer
influenced ✓
Ayer named Russell, with Wittgenstein, as source of Language, Truth and Logic (1936) and used his method of logical construction to reduce material things to sense-contents. A. J. Ayer, Language, Truth and Logic (1936), preface; Russell and Moore: The Analytical Heritage (1971); SEP “Alfred Jules Ayer”
A. J. Ayer › 1910–1989
Alan Turing
influenced
Turing studied Russell’s Introduction to Mathematical Philosophy in 1933, according to Hodges, and later adapted Russell’s theory of types (‘Practical Forms of Type Theory’, 1948). A. Hodges, Alan Turing: The Enigma (1983); A. M. Turing, “Practical Forms of Type Theory”, Journal of Symbolic Logic 13 (1948); B. Russell, Introduction to Mathematical Philosophy (1919)
Evidence: also in InPhO · InPhO
Alan Turing › 1912–1954
David Chalmers
influenced ✓
Chalmers took up Russell’s view that physics reveals only structure, leaving intrinsic natures that may ground consciousness, as ‘Russellian monism’ (‘Consciousness and its Place in Nature’, 2002). D. J. Chalmers, “Consciousness and its Place in Nature” (2002); “Panpsychism and Panprotopsychism”, Amherst Lecture in Philosophy 8 (2013); B. Russell, The Analysis of Matter (1927); SEP “Russellian Monism”
Evidence: also in Wikidata · Wikidata
David Chalmers › b. 1966
Criticism
Criticized by 6
Sarvepalli Radhakrishnan
criticised by
A chapter of The Reign of Religion (1920) examines Russell’s new realism – not, Radhakrishnan conceded, shaped by religious bias – and concludes that it is satisfactory only where it departs from its pluralism and “makes friends with absolutism”. S. Radhakrishnan, The Reign of Religion in Contemporary Philosophy (1920), ch. XI “The New Realism of Mr. Bertrand Russell”
Evidence: AI draft
Sarvepalli Radhakrishnan › 1888–1975
Ludwig Wittgenstein taughtinfluenced by
taught ✓
Wittgenstein came to Cambridge in October 1911 to study logic with Russell and in 1912 was admitted to Trinity College as his student; his Notes on Logic (1913) were written for Russell. R. Monk, Ludwig Wittgenstein: The Duty of Genius (1990); B. McGuinness, Wittgenstein: A Life. Young Ludwig (1988)
Evidence: AI draft
influenced by ✓
Russell said his lectures on logical atomism were largely concerned with explaining ideas he had learnt from his former pupil Wittgenstein (The Philosophy of Logical Atomism, 1918). B. Russell, “The Philosophy of Logical Atomism” (lectures 1918; The Monist 1918–19), preliminary note
criticised by
Wittgenstein objected that Russell’s multiple-relation theory of judgement allows nonsense to be judged (1913), and later rejected his theory of types as superfluous (Tractatus, 1921, 3.331–3.333, 5.5422). L. Wittgenstein to B. Russell, June 1913; Notes on Logic (1913); Tractatus logico-philosophicus (1921), 3.331–3.333, 5.5422
Evidence: AI draft
Ludwig Wittgenstein › 1889–1951
Kurt Gödel influenced
influenced
Gödel took Principia Mathematica as the formal system of his incompleteness theorems (1931) and welcomed Russell’s early realism about classes and concepts (‘Russell’s Mathematical Logic’, 1944). K. Gödel, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”, Monatshefte für Mathematik und Physik 38 (1931); “Russell’s Mathematical Logic”, in P. A. Schilpp (ed.), The Philosophy of Bertrand Russell (1944); SEP “Kurt Gödel”
Evidence: AI draft
criticised by
Gödel criticised Russell’s vicious-circle principle and no-class theory as too restrictive for classical mathematics, defending classes and concepts as real objects (‘Russell’s Mathematical Logic’, 1944). K. Gödel, “Russell’s Mathematical Logic”, in P. A. Schilpp (ed.), The Philosophy of Bertrand Russell (1944), 123–153
Evidence: AI draft
Kurt Gödel › 1906–1978
Wilfrid Sellars
criticised by
Sellars argued that Russell’s acquaintance either involves concepts or is not knowledge (‘Acquaintance and Description Again’, 1949), later calling such views the ‘Myth of the Given’ (1956). W. Sellars, “Acquaintance and Description Again”, Journal of Philosophy 46 (1949); “Empiricism and the Philosophy of Mind” (1956); B. Russell, The Problems of Philosophy (1912), ch. 5
Evidence: AI draft
Wilfrid Sellars › 1912–1989
P. F. Strawson
criticised by
Strawson objected that Russell’s theory of descriptions confuses sentences with uses: ‘The King of France is bald’ presupposes, not asserts, that a king exists (‘On Referring’, 1950). P. F. Strawson, “On Referring”, Mind 59 (1950), 320–344; Russell’s reply: “Mr. Strawson on Referring”, Mind 66 (1957)
Evidence: AI draft
P. F. Strawson › 1919–2006
Saul Kripke
criticised by
Kripke rejected Russell’s view that ordinary names are disguised descriptions: ‘Aristotle’ names Aristotle even in worlds where he did nothing we describe him by (Naming and Necessity, 1972/1980). S. Kripke, Naming and Necessity (1972; 1980), Lectures I–II; B. Russell, “Knowledge by Acquaintance and Knowledge by Description” (1911)
Evidence: AI draft
Saul Kripke › 1940–2022
Criticizes 6
Confucius
criticised
In the same book Russell confessed himself “unable to appreciate the merits of Confucius”, whose writings he found largely occupied with trivial points of etiquette, while granting that Confucian ethics had produced no priesthood and no persecution. B. Russell, The Problem of China (1922), ch. XI
Evidence: AI draft
Confucius › traditionally 551–479 BCE
Georg Wilhelm Friedrich Hegel
criticised
Russell rejected Hegel’s doctrine that only the whole is real: if all relations were internal, nothing could be known without knowing everything (History of Western Philosophy, 1945). B. Russell, A History of Western Philosophy (1945), ch. 22; Our Knowledge of the External World (1914), Lecture II
Evidence: AI draft
Georg Wilhelm Friedrich Hegel › 1770–1831
William James
criticised
Russell objected that James’s pragmatist theory confuses a criterion of truth with its meaning: ‘true’ cannot mean ‘useful to believe’ (‘William James’s Conception of Truth’, 1908). B. Russell, “William James’s Conception of Truth” (1908), in Philosophical Essays (1910); W. James, Pragmatism (1907), Lecture VI
Evidence: AI draft
William James › 1842–1910
Gottlob Frege influenced by
influenced by ✓
Russell recognised Frege’s logicism as close to his own, expounded it in an appendix to The Principles of Mathematics (1903) and continued it in Principia Mathematica (1910–13). B. Russell, The Principles of Mathematics (1903), appendix A; A. N. Whitehead and B. Russell, Principia Mathematica (1910–13); SEP “Bertrand Russell”
criticised
In a letter of 16 June 1902 Russell showed that Frege’s Basic Law V yields a contradiction; ‘On Denoting’ (1905) rejected Frege’s distinction of sense and reference. B. Russell to G. Frege, 16 June 1902, in J. van Heijenoort (ed.), From Frege to Gödel (1967); “On Denoting”, Mind 14 (1905); G. Frege, Grundgesetze der Arithmetik II (1903), appendix
Evidence: AI draft
Gottlob Frege › 1848–1925
Alexius Meinong
criticised
Russell objected that Meinong’s non-existent objects, such as the round square, infringe the law of contradiction, and analysed them away with his theory of descriptions (‘On Denoting’, 1905). B. Russell, “On Denoting”, Mind 14 (1905), 479–493; SEP “Alexius Meinong”
Evidence: AI draft
Alexius Meinong › 1853–1920
Henri Bergson
criticised
Russell rejected Bergson’s intuition as anti-intellectualism: his attack on the intellect rests on misunderstandings of mathematics and of Zeno’s paradoxes (‘The Philosophy of Bergson’, 1912). B. Russell, “The Philosophy of Bergson”, The Monist 22 (1912), 321–347; A History of Western Philosophy (1945), ch. 28
Evidence: AI draft
Henri Bergson › 1859–1941
Works
- 1905On Denoting
The present King of France is bald – definite descriptions analyzed.
Mathematics derived from logic – the proposition from which 1+1=2 follows comes only at *54.43, on page 379 of the first volume.
A pointed survey of the whole history – with mocking verdicts on Hegel and Nietzsche.
Position
Russell was a founder of analytic philosophy. He discovered the paradox of the set of all sets that do not contain themselves, which shook the foundations of mathematics, and with Whitehead attempted in Principia Mathematica to derive mathematics from logic. His theory of descriptions showed that sentences such as “The present King of France is bald” can be analysed so that their grammatical form no longer misleads us about what exists. This made logical analysis the central method of philosophy. In epistemology he distinguished knowledge by acquaintance from knowledge by description. Beyond academia he wrote influential books on ethics, religion, politics and the history of philosophy.
Life & context
Russell, grandson of a British prime minister, was orphaned early and raised by his grandmother. He studied mathematics and philosophy at Trinity College, Cambridge. A pacifist, he lost his lectureship and was imprisoned during the First World War. He wrote prolifically for a wide public, received the Nobel Prize in Literature in 1950 and campaigned against nuclear weapons into his nineties.
Further main works
- The Principles of Mathematics (1903)
- The Problems of Philosophy (1912)
Appears in
- Journey ‘The Linguistic Turn’ · Stop 2 of 10
- Debate ‘What Is Consciousness?’
- Debate ‘War and Peace: When Is Armed Force Justified?’
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