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Bertrand Russell
1872–1970· Philosopher· Knowledge, logic & science
Well documentedSolid records, texts or physical evidence.
British philosopher, logician and activist who co-founded analytic philosophy and tried to show that mathematics rests on logic.
See it on the Philosophy map →The idea
Idea: rigorous logic can clarify philosophy and ground mathematics. With Alfred North Whitehead he wrote Principia Mathematica (1910–13), deriving arithmetic from logic. 'On Denoting' (1905) showed how logic untangles sentences like 'The present King of France is bald.' He found a paradox in Frege's system, mentored Wittgenstein, and wrote the bestselling A History of Western Philosophy (1945). Jailed in 1918 over an anti-war article, he won the 1950 Nobel Prize in Literature. Main objection: Gödel (1931) showed no such system captures all mathematical truth.
Why it matters
He made logic the central tool of English-language philosophy and modeled the philosopher as public voice on war, nuclear weapons and free thought.
Legacy and sources
More than 70 books, tens of thousands of letters (archived at McMaster University, Canada) and a three-volume Autobiography (1967–69). Principia famously needs hundreds of pages to establish that 1 + 1 = 2.
Still debated
Whether his program of reducing mathematics to logic failed outright or partly succeeded is still argued by philosophers of mathematics.
Connections (4)
▸Bertrand Russell exposed a paradox in the work of Gottlob Frege and modern logicWell documented
The connection
As Frege's Basic Laws of Arithmetic, volume 2, was going to press, Russell wrote to him about a contradiction: the set of all sets that do not contain themselves both does and does not contain itself. Frege's system allowed such sets, so it was inconsistent. Frege added a hasty appendix admitting his foundation had been shaken.
When and how
Russell found the paradox in 1901 and wrote to Frege in Jena on 16 June 1902; volume 2 appeared in 1903 with Frege's appendix.
How we know
Both letters survive; Frege's reply of 22 June 1902 describes his 'consternation' that the basis of arithmetic had been shaken.
Debates and open questions
How best to fix the paradox is still debated: Russell's theory of types and modern set theory avoid it, but no fix is universally seen as natural.
▸Bertrand Russell co-founded Analytic philosophyWell documented
The connection
With G. E. Moore, Russell led the Cambridge revolt against British idealism, the Hegel-inspired view that reality is one mind-like whole. He argued the world consists of many separate facts that logical analysis can uncover. 'On Denoting' (1905) became the model of analysis: rewriting confusing sentences into precise logical form.
When and how
At Trinity College, Cambridge, around 1898–1905; 'On Denoting' appeared in the journal Mind in 1905.
How we know
Russell describes the revolt in My Philosophical Development (1959); Frank Ramsey called his theory of descriptions 'that paradigm of philosophy'.
Debates and open questions
Historians debate whether Russell, Moore or Frege deserves most credit, and whether 'analysis' meant the same thing to each of them.
▸Bertrand Russell mentored Ludwig WittgensteinWell documented
The connection
Russell recognized genius in the young Wittgenstein, who came to Cambridge to study logic and soon challenged his teacher. Russell hoped he would carry on his logical work, and later wrote the introduction that got the Tractatus published. Wittgenstein felt Russell misunderstood the book, and the two drifted apart.
When and how
Cambridge, from October 1911; Russell helped publish the Tractatus in 1921–22, after Wittgenstein's release from an Italian prisoner-of-war camp.
How we know
Russell's letters to Lady Ottoline Morrell vividly record Wittgenstein's arrival and progress, and their own correspondence survives.
Debates and open questions
How far Wittgenstein's 1913 criticisms made Russell abandon his book on knowledge, as Russell later suggested, is debated.
▸Bertrand Russell anticipated, with his stopped clock, The Gettier problemWell documented
The connection
Russell's example: a man looks at a clock that has stopped, without knowing it, and happens to read the correct time. His belief is true and reasonably based, yet he does not know the time. That is a Gettier case fifteen years early, though Russell used it to make a different point.
When and how
Russell, Human Knowledge: Its Scope and Limits (1948). Around 770, the Indian Buddhist philosopher Dharmottara gave a similar case of a mirage over hidden water.
How we know
The passage is in Human Knowledge (1948); Gettier did not cite Russell, and the parallel was pointed out by later epistemologists.
Debates and open questions
Russell was arguing that knowledge is a vague concept, not refuting a definition; whether he truly anticipated Gettier or just used a similar example is debated.