British Philosopher and logician
Introduction
Bertrand Arthur William Russell, 3rd
Earl Russell, OM FRS ( 18 May 1872 – 2 February 1970) was a British
philosopher, logician, mathematician, historian, writer, social critic,
political activist, and Nobel laureate. At
various points in his life, Russell considered himself a liberal, a socialist
and a pacifist, but he also admitted that he had "never been any of these
things, in any profound sense". Russell was born in Monmouthshire into one
of the most prominent aristocratic families in the United Kingdom.
In the early 20th century, Russell
led the British "revolt against idealism".He is considered one of the
founders of analytic philosophy along with his predecessor Gottlob Frege,
colleague G. E. Moore and protégé Ludwig Wittgenstein. He is widely held to be
one of the 20th century's premier logicians. With A. N. Whitehead he wrote
Principia Mathematica, an attempt to create a logical basis for mathematics.
His philosophical essay "On Denoting" has been considered a
"paradigm of philosophy". His work has had a considerable influence
on mathematics, logic, set theory, linguistics, artificial intelligence,
cognitive science, computer science (see type theory and type system) and
philosophy, especially the philosophy of language, epistemology and
metaphysics.
Russell was a prominent anti-war
activist and he championed anti-imperialism. Occasionally, he advocated
preventive nuclear war, before the opportunity provided by the atomic monopoly
had passed and "welcomed with enthusiasm" world government. He went to prison for his pacifism during
World War I. Later, Russell concluded that war against Adolf Hitler's Nazi
Germany was a necessary "lesser of two evils" and criticized
Stalinist totalitarianism, attacked the involvement of the United States in the
Vietnam War and was an outspoken proponent of nuclear disarmament. In 1950,
Russell was awarded the Nobel Prize in Literature "in recognition of his varied
and significant writings in which he champions humanitarian ideals and freedom
of thought"
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Bertrand Russell, in full Bertrand Arthur William Russell, 3rd Earl
Russell of Kingston Russell, Viscount Amberley of Amberley and of Ardsalla,
(born May 18, 1872, Trelleck, Monmouthshire, Wales—died February 2, 1970,
Penrhyndeudraeth, Merioneth), British philosopher, logician, and social reformer,
founding figure in the analytic movement in Anglo-American philosophy, and
recipient of the Nobel Prize for Literature in 1950. Russell’s contributions to
logic, epistemology, and the philosophy of mathematics established him as one
of the foremost philosophers of the 20th century. To the general public,
however, he was best known as a campaigner for peace and as a popular writer on
social, political, and moral subjects. During a long, productive, and often
turbulent life, he published more than 70 books and about 2,000 articles,
married four times, became involved in innumerable public controversies, and
was honoured and reviled in almost equal measure throughout the world.
Russell’s article on the philosophical consequences of relativity appeared in
the 13th edition of the Encyclopædia Britannica.
Russell was born in Ravenscroft, the country home of his parents, Lord
and Lady Amberley. His grandfather, Lord John Russell, was the youngest son of
the 6th Duke of Bedford. In 1861, after a long and distinguished political
career in which he served twice as prime minister, Lord Russell was ennobled by
Queen Victoria, becoming the 1st Earl Russell. Bertrand Russell became the 3rd
Earl Russell in 1931, after his elder brother, Frank, died childless.
Russell’s early life was marred by tragedy and bereavement. By the time
he was age six, his sister, Rachel, his parents, and his grandfather had all
died, and he and Frank were left in the care of their grandmother, Countess
Russell. Though Frank was sent to Winchester School, Bertrand was educated
privately at home, and his childhood, to his later great regret, was spent
largely in isolation from other children. Intellectually precocious, he became
absorbed in mathematics from an early age and found the experience of learning
Euclidean geometry at the age of 11 “as dazzling as first love,” because it
introduced him to the intoxicating possibility of certain, demonstrable
knowledge. This led him to imagine that all knowledge might be provided with
such secure foundations, a hope that lay at the very heart of his motivations
as a philosopher. His earliest philosophical work was written during his
adolescence and records the skeptical doubts that led him to abandon the
Christian faith in which he had been brought up by his grandmother.
In 1890 Russell’s isolation came to an end when he entered Trinity
College, University of Cambridge, to study mathematics. There he made lifelong
friends through his membership in the famously secretive student society the
Apostles, whose members included some of the most influential philosophers of
the day. Inspired by his discussions with this group, Russell abandoned
mathematics for philosophy and won a fellowship at Trinity on the strength of a
thesis entitled An Essay on the Foundations of Geometry, a revised version of
which was published as his first philosophical book in 1897. Following Kant’s
Critique of Pure Reason (1781, 1787), this work presented a sophisticated
idealist theory that viewed geometry as a description of the structure of
spatial intuition.
In 1896 Russell published his first political work, German Social
Democracy. Though sympathetic to the reformist aims of the German socialist
movement, it included some trenchant and farsighted criticisms of Marxist
dogmas. The book was written partly as the outcome of a visit to Berlin in 1895
with his first wife, Alys Pearsall Smith, whom he had married the previous
year. In Berlin, Russell formulated an ambitious scheme of writing two series
of books, one on the philosophy of the sciences, the other on social and
political questions. “At last,” as he later put it, “I would achieve a Hegelian
synthesis in an encyclopaedic work dealing equally with theory and practice.”
He did, in fact, come to write on all the subjects he intended, but not in the
form that he envisaged. Shortly after finishing his book on geometry, he
abandoned the metaphysical idealism that was to have provided the framework for
this grand synthesis.
Russell’s abandonment of idealism is customarily attributed to the
influence of his friend and fellow Apostle G.E. Moore. A much greater influence
on his thought at this time, however, was a group of German mathematicians that
included Karl Weierstrass, Georg Cantor, and Richard Dedekind, whose work was
aimed at providing mathematics with a set of logically rigorous foundations.
For Russell, their success in this endeavour was of enormous philosophical as
well as mathematical significance; indeed, he described it as “the greatest
triumph of which our age has to boast.” After becoming acquainted with this
body of work, Russell abandoned all vestiges of his earlier idealism and
adopted the view, which he was to hold for the rest of his life, that analysis
rather than synthesis was the surest method of philosophy and that therefore
all the grand system building of previous philosophers was misconceived. In
arguing for this view with passion and acuity, Russell exerted a profound
influence on the entire tradition of English-speaking analytic philosophy,
bequeathing to it its characteristic style, method, and tone.
Inspired by the work of the mathematicians whom he so greatly admired,
Russell conceived the idea of demonstrating that mathematics not only had
logically rigorous foundations but also that it was in its entirety nothing but
logic. The philosophical case for this point of view—subsequently known as
logicism—was stated at length in The Principles of Mathematics (1903). There
Russell argued that the whole of mathematics could be derived from a few simple
axioms that made no use of specifically mathematical notions, such as number
and square root, but were rather confined to purely logical notions, such as
proposition and class. In this way not only could the truths of mathematics be
shown to be immune from doubt, they could also be freed from any taint of
subjectivity, such as the subjectivity involved in Russell’s earlier Kantian
view that geometry describes the structure of spatial intuition. Near the end
of his work on The Principles of Mathematics, Russell discovered that he had
been anticipated in his logicist philosophy of mathematics by the German
mathematician Gottlob Frege, whose book The Foundations of Arithmetic (1884)
contained, as Russell put it, “many things…which I believed I had invented.”
Russell quickly added an appendix to his book that discussed Frege’s work,
acknowledged Frege’s earlier discoveries, and explained the differences in
their respective understandings of the nature of logic.
The tragedy of Russell’s intellectual life is that the deeper he thought
about logic, the more his exalted conception of its significance came under
threat. He himself described his philosophical development after The Principles
of Mathematics as a “retreat from Pythagoras.” The first step in this retreat
was his discovery of a contradiction—now known as Russell’s Paradox—at the very
heart of the system of logic upon which he had hoped to build the whole of
mathematics. The contradiction arises from the following considerations: Some
classes are members of themselves (e.g., the class of all classes), and some
are not (e.g., the class of all men), so we ought to be able to construct the
class of all classes that are not members of themselves. But now, if we ask of
this class “Is it a member of itself?” we become enmeshed in a contradiction.
If it is, then it is not, and if it is not, then it is. This is rather like
defining the village barber as “the man who shaves all those who do not shave
themselves” and then asking whether the barber shaves himself or not.
At first this paradox seemed trivial, but the more Russell reflected
upon it, the deeper the problem seemed, and eventually he was persuaded that
there was something fundamentally wrong with the notion of class as he had
understood it in The Principles of Mathematics. Frege saw the depth of the
problem immediately. When Russell wrote to him to tell him of the paradox,
Frege replied, “arithmetic totters.” The foundation upon which Frege and
Russell had hoped to build mathematics had, it seemed, collapsed. Whereas Frege
sank into a deep depression, Russell set about repairing the damage by
attempting to construct a theory of logic immune to the paradox. Like a
malignant cancerous growth, however, the contradiction reappeared in different
guises whenever Russell thought that he had eliminated it.
Eventually, Russell’s attempts to overcome the paradox resulted in a
complete transformation of his scheme of logic, as he added one refinement
after another to the basic theory. In the process, important elements of his
“Pythagorean” view of logic were abandoned. In particular, Russell came to the
conclusion that there were no such things as classes and propositions and that
therefore, whatever logic was, it was not the study of them. In their place he
substituted a bewilderingly complex theory known as the ramified theory of
types, which, though it successfully avoided contradictions such as Russell’s
Paradox, was (and remains) extraordinarily difficult to understand. By the time
he and his collaborator, Alfred North Whitehead, had finished the three volumes
of Principia Mathematica (1910–13), the theory of types and other innovations
to the basic logical system had made it unmanageably complicated. Very few
people, whether philosophers or mathematicians, have made the gargantuan effort
required to master the details of this monumental work. It is nevertheless
rightly regarded as one of the great intellectual achievements of the 20th
century.
Principia Mathematica is a herculean attempt to demonstrate
mathematically what The Principles of Mathematics had argued for
philosophically, namely that mathematics is a branch of logic. The validity of
the individual formal proofs that make up the bulk of its three volumes has
gone largely unchallenged, but the philosophical significance of the work as a
whole is still a matter of debate. Does it demonstrate that mathematics is
logic? Only if one regards the theory of types as a logical truth, and about
that there is much more room for doubt than there was about the trivial truisms
upon which Russell had originally intended to build mathematics. Moreover, Kurt
Gödel’s first incompleteness theorem (1931) proves that there cannot be a
single logical theory from which the whole of mathematics is derivable: all
consistent theories of arithmetic are necessarily incomplete. Principia
Mathematica cannot, however, be dismissed as nothing more than a heroic
failure. Its influence on the development of mathematical logic and the
philosophy of mathematics has been immense.
Despite their differences, Russell and Frege were alike in taking an
essentially Platonic view of logic. Indeed, the passion with which Russell
pursued the project of deriving mathematics from logic owed a great deal to
what he would later somewhat scornfully describe as a “kind of mathematical
mysticism.” As he put it in his more disillusioned old age, “I disliked the
real world and sought refuge in a timeless world, without change or decay or
the will-o’-the-wisp of progress.” Russell, like Pythagoras and Plato before
him, believed that there existed a realm of truth that, unlike the messy
contingencies of the everyday world of sense-experience, was immutable and
eternal. This realm was accessible only to reason, and knowledge of it, once
attained, was not tentative or corrigible but certain and irrefutable. Logic,
for Russell, was the means by which one gained access to this realm, and thus
the pursuit of logic was, for him, the highest and noblest enterprise life had
to offer.
In philosophy the greatest impact of Principia Mathematica has been
through its so-called theory of descriptions. This method of analysis, first
introduced by Russell in his article “On Denoting” (1905), translates
propositions containing definite descriptions (e.g., “the present king of
France”) into expressions that do not—the purpose being to remove the logical
awkwardness of appearing to refer to things (such as the present king of
France) that do not exist. Originally developed by Russell as part of his
efforts to overcome the contradictions in his theory of logic, this method of
analysis has since become widely influential even among philosophers with no
specific interest in mathematics. The general idea at the root of Russell’s
theory of descriptions—that the grammatical structures of ordinary language are
distinct from, and often conceal, the true “logical forms” of expressions—has
become his most enduring contribution to philosophy.
Russell later said that his mind never fully recovered from the strain
of writing Principia Mathematica, and he never again worked on logic with quite
the same intensity. In 1918 he wrote Introduction to Mathematical Philosophy,
which was intended as a popularization of Principia, but, apart from this, his
philosophical work tended to be on epistemology rather than logic. In 1914, in
Our Knowledge of the External World, Russell argued that the world is
“constructed” out of sense-data, an idea that he refined in The Philosophy of
Logical Atomism (1918–19). In The Analysis of Mind (1921) and The Analysis of
Matter (1927), he abandoned this notion in favour of what he called neutral
monism, the view that the “ultimate stuff” of the world is neither mental nor
physical but something “neutral” between the two. Although treated with
respect, these works had markedly less impact upon subsequent philosophers than
his early works in logic and the philosophy of mathematics, and they are
generally regarded as inferior by comparison.
Connected with the change in his intellectual direction after the
completion of Principia was a profound change in his personal life. Throughout
the years that he worked single-mindedly on logic, Russell’s private life was
bleak and joyless. He had fallen out of love with his first wife, Alys, though
he continued to live with her. In 1911, however, he fell passionately in love
with Lady Ottoline Morrell. Doomed from the start (because Morrell had no
intention of leaving her husband), this love nevertheless transformed Russell’s
entire life. He left Alys and began to hope that he might, after all, find
fulfillment in romance. Partly under Morrell’s influence, he also largely lost
interest in technical philosophy and began to write in a different, more
accessible style. Through writing a best-selling introductory survey called The
Problems of Philosophy (1911), Russell discovered that he had a gift for
writing on difficult subjects for lay readers, and he began increasingly to
address his work to them rather than to the tiny handful of people capable of
understanding Principia Mathematica.
In the same year that he began his affair with Morrell, Russell met
Ludwig Wittgenstein, a brilliant young Austrian who arrived at Cambridge to
study logic with Russell. Fired with intense enthusiasm for the subject,
Wittgenstein made great progress, and within a year Russell began to look to
him to provide the next big step in philosophy and to defer to him on questions
of logic. However, Wittgenstein’s own work, eventually published in 1921 as
Logisch-philosophische Abhandlung (Tractatus Logico-Philosophicus, 1922),
undermined the entire approach to logic that had inspired Russell’s great
contributions to the philosophy of mathematics. It persuaded Russell that there
were no “truths” of logic at all, that logic consisted entirely of tautologies,
the truth of which was not guaranteed by eternal facts in the Platonic realm of
ideas but lay, rather, simply in the nature of language. This was to be the
final step in the retreat from Pythagoras and a further incentive for Russell
to abandon technical philosophy in favour of other pursuits.
During World War I Russell was for a while a full-time political
agitator, campaigning for peace and against conscription. His activities
attracted the attention of the British authorities, who regarded him as
subversive. He was twice taken to court, the second time to receive a sentence
of six months in prison, which he served at the end of the war. In 1916, as a
result of his antiwar campaigning, Russell was dismissed from his lectureship
at Trinity College. Although Trinity offered to rehire him after the war, he
ultimately turned down the offer, preferring instead to pursue a career as a
journalist and freelance writer. The war had had a profound effect on Russell’s
political views, causing him to abandon his inherited liberalism and to adopt a
thorough-going socialism, which he espoused in a series of books including
Principles of Social Reconstruction (1916), Roads to Freedom (1918), and The
Prospects of Industrial Civilization (1923). He was initially sympathetic to the
Russian Revolution of 1917, but a visit to the Soviet Union in 1920 left him
with a deep and abiding loathing for Soviet communism, which he expressed in
The Practice and Theory of Bolshevism (1920).
In 1921 Russell married his second wife, Dora Black, a young graduate of
Girton College, Cambridge, with whom he had two children, John and Kate. In the
interwar years Russell and Dora acquired a reputation as leaders of a
progressive socialist movement that was stridently anticlerical, openly defiant
of conventional sexual morality, and dedicated to educational reform. Russell’s
published work during this period consists mainly of journalism and popular
books written in support of these causes. Many of these books—such as On
Education (1926), Marriage and Morals (1929), and The Conquest of Happiness
(1930)—enjoyed large sales and helped establish Russell in the eyes of the
general public as a philosopher with important things to say about the moral,
political, and social issues of the day. His public lecture “Why I Am Not a
Christian,” delivered in 1927 and printed many times, became a popular locus
classicus of atheistic rationalism. In 1927 Russell and Dora set up their own
school, Beacon Hill, as a pioneering experiment in primary education. To pay
for it, Russell undertook a few lucrative but exhausting lecture tours of the
United States.
During these years Russell’s second marriage came under increasing
strain, partly because of overwork but chiefly because Dora chose to have two
children with another man and insisted on raising them alongside John and Kate.
In 1932 Russell left Dora for Patricia (“Peter”) Spence, a young University of
Oxford undergraduate, and for the next three years his life was dominated by an
extraordinarily acrimonious and complicated divorce from Dora, which was
finally granted in 1935. In the following year he married Spence, and in 1937
they had a son, Conrad. Worn out by years of frenetic public activity and
desiring, at this comparatively late stage in his life (he was then age 66), to
return to academic philosophy, Russell gained a teaching post at the University
of Chicago. From 1938 to 1944 Russell lived in the United States, where he
taught at Chicago and the University of California at Los Angeles, but he was
prevented from taking a post at the City College of New York because of
objections to his views on sex and marriage. On the brink of financial ruin, he
secured a job teaching the history of philosophy at the Barnes Foundation in
Philadelphia. Although he soon fell out with its founder, Albert C. Barnes, and
lost his job, Russell was able to turn the lectures he delivered at the
foundation into a book, A History of Western Philosophy (1945), which proved to
be a best-seller and was for many years his main source of income.
In 1944 Russell returned to Trinity College, where he lectured on the
ideas that formed his last major contribution to philosophy, Human Knowledge:
Its Scope and Limits (1948). During this period Russell, for once in his life,
found favour with the authorities, and he received many official tributes,
including the Order of Merit in 1949 and the Nobel Prize for Literature in
1950. His private life, however, remained as turbulent as ever, and he left his
third wife in 1949. For a while he shared a house in Richmond upon Thames,
London, with the family of his son John and, forsaking both philosophy and
politics, dedicated himself to writing short stories. Despite his famously
immaculate prose style, Russell did not have a talent for writing great
fiction, and his short stories were generally greeted with an embarrassed and
puzzled silence, even by his admirers.
In 1952 Russell married his fourth wife, Edith Finch, and finally, at
the age of 80, found lasting marital harmony. Russell devoted his last years to
campaigning against nuclear weapons and the Vietnam War, assuming once again
the role of gadfly of the establishment. The sight of Russell in extreme old
age taking his place in mass demonstrations and inciting young people to civil
disobedience through his passionate rhetoric inspired a new generation of
admirers. Their admiration only increased when in 1961 the British judiciary
system took the extraordinary step of sentencing the 89-year-old Russell to a
second period of imprisonment.
When he died in 1970 Russell was far better known as an antiwar
campaigner than as a philosopher of mathematics. In retrospect, however, it is
possible to see that it is for his great contributions to philosophy that he
will be remembered and honoured by future generations.
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