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Bertrand Russell

http://plato.stanford.edu/

entries/russell/

Bertrand Arthur William Russell (b.1872 - d.1970) was a British philosopher, logician,

essayist, and social critic, best known for his work in mathematical logic and analytic

philosophy. His most influential contributions include his defense of logicism (the view

that mathematics is in some important sense reducible to logic), and his theories of

definite descriptions and logical atomism. Along with G.E. Moore, Russell is generally

 recognized as one of the founders of analytic philosophy. Along with Kurt Gödel, he

is also regularly credited with being one of the two most important logicians of the

twentieth century.

 

Over the course of his long career, Russell made significant contributions, not just to

logic and philosophy, but to a broad range of other subjects including education, history,

political theory and religious studies. In addition, many of his writings on a wide variety

of topics in both the sciences and the humanities have influenced generations of general

readers. After a life marked by controversy (including dismissals from both Trinity College,

Cambridge, and City College, New York), Russell was awarded the Order of Merit in

1949 and the Nobel Prize for Literature in 1950. Also noted for his many spirited

anti-war and anti-nuclear protests, Russell remained a prominent public figure until his

death at the age of 97.

A Chronology of Russell's Life

Russell's Work in Logic

Russell's Work in Analytic Philosophy

Russell's Social and Political Philosophy

Russell's Writings

Bibliography

Other Internet Resources

Related Entries

Interested readers may also wish to listen to two sound clips of Russell speaking.

(呵呵,他的声音amusing:)

 

A Chronology of Russell's Life (1872-1970长寿耶, 对科学家说来,

TA们的工作就是幸福的源泉, 在工作中,

TA们智力中的较高部分都已被工作所占据, TA们的情感通常

都是简单,质朴的, 所以是幸福的, 幸福的享受着工作,爱情和生活,

结果是长寿的)

A short chronology of the major events in Russell's life is as follows:

(1872) Born May 18 at Ravenscroft, Wales.

(1874) Death of mother and sister.

(1876) Death of father; Russell's grandfather, Lord John Russell (the former Prime

Minister), and grandmother succeed in overturning his father's will to win custody

of Russell and his brother.

(1878) Death of grandfather; Russell's grandmother, Lady Russell, supervises

 his upbringing.

(1890) Enters Trinity College, Cambridge.

(1893) Awarded first class B.A. in Mathematics.

(1894) Completed the Moral Sciences Tripos (Part II)

(1894) Marries Alys Pearsall Smith.

(1900) Meets Peano at International Congress in Paris.

(1901) Discovers Russell's paradox.

(1902) Corresponds with Frege.

(1908) Elected Fellow of the Royal Society.

(1916) Fined 110 pounds and dismissed from Trinity College as a result

of anti-war protests.

(1918) Imprisoned for five months as a result of anti-war protests.

(1921) Divorce from Alys and marriage to Dora Black.

(1927) Opens experimental school with Dora.

(1931) Becomes the third Earl Russell upon the death of his brother.

(1935) Divorce from Dora.

(1936) Marriage to Patricia (Peter) Helen Spence.

(1940) Appointment at City College New York revoked following public

 protests.

(1943) Dismissed from Barnes Foundation in Pennsylvania.

(1949) Awarded the Order of Merit.

(1950) Awarded Nobel Prize for Literature.

(1952) Divorce from Peter and marriage to Edith Finch.

(1955) Releases Russell-Einstein Manifesto.

(1957) Organizes the first Pugwash Conference.

(1958) Becomes founding President of the Campaign for Nuclear Disarmament.

(1961) Imprisoned for one week in connection with anti-nuclear protests.

(1970) Dies February 02 at Penrhyndeudraeth, Wales.

For more detailed information about Russell's life, readers are encouraged to

consult Russell's four autobiographical volumes, My Philosophical Development

(London: George Allen and Unwin, 1959) and The Autobiography of Bertrand

Russell (3 vols, London: George Allen and Unwin, 1967, 1968, 1969). In addition,

John Slater's accessible and informative Bertrand Russell (Bristol: Thoemmes, 1994)

 gives an excellent short introduction to Russell's life, work and influence.

Other sources of biographical information include Ronald Clark's The Life of

Bertrand Russell (London: Jonathan Cape, 1975), Ray Monk's Bertrand

Russell: The Spirit of Solitude (London: Jonathan Cape, 1996) and Bertrand

Russell: The Ghost of Madness (London: Jonathan Cape, 2000), and the first

volume of A.D. Irvine's Bertrand Russell: Critical Assessments (London:

Routledge, 1999).

For a chronology of Russell's major publications, readers are encouraged to

consult Russell's Writings below. For a more complete list see A Bibliography

of Bertrand Russell (3 vols, London: Routledge, 1994), by Kenneth Blackwell

and Harry Ruja. A less detailed, but still comprehensive, list also appears in

Paul Arthur Schilpp, The Philosophy of Bertrand Russell, 3rd edn (New

York: Harper and Row, 1963), pp. 746-803.

Finally, for a bibliography of the secondary literature surrounding Russell, see

A.D. Irvine, Bertrand Russell: Critical Assessments, Vol. 1 (London:

Routledge, 1999), pp. 247-312.

Russell's Work in Logic

Russell's contributions to logic and the foundations of mathematics include

his discovery of Russell's paradox, his defense of logicism (the view that

mathematics is, in some significant sense, reducible to formal logic), his

development of the theory of types, and his refining of the first-order

predicate calculus.

Russell discovered the paradox that bears his name in 1901, while working

on his Principles of Mathematics (1903). The paradox arises in connection

with the set of all sets that are not members of themselves. Such a set, if it exists,

will be a member of itself if and only if it is not a member of itself. The paradox is

significant since, using classical logic, all sentences are entailed by a contradiction.

Russell's discovery thus prompted a large amount of work in logic, set theory, and

the philosophy and foundations of mathematics.

 

Russell's own response to the paradox came with the development of his theory of

types in 1903. It was clear to Russell that some restrictions needed to be placed upon

the original comprehension (or abstraction) axiom of naive set theory, the axiom that

formalizes the intuition that any coherent condition may be used to determine a set

(or class). Russell's basic idea was that reference to sets such as the set of all sets

that are not members of themselves could be avoided by arranging all sentences

into a hierarchy, beginning with sentences about individuals at the lowest level,

sentences about sets of individuals at the next lowest level, sentences about sets

of sets of individuals at the next lowest level, and so on. Using a vicious circle

principle similar to that adopted by the mathematician Henri Poincaré, and his

own so-called "no class" theory of classes, Russell was able to explain why the

unrestricted comprehension axiom fails: propositional functions, such as the

function "x is a set," may not be applied to themselves since self-application

would involve a vicious circle. On Russell's view, all objects for which a given

condition (or predicate) holds must be at the same level or of the same "type."

Although first introduced in 1903, the theory of types was further developed

by Russell in his 1908 article "Mathematical Logic as Based on the Theory of

Types" and in the monumental work he co-authored with

Alfred North Whitehead, Principia Mathematica (1910, 1912, 1913). Thus

the theory admits of two versions, the "simple theory" of 1903 and the

"ramified theory" of 1908. Both versions of the theory later came under attack

for being both too weak and too strong. For some, the theory was too weak

since it failed to resolve all of the known paradoxes. For others, it was too

 strong since it disallowed many mathematical definitions which, although

consistent,

 violated the vicious circle principle. Russell's response was to introduce the

axiom of reducibility, an axiom that lessened the vicious circle principle's scope

of application, but which many people claimed was too ad hoc to be justified

philosophically.

 

 

Of equal significance during this period was Russell's defense of logicism, the theory

that mathematics was in some important sense reducible to logic. First defended in

his 1901 article "Recent Work on the Principles of Mathematics," and then later in

greater detail in his Principles of Mathematics and in Principia Mathematica,

Russell's logicism consisted of two main theses. The first was that all mathematical

truths can be translated into logical truths or, in other words, that the vocabulary

of mathematics constitutes a proper subset of that of logic. The second was that

all mathematical proofs can be recast as logical proofs or, in other words, that the

 theorems of mathematics constitute a proper subset of those of logic.

 

Like Gottlob Frege, Russell's basic idea for defending logicism was that numbers

may be identified with classes of classes and that number-theoretic statements may

be explained in terms of quantifiers and identity. Thus the number 1 would be

 identified with the class of all unit classes, the number 2 with the class of all

two-membered classes, and so on. Statements such as "There are two books"

would be recast as statements such as "There is a book, x, and there is a book, y,

and x is not identical to y." It followed that number-theoretic operations could be

explained in terms of set-theoretic operations such as intersection, union, and

difference. In Principia Mathematica, Whitehead and Russell were able to

provide many detailed derivations of major theorems in set theory, finite and

transfinite arithmetic, and elementary measure theory. A fourth volume was

planned but never completed.

 

Russell's most important writings relating to these topics include not only

Principles of Mathematics (1903), "Mathematical Logic as Based on the

 Theory of Types" (1908), and Principia Mathematica (1910, 1912, 1913),

but also his An Essay on the Foundations of Geometry (1897), and

Introduction to Mathematical Philosophy (1919).

 

Russell's Work in Analytic Philosophy

In much the same way that Russell used logic in an attempt to clarify issues in

the foundations of mathematics, he also used logic in an attempt to clarify issues

in philosophy. As one of the founders of analytic philosophy, Russell made

significant contributions to a wide variety of areas, including metaphysics,

epistemology, ethics and political theory, as well as to the history of philosophy.

Underlying these various projects was not only Russell's use of logical analysis,

but also his long-standing aim of discovering whether, and to what extent,

knowledge is possible. "There is one great question," he writes in 1911. "

Can human beings know anything, and if so, what and how? really the most essentially philosophical of all questions."[1]

book9.gif

This question is 

 

More than this, Russell's various contributions were also unified by his views

concerning both the centrality of scientific knowledge and the importance of

an underlying scientific methodology that is common to both philosophy and

science. In the case of philosophy, this methodology expressed itself through

Russell's use of logical analysis. In fact, Russell often claimed that he had

more confidence in his methodology than in any particular philosophical

conclusion.

 

Russell's conception of philosophy arose in part from his idealist origins.[2]

This is so, even though he believed that his one, true revolution in philosophy

came about as a result of his break from idealism. Russell saw that the idealist

doctrine of internal relations led to a series of contradictions regarding

asymmetrical (and other) relations necessary for mathematics. Thus, in 1898,

he abandoned the idealism that he had encountered as a student at Cambridge,

together with his Kantian methodology, in favour of a pluralistic realism.

As a result, he soon became famous as an advocate of the "new realism"

 and for his "new philosophy of logic," emphasizing as it did the importance

of modern logic for philosophical analysis. The underlying themes of this

"revolution," including his belief in pluralism, his emphasis upon

anti-psychologism, and the importance of science, remained central to Russell's

philosophy for the remainder of his life.[3]

 

 

Russell's methodology consisted of the making and testing of hypotheses

through the weighing of evidence (hence Russell's comment that he wished

to emphasize the "scientific method" in philosophy[4]), together with a rigorous

analysis of problematic propositions using the machinery of first-order logic.

It was Russell's belief that by using the new logic of his day, philosophers

would be able to exhibit the underlying "logical form" of natural language

 statements. A statement's logical form, in turn, would help philosophers

resolve problems of reference associated with the ambiguity and vagueness

of natural language. Thus, just as we distinguish three separate sense of "is"

 (the is of predication, the is of identity, and the is of existence) and exhibit

 these three senses by using three separate logical notations

(Px, x=y, and x respectively) we will also discover other ontologically

significant distinctions by being aware of a sentence's correct logical form.

On Russell's view, the subject matter of philosophy is then distinguished

from that of the sciences only by the generality and the a prioricity of

philosophical statements, not by the underlying methodology of the discipline.

In philosophy, as in mathematics, Russell believed that it was by applying

logical machinery and insights that advances would be made.

 

Russell's most famous example of his "analytic" method concerns denoting

phrases such as descriptions and proper names. In his

Principles of Mathematics, Russell had adopted the view that every denoting

phrase (for example, "Scott," "blue," "the number two," "the golden mountain")

denoted, or referred to, an existing entity. By the time his landmark article,

"On Denoting," appeared two years later, in 1905, Russell had modified this

extreme realism and had instead become convinced that denoting phrases

 need not possess a theoretical unity.

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