Bertrand Arthur William Russell
nació a la acostumbrada edad de 0 años el 18 de mayo de 1872, y murió
a la insólita edad de 97 años el 2 de febrero de 1970. Durante casi un
siglo vivió una vida asombrosamente rica y turbulenta, alcanzando fama
como filólogo y crítico social, como escritor y educador, como miembro
de la Cámara de los Lores y como interno de la cárcel de Brixton.
Enseñó en muchos de los más prestigiosos centros del mundo, desde
Cambridge hasta Harvard y Berkeley. Ganó un premio Nobel, se casó
cuatro veces y tuvo numerosas aventuras sentimentales. Fue
vilipendiado por su agnosticismo ateo y por su defensa del sexo extra
matrimonial. Una lista de las personas con las que trató a lo largo de
su vida es como un "Quién es quién" de la civilización occidental.
Una de las cosas sorprendentes de Russell era su
extraña mezcla de inconformidad y conformidad, de valores
tradicionales y chocante radicalismo. En algunos aspectos parecía en
gran manera un producto de la clase alta británica; en otros, parecía
un eterno enemigo de la sociedad establecida. Hay fotografías en que
aparece a la cabeza de manifestaciones
antibélicas vistiendo un traje con chaleco y reloj de bolsillo. Aunque
su promesa de "no respetar a las personas respetables" debió marcarle
como traidor a su clase social, Bertrand Russell tenía unos
antecedentes inigualablemente respetables
(1).
Su abuelo Jhon
Russell había sido primer ministro de la Reina Victoria de 1846 a 1852
y de nuevo de 1865 a 1866. Bertrand, que viviría lo suficiente para
ver a los humanos paseando por la Luna, recordaba cuando se sentaba en
las rodillas regias de Victoria durante las visitas de ésta a la
mansión de su abuelo. Claramente, el joven Bertie nació en los más
altos escalafones de la sociedad británica decimonónica.
Sin embargo, la vida puede resultar cruel incluso para los
poderosos. Russell perdió a sus padres a la edad de cuatro años. Como
consecuencia, fue criado por su abuela, quién decidió educarlo no en
la escuela, sino en casa con preceptores. El brillante y sensible
joven pasó así gran parte de su juventud entre viejos en la taciturna
mansión ancestral de Pembroke Lodge, privado de las alegrías
despreocupadas de la infancia. Según su propio relato, fue un joven
solitario y reprimido que pasó demasiado tiempo cavilando. Caviló
sobre el bien y el mal, y en más de una ocasión contempló la
posibilidad del suicidio.
Pero de esta infancia solitaria Russell comprendió una
lección que le acompañaría hasta el final de su vida. Se trataba del
pasaje bíblico favorito de su abuela -"No seguirás la multitud de los
que obran mal"-, palabras que servirían para caracterizar la vida de
Russell(2).
Llegado el
tiempo, Bertie dejó Pembroke Lodge y marchó al Trinity College, en
Cambridge, la misma institución que acogió al joven Isaac Newton, más
de dos siglos antes. Con su pobre preparación y su intensidad
intelectual, pasó por Cambridge como un bicho algo raro, aunque cuajó
bien en la vida académica y sobre todo las matemáticas cautivaron su
atención.
Fue un flechazo. Russell se vio tremendamente inepto para las
ciencias físicas o experimentales, pero las matemáticas -algo
impersonal que, en sus propias palabras, podía amar sin ser amado en
reciprocidad- se convirtieron en una obsesión. Para Russell, las
matemáticas ofrecían una única vía para la certeza y perfección. "Me
desagradaba el mundo real -confesaba-, y busqué refugio en el mundo
ucrónico, sin cambio ni corrupción ni el fuego fatuo del progreso"(3).
Con este espíritu, escribió
este ditirambo a las matemáticas, un tributo cuyo exceso está
atemperado sólo por la elocuencia:
La vida real, para la
mayoría de los hombres, es un perpetuo compromiso, en gran manera
secundario, entre lo ideal y lo posible; pero el mundo de la razón
pura no conoce compromisos, ni limitaciones prácticas, ni barreras
par ala actividad creativa que engloba en espléndidos edificios la
apasionada aspiración por lo perfecto de la que brotan todas las
grandes obras. Lejos de las personas buenas, lejos incluso de los
lastimosos hechos de la naturaleza, las generaciones han creado poco
a poco un cosmos ordenado, donde puede morar el pensamiento puro
como en su natural casa, y donde uno, al menos, de nuestros impulsos
más nobles puede escapar del triste exilio del mundo de los hechos(4).
Como se puede
barruntar de las palabras, los aspectos utilitarios de las matemáticas
tenían para Russell poco atractivo. Su pasión era por una suerte más
pura, más ascética, de razonamiento matemático. En su Introducción
a la Filosofía Matemática, Russell describía las dos grandes y
contrarias direcciones del pensamiento matemático: "La más familiar...
es constructiva, y va hacia una complejidad gradualmente creciente: de
los números enteros a las fracciones, números reales y números
complejos, de la suma y multiplicación a la diferenciación e
integración y a las matemáticas superiores. La otra dirección, menos
familiar, avanza... hasta una abstracción y simplicidad lógica cada
vez mayor"(5).
Esta otra dirección, el movimiento que se aleja
de las aplicaciones y complejidad y va hacia los fundamentos y la
simplicidad, caracterizaba para Russell a la filosofía matemática. Y
aquí es donde se encontraba intelectualmente en su casa.
Su trabajo sobre los fundamentos de las matemáticas fue
realizado en Cambridge, primero como estudiante y luego como un
miembro de Trinity College. En su empresa se le unió Alfred North
Whitehead, un reputado profesor de lógica cuya colaboración con
Russell se prolongaría durante décadas de disensiones académicas y
personales. Durante al verano de 1900, una época de "intoxicación
intelectual", Russell realizó importantes avances en lógica
matemática. Fue un período intenso y apasionante para el intelectual
de 28 años, quien más tarde recordaría que "empecé a mí mismo que por
fin ahora había hecho algo que valía la pena y era consciente de que
debía procurar no tirarme a la calle sin haberlo puesto por escrito"(6).
En 1903 Russell
publicó un libro de 500 páginas, Los principios de las matemáticas,
y más tarde él y Whitehead escribieron los enormes tres volúmenes de
los Principia Mathematica que aparecieron en 1910, 1912 y 1913.
Éste fue su intento definitivo de reducir todas las matemáticas a las
ideas básicas e irrefutables de la lógica. Los Principia
estaban tan llenos de símbolos lógicos con exclusión de palabras
inglesas que el historiador de las matemáticas, Ivor Grattan-Guinness
describió acertadamente una página típica como si fuera semejante a
"papel pintado"(7).
La implacable
exactitud de estos volúmenes agotó las reservas de Russell, Whitehead
y , posiblemente de cualquiera con la paciencia de leerlos. También
arruinó sus bolsillo, pues poquísimos lectores decidieron comprar una
publicación tan horrorosa. "Ganamos cada uno menos de 50 libras en 10
años", confesó Russell(8).
Pero lo peor es que no está claro que Russell y Whitehead hubieran
logrado su misión de reducir todas las matemáticas a la lógica. Lo que
estaba claro era que habían producido una obra que sondeó los
fundamentos de las matemáticas hasta profundidades inigualadas.
En vísperas de la Primera Guerra Mundial, el cuarentón
Bertrand Russell había establecido una marca en la filosofía
matemática. Cualquier coetáneo podía haber sospechado que Russell
pasaría sus restantes años explorando más a fondo arcanos teoremas de
la lógica. Pero esa sospecha había sido infundada, ya que la vida de
Russell estaba a punto de desplazarse en notables e inesperadas
direcciones.
Muchas fuerzas, internas y externas, le impulsaron, pero la
más importante de ellas fue la insensatez de la Primera Guerra
Mundial. Russell, al igual que muchos intelectuales británicos,
observó cómo una generación entera de jóvenes fue barrida en la
carnicería bélica. Repentinamente, la marcha de los símbolos lógicos
por una página perdió su importancia. Confesó que, frente a la guerra,
"el trabajo que he realizado es muy pequeño e irrelevante para este
mundo en el que nos encontramos viviendo"(9).
Bertrand Russell
se zambulló en la refriega. Su activismo antibélico le llevó a ser
detenido en 1916 y despedido de Cambridge con pérdida de su pasaporte.
Esto último le costó perder un puesto es Harvard que andaba esperando.
Pero nada de esto silenció sus denuncias mordaces de un esfuerzo de
guerra que cada día era más trágico, por lo que resultaba inevitable
que sobreviniera un conflicto posterior que estaba latente. Esto
ocurrió en 1918, cuando Russell fue detenido de nuevo y encarcelado
durante 6 meses en la prisión de Brixton. El vástago de la nobleza se
convirtió así en un preso de conciencia.
Pero no fue sólo su postura antibélica la que le acarreó
dificultades con la clase dirigente británica. Al menos tuvo otros dos
posicionamientos en contra de valores tradicionales. Uno fue su
agnosticismo público. Russell criticó no sólo ciertas religiones, sino
la religión en general. Era una persona que creía de todo en la
supremacía de la razón y consideraba que la teología conducía a la
humanidad en direcciones contradictorias e infortunadas. Sus denuncias
eran cortantes, poderosas y violentas. Escribió, por ejemplo, que
"cuanto más intensa había sido la religión en un período cualquiera y
más profundo había sido el pensamiento dogmático, tanto mayor había
sido la crueldad"(10).
Atacaba a la Iglesia Católica regularmente por
su prohibición del control de natalidad, y fue poco más amable con las
otras denominaciones cristianas. A los que veían la mano de Dios en el
diseño de nuestro universo, preguntaba Russell: "¿Pensáis que si se os
concediera la omnipotencia y la omnisciencia y millones de años para
perfeccionar vuestro mundo, no habríais producido algo mejor que el Ku
Klux Klan o los Fascistas?"(11).
Sus puntos de vista se pueden resumir en sus
respuestas a la pregunta de qué es lo que a él particularmente le
gustaba de este mundo: "Las matemáticas y el mar, y la teología y la
heráldica, las dos primeras cosas porque son humanas, las dos últimas
porque son absurdas"(12).
Quizá es posible que, cuando se anunció que
había muerto en un viaje a China, una revista religiosa publicara en
un editorial poco caritativo que "a los misioneros se les podía
perdonar el que hayan suspirado aliviados al oír las noticias de la
muerte del señor Russell"(13).
Pero si sus
opiniones religiosas fueron controvertidas, también lo fueron sus
opiniones sobre el sexo y el matrimonio. Había poco fundamento en
estricta educación para predecir tamaña heterodoxia. A los 22 años se
casó con Alys Pearsall Smith, una cuáquera americana que vivía en
Inglaterra. Alys insistió en contraer un matrimonio según el rito
cuáquero, a lo que accedió Bertie con su tacto característico: "No te
vayas a creer que realmente me importa una ceremonia religiosa...;
Cualquier ceremonia religiosa me fastidia"(14).
Al principio, su
matrimonio prometía ser eterno, pero en cuestiones del corazón
Bertrand Russell tenía poca estabilidad. Un día a comienzos de 1902,
mientras paseaba en bicicleta cerca de Cambridge, Russell se dio
cuenta de que no amaba a su esposa.
Al constatar esto, inició una serie de aventuras románticas
que abarcarían medio siglo y que enredaría a este hombre lógico en un
comportamiento que pareció a todo el mundo abiertamente irrazonable.
Al parecer se encaprichó de Evelyn Whitehead, la esposa de la persona
con la que estaba escribiendo los Principia Mathematica. Tuvo
una larga y duradera aventura con Lady Ottoline Morrell, una dama muy
conocida de la alta sociedad inglesa y esposa de un político
prominente. Tuvieron numerosos encuentros clandestinos en habitaciones
de oscuros hoteles. Todo ello resultaba totalmente indecoroso para una
persona de talla internacional.
Mientras todo esto ocurría, se divorció de Alys y se casó con
Dora Black en 1912. Sobre el papel, su matrimonio duró hasta 1935,
pero en 1929 Russell escribía de su segunda mujer: "Ni ella ni yo
hacíamos ningún fingimiento de fidelidad conyugal"(15).
En estas circunstancias, apenas pudo resultar sorprendente que Dora
tuviera un hijo de otro en 1930. pero cuando tuvo un segundo niño con
el mismo hombre, aquello fue bastante para Russell, quien pidió el
divorcio.
Esto preparó el camino para su tercer matrimonio con Helen
Patricia Spence, que duró de 1936 hasta 1952. Entonces, a la edad de
80 años se casó con Edith Finch, una profesora de inglés en Bryn Mawr,
y así encontró una compañera con la que pudo pasar felizmente sus
últimos años.
Tal conducta dentro y fuera del matrimonio reportó a Bertrand
Russell numerosas situaciones comprometidas, especialmente porque
siempre estaba dispuesto a discutir sus puntos de vista sobre el sexo,
la castidad, la contracepción y temas semejantes. En 1940, en un
célebre caso se le excluyó de un puesto de profesor en el City
College de Nueva York por orden de la comunidad religiosa y el alcalde
Fiorello LaGuardia. Se dijo que Russell no era apto para enseñar, ya
que sus puntos de vista se oponían a la religión y aprobaba la
promiscuidad. Con claro espíritu de clase, observó en cierta ocasión
que los matemáticos enamorados eran iguales que cualquier otro
enamorado "excepto, quizá, en que el ocio de la razón los hace ser
apasionados hasta el exceso"(16).
Bertrand Russell claramente pasó ocioso un tiempo considerable.
Pero también pasó trabajando un tiempo considerable. Durante
estos años de controversias siguió siendo un escritor prolífico, que
produjo volúmenes de crítica social, tratados de educación e incluso
artículos periodísticos de divulgación. Parece un poco incongruente, y
sin embargo este activista social se encontró escribiendo de vez en
cuando para la revista Glamour y apareciendo como un famoso
invitado en un programa de radio de la BBC. Parte de su aceptación
popular de debió al hecho de que, a pesar de sus puntos de vista,
Bertrand Russell fue una personalidad genuinamente fascinante. En
parte fue debido indudablemente al hecho de que sobrevivió a sus
enemigos.
Otros dos aspectos de su vida merecen mencionarse. Uno fue su
permanente disgusto por el sistema político comunista. En un tiempo en
el que muchos intelectuales aplaudieron el ascenso del comunismo como
la salvación de la humanidad, Russell, como de costumbre, nadó contra
corriente. Sobre unos bases puramente intelectuales, dio dos sucintas
razones para oponerse a la filosofía de Karl Marx: "una, que era
confuso, y la otra, que su pensamiento estaba casi enteramente
inspirado en el odio"(17).
El desdén de
Russell por el comunismo iba derecho a sus fuentes, ya que había
conocido a Lenin personalmente durante una visita a Moscú en 1920 y
había vuelto decepcionado. Su juicio fue tan severo como el del más
duro político occidental cuando describía el estado soviético como "un
asilo de lunáticos homicidas donde los celadores son los peores"(18).
Durante la Segunda Guerra Mundial, que
personalmente apoyó, se preguntaba si el enemigo de Inglaterra Hitler
era realmente peor que su aliado Stalin.
El otro rasgo sorprendente de Russell fue sus dotes como
escritor. Como se ha dicho. escribió sobre muy diversos temas. Pero
bien fueran temas filosóficos (por ejemplo, "Nuestro conocimiento del
mundo externo como un campo para el método científico en filosofía") o
tratados críticos ( por ejemplo, "Un esbozo de las tonterías
intelectuales") o livianos relatos populares (por ejemplo, "Si te
enamoras de un hombre casado"), su escritura era fresca, provocadora y
comprometedora.
Y su estilo tenía un instinto innegable, aunque
particularmente teñido con un toque de su mordaz sarcasmo. Cuando
escribía sobre la clasificación de la gula como pecado, Russell
reflexionaba: "Es un cierto pecado vago, pues es difícil decir dónde
el interés legítimo por el alimento cesa y se empieza a incurrir en
culpa. ¿Es malo comer algo nutritivo? En ese caso, caeríamos en un
riesgo de condenarnos cada vez que comemos una almendra salada"(19).
Ridiculizaba a los defensores de los derechos
de los animales cuando escribía: "Un igualitario decidido... se verá
forzado a considerar a los monos iguales a los seres humanos. ¿Y por
qué pararse en los monos? No sé cómo va a oponerse a una razón a favor
del voto de las ostras"(20).
Y una vez difirió
la escritura de una autobiografía porque: "Tengo una cierta vacilación
a empezar... demasiado pronto... por miedo de que algo importante no
haya sucedido todavía. Supongamos que terminara mis días como
presidente de México; la biografía parecería incompleta si no
mencionara este hecho"(21).
Su talento para
la escritura fue reconocido de la manera más pública imaginable
cuando Bertrand Russell recibió el Premio Novel de Literatura en 1950.
Pero, al describir su fórmula para escribir con éxito, Russell dejaba
desazonados a los profesores de redacción:
Mi profesor me dio varias
reglas sencillas, de las que sólo recuerdo dos: "Pon una coma cada
dos palabras y nunca uses ''y'' excepto al principio de una
sentencia". Su consejo más enfático era que siempre había que
reescribir. Lo intenté a conciencia, pero me encontré mi primer
borrador era casi siempre mejor que el segundo. Este descubrimiento
me ha ahorrado una enorme cantidad de tiempo(22).
A lo largo de su
vida, desde sus investigaciones matemáticas hasta su encarcelamiento,
desde sus numerosas aventuras amorosas hasta su Premio Nobel, Russell
se codeó con una notable serie de personas interesantes e influyentes.
Su padrino fue Jhon Stuart Mill. Hemos dicho que en una ocasión se
sentó en las rodillas de la Reina Victoria. Más tarde gozó de la
amistad de Jhon Maynard Keynes, William James y H. G. Wells. Conoció a
los escritores Beatrix Potter, D. H. Lawrence, George Bernad Shaw,
Joseph Conrad, Aldous Hexley y Rabindranath Tagore. Discípulo suyos
fueron Ludwing Wittgenstein y T. S. Eliot. En Rusia entrevistó a Lenin
y Trotsky. Y cuenta que a sus clases de 1920 en Pekín asistieron dos
jóvenes notablemente radicales,
Mao Tse-Tung y Cho En-lai. Tuvo numerosos amigos, desde Albert
Einstein hasta Peter Sellers y Winston Churchill. Con respecto a éste
último, contaba Russell que una noche cenando en una fiesta "Winston
me pidió me pidió que explicara el cálculo diferencial en dos
palabras, lo que hice a su satisfacción"(23).
Y por si estas
relaciones con los grandes no fueran adecuadas, Russell ocupó en el
Trinity College las habitaciones en las que en otro tiempo residió
Isaac Newton. Aunque temperamentalmente Russell y Newton no podían ser
más diferentes, estos dos ingleses tuvieron cada uno una inteligencia
enormemente poderosa y los dos hicieron avanzar las matemáticas de su
tiempo hasta nuevas fronteras
Stanford
Encyclopedia of Philosophy
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.
Interested readers may also wish to listen to
two sound clips of Russell speaking.
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 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).
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? This question is really the most
essentially philosophical of all questions."[1]
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.
While logically proper names (words such as "this"
or "that" which refer to sensations of which an agent is immediately
aware) do have referents associated with them, descriptive phrases (such
as "the smallest number less than pi") should be viewed as a
collection of quantifiers (such as "all" and "some") and propositional
functions (such as "x is a number"). As such, they are not to
be viewed as referring terms but, rather, as "incomplete symbols." In
other words, they should be viewed as symbols that take on meaning
within appropriate contexts, but that are meaningless in isolation.
Thus, in the sentence
(1) The present King of France is bald,
the definite description "The present King of France"
plays a role quite different from that of a proper name such as "Scott"
in the sentence
(2) Scott is bald.
Letting K abbreviate the predicate "is a
present King of France" and B abbreviate the predicate "is
bald," Russell assigns sentence (1) the logical form
(1′) There is an x such that (i) Kx,
(ii) for any y, if Ky then y=x, and (iii)
Bx.
Alternatively, in the notation of the predicate
calculus, we have
(1″) ∃x[(Kx & ∀y(Ky
→ y=x)) & Bx].
In contrast, by allowing s to abbreviate
the name "Scott," Russell assigns sentence (2) the very different
logical form
(2′) Bs.
This distinction between various logical forms
allows Russell to explain three important puzzles. The first concerns
the operation of the Law of Excluded Middle and how this law relates
to denoting terms. According to one reading of the Law of Excluded
Middle, it must be the case that either "The present King of France is
bald" is true or "The present King of France is not bald" is true. But
if so, both sentences appear to entail the existence of a present King
of France, clearly an undesirable result. Russell's analysis shows how
this conclusion can be avoided. By appealing to analysis (1′), it
follows that there is a way to deny (1) without being committed to the
existence of a present King of France, namely by accepting that "It is
not the case that there exists a present King of France who is bald"
is true.
The second puzzle concerns the Law of Identity as it
operates in (so-called) opaque contexts. Even though "Scott is the
author of Waverley" is true, it does not follow that the
two referring terms "Scott" and "the author of Waverley"
are interchangeable in every situation. Thus although "George IV
wanted to know whether Scott was the the author of Waverley"
is true, "George IV wanted to know whether Scott was Scott" is,
presumably, false. Russell's distinction between the logical forms
associated with the use of proper names and definite descriptions
shows why this is so.
To see this we once again let s abbreviate
the name "Scott." We also let w abbreviate "Waverley"
and A abbreviate the two-place predicate "is the author of."
It then follows that the sentence
(3) s=s
is not at all equivalent to the sentence
(4) ∃x[Axw & ∀y(Ayw
→ y=x) & x=s].
The third puzzle relates to true negative
existential claims, such as the claim "The golden mountain does not
exist." Here, once again, by treating definite descriptions as having
a logical form distinct from that of proper names, Russell is able to
give an account of how a speaker may be committed to the truth of a
negative existential without also being committed to the belief that
the subject term has reference. That is, the claim that Scott does not
exist is false since
(5) ~∃x(x=s)
is self-contradictory. (After all, there must exist
at least one thing that is identical to s since it is a
logical truth that s is identical to itself!) In contrast,
the claim that a golden mountain does not exist may be true since,
assuming that G abbreviates the predicate "is golden" and
M abbreviates the predicate "is a mountain," there is nothing
contradictory about
(6) ~∃x(Gx & Mx).
Russell's emphasis upon logical analysis also had
consequences for his metaphysics. In response to the traditional
problem of the external world which, it is claimed, arises since the
external world can be known only by inference, Russell developed his
famous 1910 distinction between "knowledge by acquaintance and
knowledge by description." He then went on, in his 1918 lectures on
logical atomism, to argue that the world itself consists of a complex
of logical atoms (such as "little patches of colour") and their
properties. Together they form the atomic facts which, in turn, are
combined to form logically complex objects. What we normally take to
be inferred entities (for example, enduring physical objects) are then
understood to be "logical constructions" formed from the immediately
given entities of sensation, viz., "sensibilia." It is only these
latter entities that are known non-inferentially and with certainty.
According to Russell, the philosopher's job is to
discover a logically ideal language that will exhibit the true nature
of the world in such a way that the speaker will not be misled by the
casual surface structure of natural language. Just as atomic facts (the
association of universals with an appropriate number of individuals)
may be combined into molecular facts in the world itself, such a
language would allow for the description of such combinations using
logical connectives such as "and" and "or." In addition to atomic and
molecular facts, Russell also held that general facts (facts about "all"
of something) were needed to complete the picture of the world.
Famously, he vacillated on whether negative facts were also required.
Russell's most important writings relating to these
topics include not only "On Denoting" (1905), but also his "Knowledge
by Acquaintance and Knowledge by Description" (1910), "The Philosophy
of Logical Atomism" (1918, 1919), "Logical Atomism" (1924), The
Analysis of Mind (1921), and The Analysis of Matter
(1927).
Russell's social influence stems from three main
sources: his long-standing social activism, his many writings on the
social and political issues of his day, and his popularizations of
technical writings in philosophy and the natural sciences.
Among Russell's many popularizations are his two
best selling works, The Problems of Philosophy (1912) and
A History of Western Philosophy (1945). Both of these
books, as well as his numerous but less famous books popularizing
science, have done much to educate and inform generations of general
readers. Naturally enough, Russell saw a link between education, in
this broad sense, and social progress. At the same time, Russell is
also famous for suggesting that a widespread reliance upon evidence,
rather than upon superstition, would have enormous social consequences:
"I wish to propose for the reader's favourable consideration," says
Russell, "a doctrine which may, I fear, appear wildly paradoxical and
subversive. The doctrine in question is this: that it is undesirable
to believe a proposition when there is no ground whatever for
supposing it true."[5]
Still, Russell is best known in many circles as a
result of his campaigns against the proliferation of nuclear weapons
and against western involvement in the Vietnam War during the 1950s
and 1960s. However, Russell's social activism stretches back at least
as far as 1910, when he published his Anti-Suffragist Anxieties,
and to 1916, when he was convicted and fined in connection with anti-war
protests during World War I. Following his conviction, he was also
dismissed from his post at Trinity College, Cambridge. Two years later,
he was convicted a second time. The result was six months in prison.
Russell also ran unsuccessfully for Parliament (in 1907, 1922, and
1923) and, together with his second wife, founded and operated an
experimental school during the late 1920s and early 1930s.
Although he became the third Earl Russell upon the
death of his brother in 1931, Russell's radicalism continued to make
him a controversial figure well through middle-age. While teaching in
the United States in the late 1930s, he was offered a teaching
appointment at City College, New York. The appointment was revoked
following a large number of public protests and a 1940 judicial
decision which found him morally unfit to teach at the College.
In 1954 he delivered his famous "Man's Peril"
broadcast on the BBC, condemning the Bikini H-bomb tests. A year later,
together with Albert Einstein, he released the Russell-Einstein
Manifesto calling for the curtailment of nuclear weapons. In 1957 he
was a prime organizer of the first Pugwash Conference, which brought
together a large number of scientists concerned about the nuclear
issue. He became the founding president of the Campaign for Nuclear
Disarmament in 1958 and was once again imprisoned, this time in
connection with anti-nuclear protests in 1961. The media coverage
surrounding his conviction only served to enhance Russell's reputation
and to further inspire the many idealistic youths who were sympathetic
to his anti-war and anti-nuclear protests.
During these controversial years Russell also wrote
many of the books that brought him to the attention of popular
audiences. These include his Principles of Social Reconstruction
(1916), A Free Man's Worship (1923), On Education
(1926), Why I Am Not a Christian (1927), Marriage
and Morals (1929), The Conquest of Happiness
(1930), The Scientific Outlook (1931), and Power: A
New Social Analysis (1938).
Upon being awarded the Nobel Prize for Literature in
1950, Russell used his acceptance speech to emphasize, once again,
themes related to his social activism.
- (1901) "Recent Work on the Principles of
Mathematics," International Monthly, 4, 83-101. Repr.
as "Mathematics and the Metaphysicians" in Russell, Bertrand,
Mysticism and Logic, London: Longmans Green, 1918, 74-96.
- (1905) "On Denoting," Mind, 14,
479-493. Repr. in Russell, Bertrand, Essays in Analysis,
London: Allen and Unwin, 1973, 103-119.
- (1908) "Mathematical Logic as Based on the Theory
of Types," American Journal of Mathematics, 30,
222-262. Repr. in Russell, Bertrand, Logic and Knowledge,
London: Allen and Unwin, 1956, 59-102, and in van Heijenoort, Jean,
From Frege to Gödel, Cambridge, Mass.: Harvard
University Press, 1967, 152-182.
- (1910) "Knowledge by Acquaintance and Knowledge
by Description," Proceedings of the Aristotelian Society,
11, 108-128. Repr. in Russell, Bertrand, Mysticism and Logic,
London: Allen and Unwin, 1963, 152-167.
- (1912) "On the Relations of Universals and
Particulars," Proceedings of the Aristotelian Society,
12, 1-24. Repr. in Russell, Bertrand, Logic and Knowledge,
London: Allen and Unwin, 1956, 105-124.
- (1918, 1919) "The Philosophy of Logical Atomism,"
Monist, 28, 495-527; 29, 32-63, 190-222, 345-380. Repr.
in Russell, Bertrand, Logic and Knowledge, London:
Allen and Unwin, 1956, 177-281.
- (1924) "Logical Atomism," in Muirhead, J.H.,
Contemporary British Philosophers, London: Allen and
Unwin, 1924, 356-383. Repr. in Russell, Bertrand, Logic and
Knowledge, London: Allen and Unwin, 1956, 323-343.
- (1896) German Social Democracy,
London: Longmans, Green.
- (1897) An Essay on the Foundations of
Geometry, Cambridge: At the University Press.
- (1900) A Critical Exposition of the
Philosophy of Leibniz, Cambridge: At the University Press.
- (1903) The Principles of Mathematics,
Cambridge: At the University Press.
- (1910, 1912, 1913) (with Alfred North Whitehead)
Principia Mathematica, 3 vols, Cambridge: Cambridge
University Press. Second edition, 1925 (Vol. 1), 1927 (Vols 2, 3).
Abridged as Principia Mathematica to *56, Cambridge:
Cambridge University Press, 1962.
- (1912) The Problems of Philosophy,
London: Williams and Norgate; New York: Henry Holt and Company.
- (1914) Our Knowledge of the External World,
Chicago and London: The Open Court Publishing Company.
- (1916) Principles of Social Reconstruction,
London: George Allen and Unwin. Repr. as Why Men Fight,
New York: The Century Company, 1917.
- (1917) Political Ideals, New York:
The Century Company.
- (1919) Introduction to Mathematical
Philosophy, London: George Allen and Unwin; New York: The
Macmillan Company.
- (1921) The Analysis of Mind, London:
George Allen and Unwin; New York: The Macmillan Company.
- (1923) A Free Man's Worship,
Portland, Maine: Thomas Bird Mosher. Repr. as What Can A Free
Man Worship?, Girard, Kansas: Haldeman-Julius Publications,
1927.
- (1926) On Education, Especially in Early
Childhood, London: George Allen and Unwin. Repr. as
Education and the Good Life, New York: Boni and Liveright,
1926. Abridged as Education of Character, New York:
Philosophical Library, 1961.
- (1927) The Analysis of Matter,
London: Kegan Paul, Trench, Trubner; New York: Harcourt, Brace.
- (1927) An Outline of Philosophy,
London: George Allen and Unwin. Repr. as Philosophy,
New York: W.W. Norton, 1927.
- (1927) Why I Am Not a Christian,
London: Watts, New York: The Truth Seeker Company.
- (1928) Sceptical Essays, New York:
Norton.
- (1929) Marriage and Morals, London:
George Allen and Unwin; New York: Horace Liveright.
- (1930) The Conquest of Happiness,
London: George Allen and Unwin; New York: Horace Liveright.
- (1931) The Scientific Outlook,
London: George Allen and Unwin; New York: W.W. Norton.
- (1938) Power: A New Social Analysis,
London: George Allen and Unwin; New York: W.W. Norton.
- (1940) An Inquiry into Meaning and Truth,
London: George Allen and Unwin; New York: W.W. Norton.
- (1945) A History of Western Philosophy,
New York: Simon and Schuster; London: George Allen and Unwin, 1946.
- (1948) Human Knowledge: Its Scope and
Limits, London: George Allen and Unwin; New York: Simon and
Schuster.
- (1949) Authority and the Individual,
London: George Allen and Unwin; New York: Simon and Schuster.
- (1949) The Philosophy of Logical Atomism,
Minneapolis, Minnesota: Department of Philosophy, University of
Minnesota. Repr. as Russell's Logical Atomism, Oxford:
Fontana/Collins, 1972.
- (1954) Human Society in Ethics and Politics,
London: George Allen and Unwin; New York: Simon and Schuster.
- (1959) My Philosophical Development,
London: George Allen and Unwin; New York: Simon and Schuster.
- (1967, 1968, 1969) The Autobiography of
Bertrand Russell, 3 vols, London: George Allen and Unwin;
Boston and Toronto: Little Brown and Company (Vols 1 and 2), New
York: Simon and Schuster (Vol. 3).
- (1910) Philosophical Essays, London:
Longmans, Green.
- (1918) Mysticism and Logic and Other Essays,
London and New York: Longmans, Green. Repr. as A Free Man's
Worship and Other Essays, London: Unwin Paperbacks, 1976.
- (1928) Sceptical Essays, London:
George Allen and Unwin; New York: W.W. Norton.
- (1935) In Praise of Idleness, London:
George Allen and Unwin; New York: W.W. Norton.
- (1950) Unpopular Essays, London:
George Allen and Unwin; New York: Simon and Schuster.
- (1956) Logic and Knowledge: Essays,
1901-1950, London: George Allen and Unwin; New York: The
Macmillan Company.
- (1956) Portraits From Memory and Other
Essays, London: George Allen and Unwin; New York: Simon and
Schuster.
- (1957) Why I am Not a Christian and Other
Essays on Religion and Related Subjects, London: George Allen
and Unwin; New York: Simon and Schuster.
- (1961) The Basic Writings of Bertrand
Russell, 1903-1959, London: George Allen and Unwin; New York:
Simon and Schuster.
- (1969) Dear Bertrand Russell, London:
George Allen and Unwin; Boston: Houghton Mifflin.
- (1973) Essays in Analysis, London:
George Allen and Unwin.
- (1992) The Selected Letters of Bertrand
Russell, London: Penguin Press.
The Bertrand Russell Editorial Project is currently
in the process of publishing Russell's Collected Papers.
When complete, these volumes will bring together all of Russell's
writings, excluding his correspondence and previously published
monographs.
In Print
- Vol. 1: Cambridge Essays, 1888-99,
London, Boston, Sydney: George Allen and Unwin, 1983.
- Vol. 2: Philosophical Papers, 1896-99,
London and New York: Routledge, 1990.
- Vol. 3: Toward the Principles of
Mathematics, London and New York: Routledge, 1994.
- Vol. 4: Foundations of Logic, 1903-05,
London and New York: Routledge, 1994.
- Vol. 6: Logical and Philosophical Papers,
1909-13, London and New York: Routledge, 1992.
- Vol. 7: Theory of Knowledge: The 1913
Manuscript, London, Boston, Sydney: George Allen and Unwin,
1984.
- Vol. 8: The Philosophy of Logical Atomism
and Other Essays, 1914-19, London: George Allen and Unwin,
1986.
- Vol. 9: Essays on Language, Mind and Matter,
1919-26, London: Unwin Hyman, 1988.
- Vol. 10: A Fresh Look at Empiricism,
1927-42, London and New York: Routledge, 1996.
- Vol. 11: Last Philosophical Testament,
1943-68, London and New York: Routledge, 1997.
- Vol. 12: Contemplation and Action, 1902-14,
London, Boston, Sydney: George Allen and] Unwin, 1985.
- Vol. 13: Prophecy and Dissent, 1914-16,
London: Unwin Hyman, 1988.
- Vol. 14: Pacifism and Revolution, 1916-18,
London and New York: Routledge, 1995.
- Vol. 15: Uncertain Paths to Freedom: Russia
and China, 1919-1922, London and New York: Routledge, 2000.
- Vol. 28: Man's Peril, 1954-56,
London and New York: Routledge, 2003
Planned and Forthcoming
- Vol. 5: Toward Principia Mathematica,
1906-08.
- Vol. 16: Labour and Internationalism,
1922-24.
- Vol. 17: Behaviourism and Education,
1925-28.
- Vol. 18: Science, Sex and Society, 1929-31.
- Vol. 19: Fascism and Other Depression
Legacies, 1931-33.
- Vol. 20: Fascism and Other Depression
Legacies, 1933-34.
- Vol. 21: How to Keep the Peace: The
Pacifist Dilemma, 1934-36.
- Vol. 22: The Superior Virtue of the
Oppressed and Other Essays, 1936-39.
- Vol. 23: The Problems of Democracy,
1940-44.
- Vol. 24: Civilization and the Bomb,
1944-47.
- Vol. 25: Civilization and the Bomb,
1948-50.
- Vol. 26: Respectability at Last, 1950-51.
- Vol. 27: Respectability at Last, 1952-53.
- Vol. 29: "Détente" or Destruction, 1955-57.
- Vol. 30: The Campaign for Nuclear
Disarmament, 1957-60.
- Vol. 31: A New Plan for Peace and Other
Essays, 1960-64.
- Vol. 32: The Vietnam Campaign, 1965-70.
- Vol. 33: Newly Discovered Papers.
- Vol. 34: Indexes.
- Broad, C.D. (1973) "Bertrand Russell, as
Philosopher," Bulletin of the London Mathematical Society,
5, 328-341.
- Carnap, Rudolf (1931) "The Logicist Foundations
of Mathematics," Erkenntnis, 2, 91-105. Repr. in
Benacerraf, Paul, and Hilary Putnam (eds), Philosophy of
Mathematics, 2nd ed., Cambridge: Cambridge University Press,
1983, 41-52; in Klemke, E.D. (ed.), Essays on Bertrand Russell,
Urbana: University of Illinois Press, 1970, 341-354; and in Pears,
David F. (ed.), Bertrand Russell: A Collection of Critical
Essays, Garden City, New York: Anchor Books, 1972, 175-191.
- Church, Alonzo (1976) "Comparison of Russell's
Resolution of the Semantical Antinomies with That of Tarski,"
Journal of Symbolic Logic, 41, 747-760. Repr. in A.D. Irvine,
Bertrand Russell: Critical Assessments, vol. 2, New York
and London: Routledge, 1999, 96-112.
- Church, Alonzo (1974) "Russellian Simple Type
Theory," Proceedings and Addresses of the American Philosophical
Association, 47, 21-33.
- Gandy, R.O. (1973) "Bertrand Russell, as
Mathematician," Bulletin of the London Mathematical Society,
5, 342-348.
- Gödel, Kurt (1944) "Russell's Mathematical Logic,"
in Schilpp, Paul Arthur (ed.), The Philosophy of Bertrand
Russell, 3rd ed., New York: Tudor, 1951, 123-153. Repr. in
Benacerraf, Paul, and Hilary Putnam (eds), Philosophy of
Mathematics, 2nd ed., Cambridge: Cambridge University Press,
1983, 447-469; and in Pears, David F. (ed.) (1972) Bertrand
Russell: A Collection of Critical Essays, Garden City, New
York: Anchor Books, 192-226.
- Hylton, Peter W. (1990) "Logic in Russell's
Logicism," in Bell, David, and Neil Cooper (eds), The Analytic
Tradition: Philosophical Quarterly Monographs, Vol. 1,
Cambridge: Blackwell, 137-172.
- Irvine, A.D. (1989) "Epistemic Logicism and
Russell's Regressive Method," Philosophical Studies,
55, 303-327.
- Irvine, A.D. (1996) "Bertrand Russell and
Academic Freedom," Russell, n.s.16, 5-36.
- Kaplan, David (1970) "What is Russell's Theory of
Descriptions?," in Yourgrau, Wolfgang, and Allen D. Breck, (eds),
Physics, Logic, and History, New York: Plenum, 277-288.
Repr. in Pears, David F. (ed.), Bertrand Russell: A Collection
of Critical Essays, Garden City, New York: Anchor Books,
1972, 227-244.
- Lycan, William (1981) "Logical Atomism and
Ontological Atoms," Synthese, 46, 207-229.
- Monro, D.H. (1960) "Russell's Moral Theories,"
Philosophy, 35, 30-50. Repr. in Pears, David F. (ed.),
Bertrand Russell: A Collection of Critical Essays,
Garden City, New York: Anchor Books, 1972, 325-355.
- Putnam, Hilary (1967) "The Thesis that
Mathematics is Logic," in Schoenman, Ralph (ed.), Bertrand
Russell: Philosopher of the Century, London: Allen and Unwin,
273-303. Repr. in Putnam, Hilary, Mathematics, Matter and
Method, Cambridge: Cambridge University Press, 1975, 12-42.
- Quine, W.V. (1938) "On the Theory of Types,"
Journal of Symbolic Logic, 3, 125-139.
- Ramsey, F.P. (1926) "Mathematical Logic,"
Mathematical Gazette, 13, 185-194. Repr. in Ramsey, Frank
Plumpton, The Foundations of Mathematics, London: Kegan
Paul, Trench, Trubner, 1931, 62-81; in Ramsey, Frank Plumpton,
Foundations, London: Routledge and Kegan Paul, 1978, 213-232;
and in Ramsey, Frank Plumpton, Philosophical Papers,
Cambridge: Cambridge University Press, 1990, 225-244.]
- Schultz, Bart (1992) "Bertrand Russell in Ethics
and Politics," Ethics, 102, 594-634.
- Strawson, Peter F. (1950) "On Referring,"
Mind, 59, 320-344. Repr. in Flew, Anthony (ed.), Essays
in Conceptual Analysis, London: Macmillan, 1960, 21-52, and
in Klemke, E.D. (ed.), Essays on Bertrand Russell,
Urbana: University of Illinois Press, 1970, 147-172.
- Urquhart, Alasdair (1988) "Russell's Zig-Zag Path
to the Ramified Theory of Types," Russell, 8, 82-91.
- Weitz, Morris (1944) "Analysis and the Unity of
Russell's Philosophy," in Schilpp, Paul Arthur (ed.), The
Philosophy of Bertrand Russell, 3rd ed., New York: Tudor,
1951, 55-121.
- Blackwell, Kenneth (1985) The Spinozistic
Ethics of Bertrand Russell, London: George Allen and Unwin.
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