Bertrand Arthur William Russell (1872 - 1970)

Russell was born into the Whig aristocracy and inherited many of the values of its most radical wing. His grandfather, a prominent Whig reformer of the 1830s, had twice been prime minister. Russell was orphaned before he was 4 and was brought up by his grandmother who had him educated at home. In 1890 he went to Trinity College, Cambridge, to study mathematics. He gained a first in mathematics in 1893 and then turned to philosophy for his fourth year.

In 1894 he married Alys Pearsall Smith and spent part of his honeymoon in Berlin working on his first book, German Social Democracy (1896). The following year he published An Essay on the Foundations of Geometry, a revised version of his dissertation for which he had been awarded a six-year fellowship at Trinity. This was the first of a projected series of books on the sciences. After some aborted work on physics, he turned to pure mathematics and logic, producing many of his most important contributions in the period to 1913. While doing so, he lived mainly off unearned income, but in 1910, his capital depleted, he took up a lectureship at Trinity where he taught until 1916.

Though Russell had been born with an interest in politics, it had not hitherto occupied much of his time (despite his study of the German Marxists and vigorous interventions on behalf of free trade and women's suffrage). With the outbreak of war in 1914, however, his interest in philosophy lessened and he threw himself into writing, speaking and organizing on behalf of the pacifists. A conviction under the Defence of the Realm Act led to his dismissal from Trinity in 1916; a further conviction led to his being jailed in 1918. After 1916 he had only relatively short periods of academic employment and was dependent upon writing to make his living – a fact which only partially explains his huge subsequent output.

After the war he visited Russia to see the work of the Bolshevik government, but was disillusioned with its authoritarianism. In 1920–1 he spent a year at the University of Peking (Beijing). Returning to England he married Dora Black in 1921, just in time to legitimize his son; a daughter was born in 1923. Parenthood led him to take an interest in education and with his wife he started an experimental school. It was not, in Russell's eyes, a success, and it was very expensive to run, requiring that he undertake regular lecture tours of the USA to raise money. His involvement with it ended, along with his marriage, in 1932, though Dora continued to run it on her own until 1943.

Through the 1920s and early 1930s Russell wrote prolifically on an astonishing range of topics, producing (among much else) books on Russia, China, relativity, history, education, sexual morality, international relations, religion and the future of society. Though much of this activity was necessary to make ends meet, Russell was a tireless advocate of progressive causes. By the mid-1930s, however, tiring of the precariousness of this way of life and needing now to support two families (he had remarried in 1936 and a third child was born in 1937), he hoped to return to academic life. This was not easy: positions were scarce and Russell was a controversial figure. In 1938 he lectured at Oxford, followed by visiting appointments at Chicago and UCLA and finally an offer of a permanent position at City College, New York. This last, however, provoked opposition from New York's Catholic community and the appointment was overturned in a celebrated court case.

In 1940, therefore, Russell found himself unemployed and marooned in America by the war. At this point, the eccentric millionaire Albert Barnes came to his rescue with a five-year appointment to lecture on the history of philosophy at the Barnes Foundation in Philadelphia. Although Barnes fired Russell at the end of 1942, he permanently solved Russell's financial problems, for not only did Russell collect a sizeable sum for breach of contract but the lectures he gave for Barnes became the basis for his hugely successful History of Western Philosophy (1945).

Russell returned to England in 1944 to take up a fellowship at Trinity College, where he completed his last great philosophical work, Human Knowledge (1948). His return marked not only a mending of his relations with Trinity but also with the British establishment. His continued condemnation of communism in general and the Soviet government in particular was well suited to the beginnings of the cold war and Russell enjoyed a period of unaccustomed respectability. Throughout the 1950s he continued to write prolifically, including a philosophical autobiography, My Philosophical Development (1959). He married for a fourth time in 1952.

His respectability was short-lived. After the death of Stalin his hatred of the Soviet government moderated, and the threat of nuclear war came to dominate his thoughts. He wrote extensively on the danger of war during the 1950s but increasingly felt the need for action and in 1958 helped found the Campaign for Nuclear Disarmament, and then the more militant Committee of 100. In 1961 he was jailed once more for inciting demonstrators to civil disobedience. The 1960s were a time of hectic political work for Russell. He lent support to many causes and was especially active in opposing the Vietnam War. His last political statement, on the Middle East, was written two days before his death.

"What I Have Lived For" by Bertrand Russell,1967

Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind. These passions, like great winds, have blown me hither and thither, in a wayward course, over a great ocean of anguish, reaching to the very verge of despair.
I have sought love, first, because it brings ecstasy - ecstasy so great that I would often have sacrificed all the rest of life for a few hours of this joy. I have sought it, next, because it relieves loneliness--that terrible loneliness in which one shivering consciousness looks over the rim of the world into the cold unfathomable lifeless abyss. I have sought it finally, because in the union of love I have seen, in a mystic miniature, the prefiguring vision of the heaven that saints and poets have imagined. This is what I sought, and though it might seem too good for human life, this is what--at last--I have found.

With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway above the flux. A little of this, but not much, I have achieved.

Love and knowledge, so far as they were possible, led upward toward the heavens. But always pity brought me back to earth. Echoes of cries of pain reverberate in my heart. Children in famine, victims tortured by oppressors, helpless old people a burden to their sons, and the whole world of loneliness, poverty, and pain make a mockery of what human life should be. I long to alleviate this evil, but I cannot, and I too suffer.

This has been my life. I have found it worth living, and would gladly live it again if the chance were offered me.

"Logical Atomism" by Bertrand Russell,1959

Russell's logical atomism had significant influence on the development of philosophy, especially in the first half of the 20th century. Nowhere is Russell's influence more clearly seen than in the work of his pupil Ludwig Wittgenstein. Wittgenstein's Tractatus Logico-Philosophicus appeared in 1921; in it, Wittgenstein presented in some detail a logical atomist metaphysics. (It should be noted, however, that there is significant controversy over whether, in the end, Wittgenstein himself meant to endorse this metaphysics.) In the Tractatus, the world is described as consisting of facts. The simplest facts, which Wittgenstein called “Sachverhalte”, translated either as “states of affairs” or “atomic facts”, are thought of as conglomerations of objects combined with a definite structure. The objects making up these atomic basics were described as absolutely simple. Elementary propositions are propositions whose truth depends entirely on the presence of an atomic fact, and other propositions have a determinate and unique analysis in which they can construed as built up from elementary propositions in truth-functional ways.

Partly owing to Wittgenstein's influence, partly directly, Russell's logical atomism had significant influence on the works of the logical positivist tradition, as exemplified in the works of Carnap, Waismann, Hempel and Ayer. This tradition usually disavowed metaphysical principles, but methodologically their philosophies owed much to Russell's approach. Carnap, for example, described philosophy as taking the form of providing “the logical analysis of the language of science” (Carnap 1934, 61). This originally took on the form of attempting to show that all meaningful scientific discourse could be analyzed in terms of logical combinations beginning with “protocol sentences”, or sentences directly confirmable or disconfirmable by experience. This notion of a “protocol sentence” in this tradition was originally modeled after Russellian and Wittgensteinian atomic propositions. The notion of a “logical construction” was also important for how such thinkers conceived of the nature of ordinary objects (see, e.g., Ayer 1952, chap. 3). The view that scientific language could readily and easily be analyzed directly in terms of observables gradually gave way to more holistic views, such as Quine's (see, e.g. Quine 1951), in which it is claimed that it is only a body of scientific theories that can be compared to experience, and not isolated sentences. However, even in later works growing out of this tradition, the influence of Russell can be felt.

Besides positive influence, many trends in 20th century philosophy can be best understood largely as a reaction to Russell's atomistic philosophy. Ironically, nowhere is this more true than in the later writings of Wittgenstein, especially his Philosophical Investigations (1953). Among other things, Wittgenstein there called into question whether a single, unequivocal notion of simplicity or a final state of analysis can be found (e.g., secs. 46–49, 91), and questioned the utility of an ideal language (sec. 81). Wittgenstein also called into question whether, in those cases in which analysis is possible, the results really give us what was meant at the start: “does someone who says that the broom is in the corner really mean: the broomstick is there, and so is the brush, and the broomstick is fixed in the brush?” (sec. 60). Much of the work of the so-called “ordinary language” school of philosophy centered in Oxford in the 1940s and 1950s can also been seen largely as a critical response to views of Russell (see, e.g., Austin 1962, Warnock 1951, Urmson 1956).

Nevertheless, despite the criticisms, many so-called “analytic” philosophers still believe that the notion of analysis has some role to play in philosophical methodology, though there seems to be no consensus regarding precisely what analysis consists in, and to what extent it leads reliably to metaphysically significant results. Debates regarding the nature of simple entities, their interrelations or dependencies between one another, and whether there are any such entities, are still alive and well. Russell's rejection of idealistic monism, and his arguments in favor of a pluralistic universe, have gained almost universal acceptance, with a few exceptions. Abstracting away from Russell's particular examples of proposed analyses in terms of sensible particulars, the general framework of Russell's atomistic picture of the world, which consists of a plurality of entities that have qualities and enter into relations, remains one to which many contemporary philosophers are attracted.

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Bertrand Russell described his philosophy as a kind of “logical atomism”, by which he meant to endorse both a metaphysical view and a certain methodology for doing philosophy. The metaphysical view amounts to the claim that the world consists of a plurality of independently existing things exhibiting qualities and standing in relations. According to logical atomism, all truths are ultimately dependent upon a layer of atomic facts, which consist either of a simple particular exhibiting a quality, or multiple simple particulars standing in a relation. The methodological view recommends a process of analysis, whereby one attempts to define or reconstruct more complex notions or vocabularies in terms of simpler ones. According to Russell, at least early on during his logical atomist phase, such an analysis could eventually result in a language containing only words representing simple particulars, the simple properties and relations thereof, and logical constants, which, despite this limited vocabulary, could adequately capture all truths.

"Logic and Knowledge" by Bertrand Russell,1956,

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).

"An inquiry into Meaning and Truth" by Bertrand Russell,1940

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Empirical knowledge has its basis in percepts -sense experiences- ;
from basic propositions about percepts empirical knowledge is constructed.
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Although basic propositions are not indubitably true,
as propositions of the utmost particularity,
referring to percepts,
they are the most dependable propositions of empirical inquiry.
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Empirical knowledge requires provision for general statements,
for stating logical relationships,and for modes of inference.
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Propositions are both objective and subjective ;
they are objective in that they indicate factually,
and they are subjective in that they express the state of mind of the speaker
-belief,denial,or doubt-.
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Sentences are true if what they indicate is the case ;
to know a sentence to be true one must perceive its verifier
-the event the sentence indicates-.
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"Introduction to Mathematical Philosophy" by Bertrand Russell,1919

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Mathematics can be shown to be a logical development of certain basic ideas ;
mathematics can be reduced to logic.
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The number of a class is the class of all those classes which are similar to it,.
(Classes are similar when their members can be put into a one-to-one relation with each other.)
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A relation is symmetrical when if one thing has the relation to another,
the other has the same relation to it ;
a relation is transitive when if one thing has the relation to a second,
and the second has the same relation to a third,
the first has the relation to the third.
(Other relations are defined.)
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An infinite cardinal number satisfies the equation,n equals n plus l.
(An infinite collection has parts which have as many terms as the infinite collection itself.)
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By distinguishing between types of entities it is possible to avoid paradoxes which have perplexed philosophers for centuries.
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Mathematical truths are a priori and have nothing to do with facts about the world ;
they are logical tautologies.
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"Our knowledge of external World" by Bertrand Russell,1914

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The method of logical analysis makes the resolution of philosophical problems possible by defining the limits of scientific philosophy so as to exclude speculative metaphysics.
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We can account for our knowledge of the external world by realizing,through logical analysis,that the world as we know it is a construction from the data given in sense experience ; an individual's "private world" is the class of all data within his perspective,and a perceived object is the class of all aspects to be found in all the perspectives which include the object.
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The conception of permanent things can be constructed by reference to appearances if points are defined by reference to enclosure series of spaces,and if time is defined by reference to classes of events simultaneous with each other.
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Zeno's paradoxes of motion can be resolved by use of the mathematical theory of continuity.
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