Russell’s Paradox

The years between 1872 and 1914 are indeed “the private years” of Bertrand Russell’s long life, if they are compared with the period following 1914, the years of his militant pacifism and imprisonment for opposing World War I. But even during his lonely childhood in the splendid late Victorian house, Pembroke Lodge, of his grandfather Lord John Russell and his grandmother the formidable Lady Stanley, he learned to take for granted the daily arguments about great affairs of state among those who were directly or indirectly involved in them as members of the aristocratic ruling class; and this included his own family and his numerous cousins. It was naturally assumed that he would in due time appear on the public stage as a leader in liberal politics, and perhaps also as publicly supporting the most advanced radical causes as his parents, Lord and Lady Amberley, did before they prematurely died, of diphtheria.

Something of the vast wealth and worldwide predominance of the British aristocracy in this Jubilee and Edwardian period is reflected in Russell’s early letters, if only faintly. Russell rejected his golden opportunities, and, in spite of his furious grandmother, he married beneath him into the middle class, falling in love with a Philadelphian Quaker. He chose as his true home Trinity College, Cambridge, where he was both undergraduate and Fellow. As in all collected letters and memoirs from 1900–1914, the shadow of the impending catastrophe, the Great War, lies on the pages, and this throws into relief the never-to-be-recovered ease and self-confidence of a very fortunate Englishman at that peak of Britain’s power and wealth.

The douceur de vivre enjoyed in the country houses of the very rich in those long Edwardian summers, free from any pressing social anxiety, would never recur within that century or the next. Admittedly there were the Irish question, the woman question, and the suffragettes, there were slums and strikes, and Russell’s family was actively involved in all the issues of the day. But the reserves of stability and accumulated wealth were so great that Meredith’s heroines and the Cambridge Apostles could afford earnestly to refine their sentiments without worrying too much about what was happening on the margins of society, away from the obvious centers. Russell was free to design his life with the highest moral purposes in view rather than merely to respond to commonplace needs or to seek commonplace forms of success.

The lofty tone and the rather self-conscious nobility of most of these letters, particularly those written during his courtship of his first wife, Alys, are now strange and sometimes disconcerting, but they certainly are neither insincere nor unnatural. Russell repeatedly remarks that he must be thought a prig, and in his letters he copiously describes his longing for perfection, his moral uncertainties, his moments of mystical exaltation, and his moments of black despair. In his early life suicide on several occasions seemed to him a real possibility.

From childhood onward Russell was so intensely literate that one sometimes has the impression in these letters that the young Russell lived in words and sentences as much as in the states of mind which the sentences describe. His extreme articulateness was a byproduct of his loneliness, the loneliness of an orphan talking to himself, because his brother did not share his ambitions, and his father and mother were gone. Russell’s letters to Alys are a deluge of superlatives and rapturous invocations and declarations of bliss and of hope. When his love for her very suddenly disappears, as famously described in his Autobiography, his letters to his friends become a testament of despair and of self-accusation and of spiritual aridity.

The long series of letters to Lady Ottoline Morrell from 1911 onward are equally rapturous, sometimes even ecstatic, but they are happily tempered by some worldly allusions and a welcome uncharitableness. They both came from ducal families and they felt themselves entirely at ease in cultivating the most gifted and intellectually distinguished of their contemporaries; consequently from 1911 onward the letters become livelier and more open to the world. He writes to, or about, Gilbert Murray (a close friend), W.B. Yeats, Maynard Keynes, Whistler, Augustus John, the Webbs, Bernard Shaw, Bergson. Meeting the Webbs in France, Russell writes to Gilbert Murray, “I minded them more than usual. They have a competent way of sizing up a Cathedral, and pronouncing on it with an air of authority and an evident feeling that the LCC [London County Council] would have done it better. They take all the colour out of life and make everything one cares for turn to dust and ashes.” About Yeats he reports—“Yeats, whom I have met only twice, seemed to me a snob and a very acute man of business. But I dare say he is interesting really.” About Bergson,

Bergson’s philosophy, though it shows constructive imagination, seems to me wholly devoid of argument and quite gratuitous, he never thinks about fundamentals, but just invents pretty fairy-tales.

This is the voice of the new, scientific, philosophy which Russell masterminded, particularly evident here in the application of the word “gratuitous” to metaphysics. In 1898, partly under the influence of G.E. Moore, Russell had made the break with traditional speculative metaphysics, the “gratuitous” philosophy which for him had meant F.H. Bradley and neo-Hegelianism. From that date onward philosophy was to be a rigorous discipline, narrowly constrained by mathematical logic, and responsive only to demonstrative argument. All this he could explain to Ottoline Morrell in the marvelous prewar bicycling summers, the summers in which Edward Thomas and Wilfred Owen began to write, and the New Women and the Fabians flourished alongside the suffragettes, and when Minoru won the Derby for Edward VII.

Day after day the weather was hot and cloudless. Bertie…came over every day to see me…. We took tea into the woods, and read such things as Plato and Spinoza and Shelley…. Bertie would…urge me on…telling me that I was not being honest, and that I must face the truth

—so in 1911 Ottoline Morrell, who was encouraged by Russell to discard “the gratuitous” and all philosophical fairy-tales.

This love affair is vastly documented by memoris, letters, and by subsequent thorough biographies, in embarrassing detail. Long literary biographies of twentieth-century writers and artists now have the readership that would formerly have supported the three-decker novel, with the ramified love affairs of the Bloomsbury Group, for example, taking the place of the staid adventures of the Forsytes. The first volume of Russell’s letters contributes to this genre, and once again one can learn about the Apostles at Cambridge, if one wishes, and about their solemn discussions of sexual possibilities. But these “private years” were also the years of Russell’s greatest intellectual achievements, and a splendid story of maturing genius can be traced running through them. And there is a third thread: the drama, probably unique in the history of philosophy, of Russell’s fateful friendship with Wittgenstein, beginning with love and exaltation and with a passionate discipleship, and ending in bitterness in the years that were to come after the war.

The story of Russell’s vocation begins very early in the letters when he writes to his friend C.P. Sanger in 1894 explaining an argument that will enter into his first philosophical book, An Essay on the Foundations of Geometry. This concerned the uniform curvature of space: Russell was in these years asking himself whether the basic propositions of geometry were contingent truths traceable to observation or whether they are necessary truths in the light of reason prior to all experience, or, a third possibility then recently suggested, truths that are true by convention only, accepted by us because they simplify the statement of our theories in physics. In his Autobiography Russell describes these early years of his marriage to Alys as “the most fruitful period of my life,” when he laid the foundations of his later work in the philosophy of mathematics and began his intellectual partnership with Whitehead. From the age of eleven, when he was first introduced to Euclid by his brother, he had loved mathematics for its certainty, its lucidity, and its independence of time and change, three distinguishable properties which he always considered interdependent. “Love” is the right word, because thinking about mathematics for him satisfied a deep emotional need and deflected his fears, his sense of instability and of emptiness, as he repeatedly explains in these letters. He needed the hard, unblurred edges and the constancy of mathematical truths, which are beautiful because they are taut and coherent, and because they are untainted by subjectivity. When he writes the word “Truth” as a sacred invocation in these letters to Lady Ottoline, he means not “truth as it seems to me,” or “the truth here and now,” or “in our science,” or even “all humanity’s truth,” but that which is true absolutely and without qualification.

Judged by this standard, mathematics, he found, still has a nagging imperfection, a gap in its very foundations, through which uncertainty and skeptical doubts could seep in. Does the whole fabric of mathematical truths rest on an untidy and not further analyzable list of axioms, merely assumed and not further demonstrable? If so, are we justified in assuming that the physical world really has the structure which our geometry attributes to it? Kant had proposed a dazzling answer to this question, but the development of non-Euclidean geometries in the nineteenth century had undermined its credibility. When in 1900 Russell met at a conference the Italian logician Giuseppe Peano and studied his new notation, he suddenly saw his way forward, his work in the foundation of mathematics mapped out for him for years ahead. Peano had invented a notation in which five axioms could be formulated from which both the truths of logic required for formal inference, and also the propositions of classical mathematics, might be derived. So logic and mathematics would be shown to constitute a seamless whole, a single fabric of knowledge.

With fierce energy, and very happily, Russell set to work on his program, and it culminated finally, and after many years of concentrated and sometimes feverish work, in the publication of Principia Mathematica, written jointly with Whitehead: a vast work, heavy with detailed derivations and elucidations, which in manuscript required a carriage to deliver it to the Cambridge University Press. Almost no one could be expected to read it other than a few logicians, Russell told Ottoline Morrell. The intended last volume never appeared, and Russell was exhausted for some years by the labor. Its notation constitutes the foundation of the modern logic which is taught all over the world, largely replacing the Aristotelian logic which had hitherto dominated the textbooks.

As a byproduct of this strictly logical program to uncover the foundations of mathematics, Russell in these years also made a number of substantial discoveries in the philosophy of language which have been discussed by philosophers ever since. Faintly and with long gaps, the letters to Lady Ottoline in these prewar years reflect the excitement and, also, the setbacks and crises along the way. The first crisis was Russell’s discovery that an unknown German philosopher of mathematics and of language, Gottlob Frege, had anticipated his program and, pursuing a parallel path, had also anticipated some of his major discoveries. A now famous exchange of letters took place between these two great men, each acknowledging the other without pettiness or caution.

The second and greater and more long-lasting crisis was the sudden appearance of an intellectual monster, called Russell’s Paradox, which threatened to destroy the supposedly harmonious structure of mathematical logic. The monster was and is composed (very roughly) like this: Russell had defined numbers in terms of (among other notions) classes and of classes of classes, so, for example, the class of all many-membered classes is itself a many-membered class. But most classes are not members of themselves: for instance, the class of all persons is not itself a person. Call this latter kind of class a normal class. Consider now the class of all normal classes: Is this class normal? If we assume that it is, i.e., that it must not be a member of itself, we can infer that it isn’t. If we assume that the class of all normal classes is not normal, we can infer that it is. Therefore it is impossible to say that it is and impossible to say that it is not normal. So it has to be admitted that the notion of class, supposedly essential to understanding the notion of number, is infected with a paradox. Not only are the foundations of mathematics insecure: but logic itself, which begins as the theory of predicates, classes (or sets), and class membership, has this paradox built into it.

Russell discovered the paradox in 1901, and for more than a decade tried various means of sealing off the infection, always unsuccessfully. This was no minor technical hitch in his design. It seems that in our proofs and derivations we may always stumble across paradoxical and undecidable propositions, which we cannot either affirm as true or dismiss as false. Russell had always believed that the concepts which we employ in our ordinary speech are riddled with contradiction, paradox, and indeterminacy: Hegel, Bradley, McTaggart had claimed this, and he had agreed with them. So the parallel paradox of the ship’s barber, plausibly defined as the man who shaves everyone who does not shave himself, need not have caused him to write letters of despair when he realized that the harmless question—“Does the ship’s barber shave himself or not?”—can have no answer: if he does he doesn’t, and if he doesn’t he does. But that the basic notions of mathematics and of logic are not immune to this fallacy undermined Russell’s theory of knowledge, which required that ordinary language should be remodeled to approximate to the perfect lucidity and consistency of mathematics, within which all properly formed questions ought to have a yes or no answer. What looks like a “technical” problem in formal logic had within Russell’s program immense consequences for what he called “popular” philosophy, that is, the philosophical account of human knowledge and of its limits.

In these letters one can see more clearly than in the Autobiography the very strong influence in Russell’s development of Wittgenstein, the pupil of genius who had come from Vienna to work with him and whom Russell loved. He wrote to Lady Ottoline in March 1912,

I love him and feel he will solve the problems that I am too old to solve—all kinds of vital problems that are raised by my work, but want a fresh mind and the vigour of youth…. His vigour and life is such a comfort after the washedout Cambridge type.

Wittgenstein had spoken with intense feeling about the beauty of Principia Mathematica, which he found like music, and the happiest hours of his life, he said, had been passed in Russell’s room. But the more fiercely he delved into Russell’s program, the more he came to wonder whether it was not radically and from the beginning misconceived and impossible. Both by temperament and by his upbringing in Vienna he was vastly more skeptical of the grand pretensions of philosophical theory and of rational reconstruction than Russell, who could never bear to doubt that the world, including both the atoms and the numbers in it, is “adapted to our powers of cognition,” in Kant’s phrase, when these powers are relentlessly applied. Truth and perfect intelligibility could be combined if only as philosophers we worked at combining them.

Step by tentative step, and over many years, and after many diversions and interruptions, Wittgenstein came to believe that there could not in principle be a logical reconstruction of the validity of all our diverse claims to knowledge within a single system as Russell had proposed.

In this volume only the first steps in Wittgenstein’s skepticism appear: in May 1913 Russell wrote

Wittgenstein came to see me…. I showed him a crucial part of what I have been writing. He said it was all wrong, not realizing the difficulties…. I couldn’t understand his objection—in fact he was very inarticulate—but I feel in my bones that he must be right.

It is a moving story, as the shadow of Wittgenstein gradually smothered the light of Russell’s philosophical optimism, which was shining so brightly in the letters to Alys Russell in the first decade of the century.

By 1912 Russell felt himself to be exhausted by his labors on Principia Mathematica and incapable of sustaining any longer the intense concentration which mathematical logic required. “All through the autumn of 1900,” he had told Lady Ottoline, “I worked like one inspired—every day new worlds opened before me, and I saw clearly things which had been in a dim mist before.” Late in 1911 Russell writes in a letter—“I have an uneasiness about philosophy altogether; what remains for me to do in philosophy (I mean in technical philosophy) does not seem to me of first-rate importance.”

Therefore he had decided to turn away from “technical” philosophy to write popular philosophy, in fact a short book which he called “the shilling shocker.” Its title was Problems of Philosophy. He intended this to be popular in the sense that it may help “the man who wants to see his own special pursuit connected with the cosmos.” This connection is to be established by the theory of knowledge, which will show the grade and type of knowledge involved in each of the “special pursuits.” The book was a brilliant and lasting success, serving to distinguish the outstanding problems in the theory of knowledge for fifty years or more after its publication. Even now it is often recommended to students as a superbly clear, though very fallible, introduction to philosophy.

These letters show that Russell knew at the time that he must now turn to his second career as the great popularizer, who was to present questions of Weltanschauung and of morality and politics in a style that was at once familiar and also decently argumentative and logical. In conveying clear and distinct ideas to a large public he was to be unequaled in his lifetime. Shaw, his only rival, lacked the thump of conviction in his prose, and there was in Shaw no undertone of strong emotion, which could always be felt in Russell’s praise of enlightenment. In these letters, as in his conversation, he seems never to produce a slack or stodgy sentence, and, more striking still, he seems as incapable of of breaking off a thought in his letters as he was in conversation. His thought never trailed away or faded into mere suggestion. His was a fully punctuated style and the firm full stops could always be heard in his talk: no Proustian channels and rivulets and no Jamesian coils were allowed. Like Leibniz and perhaps other mathematical thinkers, he had an almost tactual sense of propositions as entities, vehicles of truth or falsity, and as something different from the written or heard sentences which expressed them. Propositions are abstract objects, but for Russell they had, or ought to have, hard edges and they presented themselves to him as distinct existences, one by one. Many of us, plodding behind Russell in later years, used to doubt that propositions could be so sharply individuated and held apart, that they could be counted, as Russell seemed to assume that they could be. But his mind regularly and effortlessly moved in this punctuated mode, and these letters illustrate how supremely natural and unavoidable the movement was, even in extremely intimate and emotional contexts.

The letters have been so interestingly and skilfully edited by Nicholas Griffin that one has the impression of following a continuous thread of life month by month. Griffin provides linking passages that fill in the circumstances surrounding the letters and supply the known events of the life which are not reflected in what he wrote. Footnotes explain references in exactly the right amount of detail, and Griffin comments on his hero’s adventures without too much reverence and with a pleasing dryness and concision that are appropriate to the subject. Because most of the letters here collected are extremely intimate outpourings and designedly self-revealing and confessional, they compel one to think about Russell as a person, and not only as a philosopher.

The outcome of this reflection is not pleasant, I think. There is a story, told here and elsewhere, of Russell announcing his intention of coming one year as a member of G. E. Moore’s summer reading party for close friends at a cottage in the country, which was an annual event. Russell and Moore had talked about philosophy at very great length over a decade or more, and these discussions had been very important for both of them. But Moore could not bear the thought of having Russell among his close friends at the reading party, and Desmond MacCarthy, the literary critic and friend of Moore, had tactfully to intervene with Russell to avert the disaster. This ought to be a surprising story, but to anyone who remembers the two men, even if he knew them only very superficially, it is not at all surprising. Also it is not surprising that Lady Ottoline could not respond with love to Russell’s ardent, and often desperate, declarations of love: she responded rather with admiration and affection. His physical presence was often distressing to her. Russell, whenever encountered, showed wonderful vitality and the power of genius. He was also a very generous man and extremely high-principled, even noble, particularly in these early years, before the bitterness and disillusionments of the Great War. These letters provide several examples of his generosity, his giving money to Newnham College, to Cambridge, for example, and to other deserving institutions, and to many friends while living very austerely himself. In every crisis he was undaunted and courageous, and public-spirited in spite of his dissatisfaction with life and with human beings.

Yet Russell appears in these letters, as he often appeared in life, deeply unamiable, a person whom it was natural to admire, and difficult to like. What was wrong? Or, perhaps better, what was missing? I think it comes back to propositions and to the lonely person’s love of abstraction and his flight from the triviality of local and personal interests. The extraordinary fluency and literacy of the long letters to Alys Russell, and later to Lady Ottoline Morrell, are dismaying because they are so like classical prose, the prose of a noble orator. In their rhetoric they invoke great abstractions, such as Nature, Truth, Love, Reason; and all the appeals to abstractions and the invocations are obviously and overwhelmingly sincere.

This was Russell’s world, traceable to the isolation of his parentless childhood, as if he had talked only to classical statues and heroic monuments in the ample gardens of Pembroke Lodge. There were rarely any concrete details, any unexpected memories, or accidental associations, in his utterances. When he thought and wrote about the beauty of Nature, he did not see a waterfall or a face or a particular quality of light. There is authentic passion in his letters and in the expressions of distinguished, even aweinspiring, ambition, but it is the passion that fits well into soliloquy and declamation.

Russell did not remember, and knew that he did not remember, faces. He used to say that he remembered people by committing to memory a verbal description of them and then later matching the description to the object appearing before him. He was not interested in the diversity of surfaces, in accidental marks, in colors, unusual symmetries, different tones of voice. There could not be for him a great difference between talking to himself and talking to someone else—or to anyone else, provided he or she was capable of understanding an argument. Hence there was a devastating lack of charm, in these letters as in life, alongside the greatness of scope and achievement. The voice is clear, the enunciation distinct and strong, but the voice is a public voice and the note is unchanging. He seemed to speak from within some hard and scaly carapace. This is of course a subjective impression, but a collection of letters, particularly if most of them are love letters, drives one to subjectivity. This is a splendidly arranged and edited collection, opening the way for many different impressions.