Modern Mind: An Intellectual History of the 20th Century (20 page)

Russell – slight and precise, a finely boned man, ‘an aristocratic sparrow’ –
is shown in Augustus John’s portrait to have had piercingly sceptical eyes, quizzical eyebrows, and a fastidious mouth. The godson of the philosopher John Stuart Mill, he was born halfway through the reign of Queen Victoria, in 1872, and died nearly a century later, by which time, for him as for many others, nuclear weapons were the greatest threat to mankind. He once wrote that ‘the search for knowledge, unbearable pity for suffering and a longing for love’ were the three passions that had governed his life. ‘I have found it worth living,’ he concluded, ‘and would gladly live it again if the chance were offered me.’
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One can see why. John Stuart Mill was not his only famous connection – T. S. Eliot, Lytton Strachey, G. E. Moore, Joseph Conrad, D. H. Lawrence, Ludwig Wittgenstein, and Katherine Mansfield were just some of his circle. Russell stood several times for Parliament (but was never elected), championed Soviet Russia, won the Nobel Prize for Literature in 1950, and appeared (sometimes to his irritation) as a character in at least six works of fiction, including books by Roy Campbell, T. S. Eliot, Aldous Huxley, D. H. Lawrence, and Siegfried Sassoon. When Russell died in 1970 at the age of ninety-seven there were more than sixty of his books still in print.
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But of all his books the most original was the massive tome that appeared first in 1910, entitled, after a similar work by Isaac Newton,
Principia Mathematica.
This book is one of the least-read works of the century. In the first place it is about mathematics, not everyone’s favourite reading. Second, it is inordinately long – three volumes, running to more than 2,000 pages. But it was the third reason which ensured that this book – which indirectly led to the birth of the computer – was read by only a very few people: it consists mostly of a tightly knit argument conducted not in everyday language but by means of a specially invented set of symbols. Thus ‘not’ is represented by a curved bar; a boldface B stands for ‘or’; a square dot means ‘and,’ while other logical relationships are shown by devices such as a U on its side (⊃) for ‘implies,’ and a three-barred equals sign (≡) for ‘is equivalent to.’ The book was ten years in the making, and its aim was nothing less than to explain the logical foundations of mathematics.

Such a feat clearly required an extraordinary author. Russell’s education was unusual from the start. He was given a private tutor who had the distinction of being agnostic; as if that were not adventurous enough, this tutor also introduced his charge first to Euclid, then, in his early teens, to Marx. In December 1889, at the age of seventeen, Russell went to Cambridge. It was an obvious choice, for the only passion that had been observed in the young man was for mathematics, and Cambridge excelled in that discipline. Russell loved the certainty and clarity of math. He found it as ‘moving’ as poetry, romantic love, or the glories of nature. He liked the fact that the subject was totally uncontaminated by human feelings. ‘I like mathematics,’ he wrote, ‘because it is
not
human & has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza’s God, it won’t love us in return.’ He called Leibniz and Spinoza his ‘ancestors.’
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At Cambridge, Russell attended Trinity College, where he sat for a scholarship.
Here he enjoyed good fortune, for his examiner was Alfred North Whitehead. Just twenty-nine, Whitehead was a kindly man (he was known in Cambridge as ‘cherub’), already showing signs of the forgetfulness for which he later became notorious. No less passionate about mathematics than Russell, he displayed his emotion in a somewhat irregular way. In the scholarship examination, Russell came second; a young man named Bushell gained higher marks. Despite this, Whitehead convinced himself that Russell was the abler man – and so burned all of the examination answers, and his own marks, before meeting the other examiners. Then he recommended Russell.
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Whitehead was pleased to act as mentor for the young freshman, but Russell also fell under the spell of G. E. Moore, the philosopher. Moore, regarded as ‘very beautiful’ by his contemporaries, was not as witty as Russell but instead a patient and highly impressive debater, a mixture, as Russell once described him, of ‘Newton and Satan rolled into one.’ The meeting between these two men was hailed by one scholar as a ‘landmark in the development of modern ethical philosophy.’
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Russell graduated as a ‘wrangler,’ as first-class mathematics degrees are known at Cambridge, but if this makes his success sound effortless, that is misleading. Russell’s finals so exhausted him (as had happened with Einstein) that afterward he sold all his mathematical books and turned with relief to philosophy.
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He said later he saw philosophy as a sort of no-man’s-land between science and theology. In Cambridge he developed wide interests (one reason he found his finals tiring was because he left his revision so late, doing other things). Politics was one of those interests, the socialism of Karl Marx in particular. That interest, plus a visit to Germany, led to his first book,
German Social Democracy.
This was followed by a book on his ‘ancestor’ Leibniz, after which he returned to his degree subject and began to write
The Principles of Mathematics.

Russell’s aim in
Principles
was to advance the view, relatively unfashionable for the time, that mathematics was based on logic and ‘derivable from a number of fundamental principles which were themselves logical.’
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He planned to set out his own philosophy of logic in the first volume and then in the second explain in detail the mathematical consequences. The first volume was well received, but Russell had hit a snag, or as it came to be called, a paradox of logic. In
Principles
he was particularly concerned with ‘classes.’ To use his own example, all teaspoons belong to the class of teaspoons. However, the class of teaspoons is not itself a teaspoon and therefore does not belong to the class. That much is straightforward. But then Russell took the argument one step further: take the class of all classes that do not belong to themselves – this might include the class of elephants, which is not an elephant, or the class of doors, which is not a door. Does the class of all classes that do not belong to themselves belong to itself? Whether you answer yes or no, you encounter a contradiction.
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Neither Russell nor Whitehead, his mentor, could see a way around this, and Russell let publication of
Principles
go ahead without tackling the paradox. ‘Then, and only then,’ writes one of his biographers, ‘did there take place an event which gives the story of mathematics one of its moments of high drama.’ In the 1890s Russell had read
Begriffsschrift
(‘Concept-Script’), by the German
mathematician
Gottlob Frege,
but had failed to understand it. Late in 1900 he bought the first volume of the same author’s
Grundgesetze der Arithmetik
(Fundamental Laws of Arithmetic) and realised to his shame and horror that Frege had anticipated the paradox, and also failed to find a solution. Despite these problems, when
Principles
appeared in 1903 – all 500 pages of it – the book was the first comprehensive treatise on the logical foundation of mathematics to be written in English.
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The manuscript for
Principles
was finished on the last day of 1900. In the final weeks, as Russell began to think about the second volume, he became aware that Whitehead, his former examiner and now his close friend and colleague, was working on the second volume of
his
book
Universal Algebra.
In conversation, it soon became clear that they were both interested in the same problems, so they decided to collaborate. No one knows exactly when this began, because Russell’s memory later in his life was a good deal less than perfect, and Whitehead’s papers were destroyed by his widow, Evelyn. Her behaviour was not as unthinking or shocking as it may appear. There are strong grounds for believing that Russell had fallen in love with the wife of his collaborator, after his marriage to Alys Pearsall Smith collapsed in 1900.
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The collaboration between Russell and Whitehead was a monumental affair. As well as tackling the very foundations of mathematics, they were building on the work of Giuseppe Peano, professor of mathematics at Turin University, who had recently composed a new set of symbols designed to extend existing algebra and explore a greater range of logical relationships than had hitherto been specifiable. In 1900 Whitehead thought the project with Russell would take a year.
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In fact, it took ten. Whitehead, by general consent, was the cleverer mathematician; he thought up the structure of the book and designed most of the symbols. But it was Russell who spent between seven and ten hours a day, six days a week, working on it.
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Indeed, the mental wear and tear was on occasions dangerous. ‘At the time,’ Russell wrote later, ‘I often wondered whether I should ever come out at the other end of the tunnel in which I seemed to be…. I used to stand on the footbridge at Kennington, near Oxford, watching the trains go by, and determining that tomorrow I would place myself under one of them. But when the morrow came I always found myself hoping that perhaps
“Principia Mathematica”
would be finished some day.’
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Even on Christmas Day 1907, he worked seven and a half hours on the book. Throughout the decade, the work dominated both men’s lives, with the Russells and the Whiteheads visiting each other so the men could discuss progress, each staying as a paying guest in the other’s house. Along the way, in 1906, Russell finally solved the paradox with his theory of types. This was in fact a logicophilosophical rather than a purely logical solution. There are two ways of knowing the world, Russell said: acquaintance (spoons) and description (the class of spoons), a sort of secondhand knowledge. From this, it follows that a description about a description is of a higher order than the description it is about. On this analysis, the paradox simply disappears.
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Slowly the manuscript was compiled. By May 1908 it had grown to ‘about
6,000 or 8,000 pages.’
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In October, Russell wrote to a friend that he expected it to be ready for publication in another year. ‘It will be a very big book,’ he said, and ‘no one will read it.’
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On another occasion he wrote, ‘Every time I went for a walk I used to be afraid that the house would catch fire and the manuscript get burnt up.’
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By the summer of 1909 they were on the last lap, and in the autumn Whitehead began negotiations for publication. ‘Land in sight at last,’ he wrote, announcing that he was seeing the Syndics of the Cambridge University Press (the authors carried the manuscript to the printers on a four-wheeled cart). The optimism was premature. Not only was the book very long (the final manuscript was 4,500 pages, almost the same size as Newton’s book of the same title), but the alphabet of
symbolic logic
in which it was half written was unavailable in any existing printing font. Worse, when the Syndics considered the market for the book, they came to the conclusion that it would lose money – around £600. The press agreed to meet 50 percent of the loss, but said they could publish the book only if the Royal Society put up the other £300. In the event, the Royal Society agreed to only £200, and so Russell and Whitehead between them provided the balance. ‘We thus earned minus £50 each by ten years’ work,’ Russell commented. ‘This beats “Paradise Lost.” ‘
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Volume I
of Principia Mathematica
appeared in December 1910, volume 2 in 1912, volume 3 in 1913. General reviews were flattering, the
Spectator
concluding that the book marked ‘an epoch in the history of speculative thought’ in the attempt to make mathematics ‘more solid’ than the universe itself.
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However, only 320 copies had been sold by the end of 1911. The reaction of colleagues both at home and abroad was awe rather than enthusiasm. The theory of logic explored in volume I is still a live issue among philosophers, but the rest of the book, with its hundreds of pages of formal proofs (page 86 proves that 1 + 1=2), is rarely consulted. ‘I used to know of only six people who had read the later parts of the book,’ Russell wrote in the 1950s. ‘Three of these were Poles, subsequently (I believe) liquidated by Hitler. The other three were Texans, subsequently successfully assimilated.’
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Nevertheless, Russell and Whitehead had discovered something important: that most mathematics – if not all of it – could be derived from a number of axioms logically related to each other. This boost for mathematical logic may have been their most important legacy, inspiring such figures as Alan Turing and John von Neumann, mathematicians who in the 1930s and 1940s conceived the early computers. It is in this sense that Russell and Whitehead are the grandfathers of software.
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In 1905 in the British medical periodical the
Lancet,
E. H. Starling, professor of physiology at University College, London, introduced a new word into the medical vocabulary, one that would completely change the way we think about our bodies. That word was
hormone.
Professor Starling was only one of many doctors then interested in a new branch of medicine concerned with ‘messenger substances.’ Doctors had been observing these substances for decades, and countless experiments had confirmed that although the body’s ductless glands –
the thyroid in the front of the neck, the pituitary at the base of the brain, and the adrenals in the lower back – manufactured their own juices, they had no apparent means to transport these substances to other parts of the body. Only gradually did the physiology become clear. For example, at Guy’s Hospital in London in 1855, Thomas Addison observed that patients who died of a wasting illness now known as Addison’s Disease had adrenal glands that were diseased or had been destroyed.
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Later Daniel Vulpian, a Frenchman, discovered that the central section of the adrenal gland stained a particular colour when iodine or ferric chloride was injected into it; and he also showed that a substance that produced the same colour reaction was present in blood that drained away from the gland. Later still, in 1890, two doctors from Lisbon had the ostensibly brutal idea of placing half of a sheep’s thyroid gland under the skin of a woman whose own gland was deficient. They found that her condition improved rapidly. Reading the Lisbon report, a British physician in Newcastle-upon-Tyne, George Murray, noticed that the woman began her improvement as early as the day after the operation and concluded that this was too soon for blood vessels to have grown, connecting the transplanted gland. Murray therefore concluded that the substance secreted by the gland must have been absorbed directly into the patient’s bloodstream. Preparing a solution by crushing the gland, he found that it worked almost as well as the sheep’s thyroid for people suffering from thyroid deficiency.
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