In​ November 1910 a Jewish engineer at Victoria University in Manchester obtained a patent for a new kind of aeronautical propeller. He was just 21, and well on the way to achieving his childhood dream of becoming the greatest aviator since Orville and Wilbur Wright. But he hesitated. He had been reading Gottlob Frege and Bertrand Russell in his spare time, and believed that their inquiries into the foundations of logic heralded a revolution even more exciting than the invention of powered flight. He wanted to be part of it if he could. The following year he was knocking on Russell’s door at Trinity College Cambridge, and the great man was sufficiently impressed to let him enrol at once as an undergraduate student. After a while Russell regretted his decision, writing in letters to his friend Ottoline Morrell that his ‘German engineer’ was a ‘fool’ who kept pestering him with stupid questions. But then he changed his mind, saying that the ‘ferocious German (who is an Austrian I find)’ appeared to be ‘really intelligent’ after all.

A few weeks more and Russell was completely won over, treating Ludwig Wittgenstein as a brilliant colleague rather than a tiresome student, and as living proof that ‘making machines’ is a better preparation for work in philosophy than a British classical education. On the other hand he didn’t want to accept Wittgenstein’s main contention: that logic is concerned with ‘forms’ rather than ‘objects’ – specifically, the forms of human thought and language rather than timeless objects located in some ideal world. Russell’s friend G.E. Moore had already wowed the gilded youth of Cambridge with his doctrine that ‘goodness’ and ‘beauty’ are supernatural entities accessible only to first-class minds, and Russell was trying to do something similar for logic, maintaining that anyone clever enough to understand it gains access to a realm of intellectual perfection beyond the hurly-burly of earthly existence. Wittgenstein’s scepticism about logical ‘objects’ was an affront to all that Russell held dear, and he resisted it fiercely. But then he was mollified by a gift of ‘lovely roses’: Wittgenstein was ‘the young man one hopes for’, he now wrote to Morrell, and ‘I like him very much.’ After undergoing further bouts of ruthless criticism, he confessed to being ‘strangely excited’ by Wittgenstein: ‘I love him,’ he said, and he hoped to appoint him as his successor and watch him ‘solve the problems I am too old to solve’.

Wittgenstein wasn’t particularly impressed by Russell’s adoration. If his philosophical capacities were as exceptional as Russell seemed to think, then this was a curious fact – like having beautiful ears or excellent eyesight – but not an occasion for pride, still less for boasting. So when his sister Hermine came over to visit she was utterly unprepared for Russell’s remark, over tea, that ‘we expect the next big step in philosophy to be taken by your brother.’ The only snag was that Wittgenstein seemed incapable of putting his ideas into writing. ‘His artistic conscience got in the way,’ as Russell put it, and ‘because he couldn’t do it perfectly he couldn’t do it at all.’ He allowed Russell to take notes of their conversations – a curious reversal of roles – and dictated some remarks to a typist, but he remained dissatisfied, and two years after first arriving in Cambridge he went off to Norway in search of solitude.

Then there was war. Wittgenstein served for five years in the Austrian army – an experience he never regretted – while Russell threw himself into campaigning for peace. They lost touch but continued to work separately on the problems they had clashed over before the war: the nature of logic and its relation to eternal truths on the one hand and human experience on the other. In a series of public lectures Russell alluded to certain ‘vitally important discoveries, not yet published, by my friend Mr Ludwig Wittgenstein’, and in a book on mathematics he paid tribute to his ‘former pupil’ and wondered ‘whether he is alive or dead’. It wasn’t until 1919 that he received a postcard from Wittgenstein, now a prisoner of war in Italy, saying that he had ‘done lots of logical work’ and, in his next message, that he had completed a book, in German, which ‘solved our problems finally’. (‘This may sound arrogant,’ he said, ‘but I can’t help believing it.’)

The working title of the book was Der Satz (a word that evokes not only ‘sentence’ but also ‘set’ or ‘musical movement’). It combined philosophical boldness, of a kind that Russell appreciated, with ingenious literary experimentation, which Russell didn’t like at all. It opened with the statement ‘The world is everything that is the case,’ and proceeded through several hundred further statements, ordered by a complex system of decimal numbering, finally concluding that ‘There is indeed the inexpressible,’ that ‘Philosophy is not a theory but an activity,’ and hence: ‘Whereof one cannot speak, thereof one must be silent.’ Wittgenstein tried to place Der Satz with an avant-garde publisher in Innsbruck who had previously promoted stylish philosophical authors such as Kierkegaard, Nietzsche and Karl Kraus, but he was rebuffed. He seems to have taken the rejection in his stride: if his ‘new method’ was worthless, he said, then it was best forgotten, and if it was any good then it would be recognised in due course. In that event philosophers would stop flouncing around like some kind of intellectual royalty, imagining that they hold the keys to eternal truth, and learn to confine themselves to the activity of exploring the various forms of human thought: more specifically they would try to figure out what we really mean by all the different sorts of things we say – which might sound easy, but would turn out to be hard. As with the propeller he had invented ten years before, he decided to forget about his book and move on.

When Wittgenstein got back from prison camp in Italy, he spent a year in Vienna training as a teacher, after which he worked with pre-adolescent children in a series of village schools in the Austrian Alps. His methods were in keeping with his approach to philosophy: he did not lay claim to any special authority and instead of expounding facts and theories he asked his pupils questions and left them to work out the answers for themselves. When Hermine happened to see him at work she marvelled at his capacity to hold their attention. After six years he gave up teaching and returned to Vienna, where he resumed his original vocation as an engineer, supervising work on a modernist house for his sister Margarete, which was completed at the end of 1928.

Wittgenstein may have forgotten about the philosophical world, but it had not forgotten about him. Russell had taken pity on his abandoned book and got it published in 1922, though with a rebarbative title – Tractatus Logico-Philosophicus – and a ponderous introduction in which he claimed that Wittgenstein’s aim was to ‘prevent nonsense’ by constructing a ‘logically perfect language’. This may be what Russell would have liked Wittgenstein to say, but it was a spectacular misrepresentation of what he had actually written. In the first place, Wittgenstein had never said anything about replacing the ordinary statements of ordinary people with some artificial logical language; he had argued, on the contrary, that they are – despite the antics of conceited philosophers – ‘logically completely in order, just as they are’. Second, he wanted to praise nonsense rather than bury it: he thought that the best things in life – not only philosophical insights, but also religious, moral, musical or artistic experiences – confounded any attempt to articulate them, and he had indeed sent a letter to Russell telling him that the ‘main point’ of his book was to create a philosophical safe haven for those things that ‘can not be expressed … but only shown’. But Wittgenstein’s efforts were wasted: Russell had clearly fallen out of love with him, and he concluded his introduction by sniping at his former pupil for relapsing into ‘mysticism’, joking with supreme self-satisfaction that ‘Mr Wittgenstein manages to say a good deal about what cannot be said.’

Despite Wittgenstein’s indifference, the Tractatus quickly found its way to readers all around the world, accompanied by Russell’s obtuse and unhelpful introduction. Many of them drew inspiration from it, in one way or another, and started to practise philosophy in a more or less Wittgensteinian style, not as a ‘theory’ that articulates esoteric truths, but an ‘activity’ that explores the rich and surprising logics of natural languages. Wittgenstein allowed himself to be gratified when he got wind of these developments, but only up to a point. He took issue with a group of self-appointed disciples in Vienna who, like Russell, insisted on treating religion as a meaningless relic of an unenlightened age – an attitude that Wittgenstein regarded as brash, incurious and mean-spirited. (‘I am not a religious man,’ he once explained to a friend, ‘but I cannot help seeing every problem from a religious point of view.’) When he returned to Cambridge in 1929 – he had intended the trip as a brief holiday, but ended up teaching there, on and off, for almost twenty years – he was appalled to discover a band of philosophical enthusiasts for something called ‘scientific method’. They seemed to believe that the Tractatus justified them in treating religion as a joke and morality as no more than an expression of raw emotion.

Self-styled Wittgensteinians in the ‘Vienna Circle’ and the ‘Cambridge School’ were of course taken aback when Wittgenstein repudiated their dogmas, and many retaliated not with reasoned argument but with speculative gossip, suggesting that there were two different Wittgensteins, and that after the incisive youthful brilliance of the Tractatus he had declined into doddering incoherence. Russell put it about that he had suffered some kind of mental breakdown, perhaps connected with the war – why else would he have gone off to teach the children of Austrian peasants instead of getting himself elected to a Cambridge fellowship? C.D. Broad, chief fixer of the philosophy faculty at Cambridge, was prepared to admit that the Tractatus had been a significant book in its time, but said he had always disliked its literary pretentions, summing up his concerns with a donnish quip about bright young things who ‘dance to the highly syncopated pipings of … Herr Wittgenstein’s flute’ – a remark that conveniently combined an antisemitic allusion to the pied piper with a reminder that Wittgenstein (‘Herr Wittgenstein’) had fought on the wrong side in the Great War.

When Wittgenstein started teaching undergraduates in Cambridge, he put into practice the precepts of the Tractatus. Instead of delivering lectures he simply posed disarming questions. Is pain really the opposite of pleasure? Is our awareness of pain more like listening, or hearing? When you imagine a red rose, how do you know it’s really red, and why might we think that blue is closer to green than red? ‘Say what you really think,’ he told his students, and ‘don’t try to be intelligent.’ The classes often ‘felt like the day of judgment’, as one awestruck participant put it, but they continued successfully year after year. Broad had to admit that students seemed to ‘get a great deal’ out of Wittgenstein, but he was decidedly unimpressed: the students seemed unable to give a clear account of what exactly they were getting, and they could never make it pay in their exams.

By the 1940s the British philosophical establishment was more or less united in seeing Wittgenstein as a burnt-out wreck and a disgrace to the profession: A.J. Ayer, for example, described him as a maniacal egotist who took refuge within a ‘cénacle of the faithful’, and Isaiah Berlin thought he had been reduced to peddling some trashy variety of ‘imaginative romanticism’. The gossip did not cease with Wittgenstein’s death (in 1951, at the age of 62) and it has since taken a neuroscientific turn, with speculative talk about autism and Asperger’s. If this is meant to imply a pathological incapacity for insight into other people rather than a simple dislike for Cambridge dons, then it is contradicted by the memoirs of some of Wittgenstein’s devoted friends (Norman Malcolm, Rush Rhees, Con Drury and others), and by a fascinating collection of family letters, published in German in 1996 and now available in English.

Wittgenstein’s father was a self-made industrialist who saw himself as the Carnegie of Austria and took pride in his highly cultivated wife and a close-knit set of unconventional, artistic children. They were Jewish by heritage, but they went along with Christianity at least to the extent of holding big family parties at Christmas. After the father’s death, the family traditions were sustained by Hermine, the eldest child, with help and support from Ludwig, who was the youngest. ‘One could ask him for advice about any and everything,’ as Hermine put it: he was ‘interested in everything about everyone’ and always managed to ‘bring out the good in people’. As she made plans for Christmas in 1920 – involving three sisters and two brothers, along with their elderly mother and spouses and nephews and nieces – she relied on him to ensure that they would all get along together, without lapsing into meaningless routine. (‘Affection alone can be dreadful,’ as she told him, but ‘nothing is as beautiful as being understood by another person.’) A few years later she accepted his suggestion that she add a judicious ‘seasoning of friends’ to their Christmas gathering, to stimulate their family conversations. He also warned her of the risks of uncomprehending goodwill: it might sometimes be a good idea to ‘embrace someone with whom you are not entirely on good terms’, as he put it, but ‘only if the embrace is capable of … bringing about a reconciliation … for if the embrace can’t do that, then it’ll just be a new misunderstanding’.

The exchanges are not confined to family Christmases. Wittgenstein’s work as a schoolmaster makes several appearances, for example in a letter about getting his pupils to design and build tables and chairs. When it comes to philosophy, however, he tends to be flippant rather than forthcoming. He tells his brother-in-law Max that he is going to bring out a really useful book called Philosophischer Hausschatz, a treasury of philosophical wisdom printed on detachable sheets of hygienic tissue, and is delighted when his brother Paul joins him in ridiculing the cult of Einstein’s philosophical sagaciousness (‘An unshared joy is really only half a joy’). When his sister Helene tells him that he is supposed to be a ‘great philosopher’, he replies that his greatness is so enormous that even he can’t fathom it, and follows up by saying that he has been invited to give a weekly Talkstündchen on the BBC in order to ‘promote understanding between nations’.

On occasion, though, he did speak seriously about his philosophical work. In November 1929 he wrote to his sister Margarete about a talk he was giving to a student club in Cambridge, concerning ‘the ultimate meaning of life’ and our ‘desire to say something’ about it. The doctrines of logic and language in the Tractatus implied that such things cannot be put into words, any more than a gallon of water can be poured into a teacup; but – contrary to what his more hard-headed followers seemed to think – that did not mean he wanted to disparage or diminish them. As far as he was concerned, the fact that ethical and religious attitudes fall outside the limits of articulate thought was not their weakness but their glory. Margarete wrote back to say she was looking forward to receiving the typescript (‘I could hardly imagine a greater joy’) and – though there is no trace of it in their letters – it seems a safe bet that they read it together over Christmas.

Another matter on which Wittgenstein shared his intellectual concerns with his family was that of sainthood. The fact that he had once told Russell he was interested in becoming a saint was perfect fuel for the Cambridge gossip-machine, but Wittgenstein’s siblings knew what his detractors apparently did not: that he was referring not to canonisation by some church but to a favourite theme from one of his favourite books: William James’s Varieties of Religious Experience. James’s argument was that moral progress, such as it is, arises not from the insight and ingenuity of ethical theorists, but from the boldness of those rare individuals who manage to overcome ‘shyness, laziness and stinginess’ in order to live simple, honest lives in which, as he put it, ‘paltry conventionalities and mean incentives … hold no sway’. That was the spirit in which Wittgenstein committed himself – as he explained in an exchange of letters with Hermine – to the project of becoming ein anständiger Mensch, or ‘a decent human being’. She worried for him, because she knew he would always chastise himself for falling short of this seemingly modest goal; but she also knew – as readers of this book will too – that he often came very close.