Wittgenstein: Philosophy in an Hour. Paul Strathern

and immediately he began reading Russell’s Principles of Mathematics, the very latest work on the subject. In this, Russell set out to prove that the fundamentals of mathematics were in fact logical, and that all pure mathematics could be derived from a few basic logical principles. But Russell’s attempt foundered on a paradox. Russell attempted to define numbers by using classes. Some classes are members of themselves, and some are not. For example, the class of human beings is not a member of itself because it is not a human being. The class of nonhuman beings, however, is a member of itself. But is the class of ‘all classes which are not members of themselves’ a member of itself? If it is, it is not. Yet if it is not, it is. The entire status of mathematics hung on this seemingly trivial paradox, which according to Russell affected ‘the very foundations of reasoning.’ He ended his book by issuing a challenge to ‘all students of logic’ to solve it. Wittgenstein immediately launched into the fray. He emerged with a radical solution, dismissing the entire concept of classes as an unwarranted assumption.

      Russell in his turn dismissed Wittgenstein’s solution while at the same time admiring its ingenuity. But Wittgenstein was not so easily put off. In 1911 he travelled to Cambridge to see Russell, and there he decided to study philosophy with Russell and abandon engineering, the profession his father had chosen for him.

      Russell had taken on a lot more than he’d bargained for. At the time he was arguably the leading philosopher in Europe; Wittgenstein had hardly read a book on the subject. Yet Wittgenstein took to turning up at Russell’s rooms at all times of day and night, insisting upon engaging him for hours on end in the most intense ‘philosophical’ speculations – sometimes to do with logic, sometimes to do with suicide. According to Russell, Wittgenstein had ‘passion and vehemence’ and a feeling that ‘one must understand or die.’ Yet when he was convinced that he did understand, nothing would persuade him to the contrary. He refused to accept Russell’s belief in empiricism, that we can gain knowledge from our experience. In Wittgenstein’s view, knowledge was limited to logic. When Russell claimed that he knew there was no rhinoceros in the room, Wittgenstein refused to accept this. It was logically possible that there was a rhinoceros in the room. Russell then asked him where this rhinoceros could possibly be, and began looking behind the chairs and under the table. Still Wittgenstein adamantly refused to accept that Russell knew for certain there was no rhinoceros in the room.

      Fortunately (or perhaps unfortunately for philosophy) Russell quickly realised that his impossibly intense and egotistical new student was more than just an obstinate, pestering bore. But he also realised that his new student needed to learn basic logic. At some inconvenience, Russell used his influence and arranged for Wittgenstein to be tutored by a leading Cambridge logician, W. E. Johnson, a fellow of Kings College. The result was a fiasco. ‘I found in the first hour that he had nothing to teach me,’ declared Wittgenstein. Johnson ironically observed, ‘At our first meeting he was teaching me.’ This arrogant rudeness and inability to listen were to become an increasingly dominant trait in Wittgenstein’s character.

      Russell generously characterised this period of getting to know Wittgenstein as ‘one of the most exciting intellectual adventures of my life.’ He and Wittgenstein began discussing mathematical logic, which at the time was so complex that only half a dozen people in the world could understand it. Yet according to Russell, within two years Wittgenstein ‘knew all I had to teach.’ More than this, Wittgenstein had managed to convince Russell that he would never do any creative philosophy again. It was too difficult for him. Only he, Wittgenstein, could possibly discover the way forward.

      Wittgenstein had thus found a substitute father and destroyed him. Fortunately Wittgenstein’s intellect was just as powerful as his personality. Indeed, it’s almost impossible to separate the two, and both had now found their purpose in life. This was more than just a psychological hatchet job by Wittgenstein. The only thing that could stop him from destroying everything, including himself, was the ‘truth.’

      It is no exaggeration to compare Wittgenstein wrestling with the problems of logic to Jacob wrestling with his angel. As soon as Wittgenstein discovered philosophy, it became a matter of life and death for him. Anyone who felt it as less than this he viewed with contempt.

      But this period of self-realisation led to some rather less exalted discoveries. Wittgenstein realised that he was homosexual. He enjoyed spending his time in intense conversation with lonely, intellectual young men but couldn’t bring himself to sully these relationships with sensuality. This element in his nature was almost certainly relieved by rare visits to London, or occasional night pickups in the Prater, the main park in Vienna, when he went home. All this only contributed to his psychological turmoil. Here was demonic genius at its purest, aspiring to the heights yet living in shadow, driven to the point where it was all but out of control. After Wittgenstein’s father died (‘the most beautiful death I can imagine, falling asleep like a child’), he returned to Cambridge to battle the problems of logic with renewed vigor.

      There were moments of comparative bliss. In 1913 Wittgenstein went with his friend, the gifted young mathematician David Pinsent, on a summer holiday to Skjolden, a remote village nearly ninety miles up the Hardangerfjord in Norway. Here the two of them enjoyed themselves like thirteen-year-old schoolboys. But Wittgenstein could be an exacting travelling companion, even for an easygoing, self-effacing character like Pinsent. Each morning Wittgenstein insisted on doing logic for several hours. In Pinsent’s words: ‘When he is working he mutters to himself (in a mixture of German and English) and strides up and down all the while.’ At other times he might take extreme offense over trifles. When Pinsent stopped to photograph the scenery, or even spoke to someone else on a train, this would provoke an emotional outburst from Wittgenstein, followed by a long sulk. It is difficult to gauge how much this stemmed from his overriding need to dominate, and how much it was due to lover’s jealousy (or other conflicts arising from his unspoken love).

      As the holiday progressed, Wittgenstein grew increasingly eccentric and neurotic. He became convinced that he was about to die and kept harping on this to Pinsent, who concluded that ‘he was mad.’ By now Wittgenstein was breaking new ground in logic and felt he was close to solving the problems that had prevented Russell from discovering the logical foundation for mathematics. The only trouble was, he now felt sure he would die before he could publish the truth. Wittgenstein wrote to Russell, demanding that they meet ‘as soon as possible’ so that Wittgenstein could tell him where he had gone wrong.

      Despite this turmoil, when the two vacationers returned to England Wittgenstein informed Pinsent that this was the best holiday he had ever had. In the understatement of a true Englishman, Pinsent confided to his diary that Wittgenstein had been ‘trying at times,’ but he had enough sense to promise himself that he would never vacation with him again.

      Meanwhile Wittgenstein was having a series of urgent meetings with Russell. Wittgenstein was in an excited state, and Russell found it impossible to follow his complex logical arguments. But Russell became even more exasperated when Wittgenstein refused to commit himself to paper until he had brought his ideas to perfection. In the end Russell managed to persuade Wittgenstein to let a stenographer be present at their meetings, so that Wittgenstein’s answers to Russell’s probing questions could be taken down in shorthand.

      These stenographer’s notes form the basis of Wittgenstein’s first work, ‘Notes on Logic.’ In it he makes numerous insightful remarks, some of breathtaking simplicity (such as: ‘“A” is the same as the letter “A”’). Russell understood at once what Wittgenstein was trying to establish: in order to overcome the paradoxical difficulties of Russell’s classes, things needed to be shown in symbolic form rather than said (because they simply could not be said, and were in fact unsayable). This was difficult to grasp at the best of times. Indeed, probably only Russell really understood what Wittgenstein was getting at. And it looked like it would remain that way, for, as Russell said, ‘I told him he ought not simply to state what he thinks true, but to give arguments for it, but he said arguments spoil its beauty, and that he would feel as if he was dirtying a flower with muddy hands.’ Wittgenstein was a perfectionist: either you understood perfectly, completely, and at once what he said, or there was no point in listening to what he said at all.

      Yet in this unpublished work Wittgenstein did