My first serious contact with the German learned world consisted in the reading of Kant, whom, while a student, I viewed with awed respect. My teachers told me to feel at least equal respect for Hegel, and I accepted their judgment until I read him. But when I read him I found his remarks in the philosophy of mathematics (which was the part of philosophy that most interested me) both ignorant and stupid. This led me to reject his philosophy, and at the same time, for somewhat different reasons, I rejected the philosophy of Kant. But while I was abandoning the traditional German philosophy I was becoming aware of the work of German mathematicians on the principles of mathematics, which was at that time very much better than any work on the subject elsewhere. I read avidly the work of Weierstrass and Dedekind which swept away great quantities of metaphysical lumber that had obstructed the foundations of mathematics ever since the time of Leibniz. More important than either of these, both intrinsically and in his influence on my work, was Georg Cantor. He developed the theory of infinite numbers in epoch-making work which showed amazing genius. The work was very difficult and for a long time I did not fully understand it. I copied it, almost word for word, into a notebook because I found that this slow mode of progression made it more intelligible. While I was doing so I thought his work fallacious, but nevertheless persisted. When I had finished, I discovered that the fallacies had been mine and not his. He was a very eccentric man and, when he was not doing epoch-making work in mathematics, he was writing books to prove that Bacon wrote Shakespeare. He sent me one of these books with an inscription on the cover saying, “I see your motto is Kant or Cantor.” Kant was his bugbear. In a letter to me he described him as, “Yonder sophistical Philistine who knew so little mathematics.” He was a very pugnacious man and, when he was in the middle of a great controversy with the French mathematician Henri Poincaré, he wrote to me, “I shall not be the succumbent!” which indeed proved to be the case. To my lasting regretyl never met him. Just at a moment when I was to have met him, his son fell ill and he had to return to Germany.
The influence of these men on my work belonged to the last years of the nineteenth century. With the beginning of the twentieth, I became aware of a man for whom I had and have the very highest respect although at that time he was practically unknown. This man is Frege. It is difficult to account for the fact that his work did not receive recognition. Dedekind had been justly acclaimed, but Frege on the very same topics was much more profound. My relations with him were curious. They ought to have begun when my teacher in philosophy, James Ward, gave me Frege’s little book Begriffsschrift saying that he had not read the book and did not know whether it had any value. To my shame I have to confess that I did not read it either, until I had independently worked out a great deal of what it contained. The book was published in 1879 and I read it in 1901. I rather suspect that I was its first reader. What first attracted me to Frege was a review of a later book of his by Peano accusing him of unnecessary subtlety. As Peano was the most subtle logician I had at that time come across, I felt that Frege must be remarkable. I acquired the first volume of his book on arithmetic (the second volume was not yet published). I read the introduction with passionate admiration, but I was repelled by the crabbed symbolism which he had invented and it was only after I had done the same work for myself that I was able to understand what he had written in the main text. He was the first to expound the view which was and is mine, that mathematics is a prolongation of logic, and he was the first to give a definition of numbers in logical terms. He did this in 1884 but nobody noticed that he had done it.
Frege thought, as I thought for a few months at the turn of the century, that the reduction of mathematics to logic had been definitively completed. But in June 1901 I came across a contradiction which proved that something was amiss. I wrote to Frege about it and he behaved with a noble candor which cannot be too highly praised. The second volume of his arithmetic had been passed through the press but not yet published. He added an appendix saying that in view of the contradiction that I had brought to his notice “die Arithmetik ist ins Schwanken geraten” I understand that in later years, like the Pythagoreans when confronted with irrationals, he took refuge in geometrical treatment of arithmetic. In this I cannot follow him, but it is interesting to observe the repetition of ancient history in a new context. To my lasting regret, I never met Frege, but I am glad to have done all that lay in my power to win him the recognition which he deserved.
An even more important philosophical contact was with the Austrian philosopher Ludwig Wittgenstein, who began as my pupil and ended as my supplanter at both Oxford and Cambridge. He had intended to become an engineer and had gone to Manchester for that purpose. The training for an engineer required mathematics, and he was thus led to interest in the foundations of mathematics. He inquired at Manchester whether there was such a subject and whether anybody worked at it. They told him about me, and so he came to Cambridge. He was queer, and his notions seemed to me odd, so that for a whole term I could not make up my mind whether he was a man of genius or merely an eccentric. At the end of his first term at Cambridge he came to me and said: “Will you please tell me whether I am a complete idiot or not?” I replied, “My dear fellow, I don’t know. Why are you asking me?” He said, “Because, if I am a complete idiot, I shall become an aeronaut; but, if not, I shall become a philosopher.” I told him to write me something during the vacation on some philosophical subject and I would then tell him whether he was complete idiot or not. At the beginning of the following term he brought me the fulfillment of this suggestion. After reading only one sentence, I said to him: “No, you must not become an aeronaut.” And he didn’t. He was not, however, altogether easy to deal with. He used to come to my rooms at midnight, and for hours he would walk backward and forward like a caged tiger. On arrival, he would announce that when he left my rooms he would commit suicide. So, in spite of getting sleepy, I did not like to turn him out. On one such evening, after an hour or two of dead silence, I said to him, “Wittgenstein, are you thinking about logic or about your sins?” “Both,” he said, and then reverted to silence. However, we did not meet only at night. I used to take him long walks in the country round Cambridge. On one occasion I induced him to trespass with me in Madingley Wood where, to my surprise, he climbed a tree. When he had got a long way up a gamekeeper with a gun turned up and protested to me about the trespass. I called up to Wittgenstein and said the man had promised not to shoot if Wittgenstein got down within a minute. He believed me, and did so. In the First War he fought in the Austrian army and was taken prisoner by the Italians two days after the armistice. I had a letter from him from Monte Cassino, where he was interned, saying that fortunately he had had his manuscript with him when he was taken prisoner. This manuscript, which was published and became famous, had been written while he was at the front. He inherited a great fortune from his father, but he gave it away on the ground that money is only a nuisance to a philosopher. In order to earn his living, he became a village schoolmaster at a little place called Trattenbach, from which he wrote me an unhappy letter saying, “The men of Trattenbach are wicked.” I replied, “All men are wicked.” He rejoined, “True, but the men of Trattenbach are more wicked than the men of any other place.” I retorted that my logical sense rebelled against such a statement; and there the matter rested until residence elsewhere enlarged his view as to the prevalence of sin. In his later years he was professor of philosophy at Cambridge, and most philosophers both there and at Oxford became his disciples. I myself was very much influenced by his earlier doctrines, but in later years our views increasingly diverged. I saw very little of him in his later years, but at the rime when I knew him well he was immensely impressive as he had fire and penetration and intellectual purity to a quite extraordinary degree.
These are only a few of the men who have influenced me. I can think of two who have influenced me even more. They are the Italian Peano, and my friend G.E. Moore.
— The collected papers of Bertrand Russell: Last Philosophical Testament 1943-1968, Vol. 11, Routledge, 1997, pp. 106-109
Portrait from Memory
Presenter: This is the BBC Third Programme. We have in the studio Bertrand Russell, who talks to us in the series, “Sense, Perception, & Nonsense, Number Seven: Is this a dagger I see before me?”
Bertrand Russell: One of the advantages of living in Great Court, Trinity, I seem to recall, was the fact that one could pop across at any time of the day or night and trap the then young G.E. Moore into a logical falsehood by means of a cunning semantic subterfuge. I recall one occasion with particular vividness. I had popped across and had knocked upon his door. “Come in”, he said. I decided to wait awhile in order to test the validity of his proposition. “Come in”, he said once again. “Very well”, I replied, “if that is in fact truly what you wish”.
I opened the door accordingly and went in, and there was Moore seated by the fire with a basket upon his knees. “Moore”, I said, “do you have any apples in that basket?” “No”, he replied, and smiled seraphically, as was his wont. I decided to try a different logical tack. “Moore”, I said, “do you then have some apples in that basket?” “No”, he replied, leaving me in a logical cleft stick from which I had but one way out. “Moore”, I said, “do you then have apples in that basket?” “Yes”, he replied. And from that day forth, we remained the very closest of friends.”
— Jonathan Miller, Beyond the Fringe, 1962