Wittgenstein

The greatest modern philosopher

Wittgenstein’s originality

The word ‘genius’ is frequently applied to mathematicians, scientists, artists, and musicians, but rarely to philosophers. However, there is a notable exception: Ludwig Wittgenstein. Echoing others, Bertrand Russell described him as ‘perhaps the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating.’ In a memorable phrase Wittgenstein once wrote: ‘Uttering a word is like striking a note on the keyboard of the imagination’ (Philosophical Investigations, 6). No other twentieth-century philosopher has uttered so many words that struck the keyboard of the imagination. That he was a genius is beyond serious doubt. Because of the originality and depth of his thought, he is widely regarded as the greatest modern philosopher.

Since his death at the age of sixty-two on 29 April 1951, a vast number of articles, monographs, essays, commentaries, and books, have been devoted to his life, personality, and work. Some researchers estimate the number of such items to be more than 7000. Not all of these are technical pieces. There are biographies, plays, a novel, a television drama, and even a video for children in which he is depicted as a computer. Even outside of philosophy he has become a legend. Today his ideas are discussed in anthropology, literature, sociology, psychology, and linguistics. No other twentieth-century philosopher has been the focus of such intense scholarly concentration.

Given this vast outpouring of materials it is sensible to ask: Why do we need another book – the one you are now reading – on Wittgenstein? There are at least two answers to the question. Both are somewhat lengthy. Here is the first. It deals with the need to update and extend the scope of existing commentaries. During his lifetime, Wittgenstein published only two things: a book – the Tractatus Logico-Philosophicus in 1922, and a short essay on logical form in 1929. In the twenty-two remaining years of his life, he continued to write incessantly. After his death his executors discovered an enormous legacy of unpublished writings. The amount of material, most of which is still being edited, is estimated to consist of about ninety-five volumes, some of which are non-philosophical, some of which are differing versions of the same works, but most of which are new. The first document to be issued was Philosophical Investigations, which appeared in 1953. This is generally regarded as Wittgenstein’s masterpiece. Since the Investigations another twenty or so volumes have been released, some of them only recently. Exegetes are just now beginning to explore these materials. Most existing studies do not deal with these works. They tend to stop with the Investigations. David Pears’s The False Prison (1987) and P. M. S. Hacker’s Wittgenstein’s Place in Twentieth-Century Analytic Philosophy (1996) exemplify the point. Both are superb books yet they focus entirely on the Tractatus and the Investigations. A need to update and extend the coverage of the existing scholarship is thus mandatory. This is what I will do in this study. It will deal with Wittgenstein’s latest contributions in a way that no other general work does, and this constitutes one justification for writing it.

The second answer is closely related to the first. It provides a new picture of Wittgenstein’s intellectual development. Almost all scholars divide Wittgenstein’s career into two phases. In their view the first is the time span between 1911 and 1922, and the second is the period from 1929 until his death in 1951. The former begins when he came to Cambridge University to study logic with Bertrand Russell and ends with the publication of the Tractatus. That initial stage was interrupted by the outbreak of the First World War in 1914. An Austrian patriot, Wittgenstein immediately left Cambridge and joined the Austrian army. During the war he fought with distinction. In the declining days of the conflict he was captured by the Italians and spent a year in a prison camp near Monte Cassino. During the war he finished writing the Tractatus and while in captivity arranged to send the manuscript to Russell who was eventually instrumental in having it published. Thinking that in this work he had solved all the major problems of philosophy, he spent the next decade as an elementary school teacher in Lower Austria and as a self-proclaimed architect, designing a house in Vienna for his sister (Margarete Stonborough) that has since become a national monument.

The second phase begins when he decided to resume his philosophical career. He returned to Cambridge as a graduate student in 1929. Intellectually, this is his most creative period. Much, though not all, of it was spent in England. It was during this ‘second phase’ that his philosophical ideas changed radically, being based on a new method he invented for dealing with philosophical problems (see Chapter 3). The commentators generally describe this segment as ‘the later philosophy of Wittgenstein.’ But after Part I of the Investigations was completed (probably in 1945), Wittgenstein’s philosophical explorations continued unabated and reached new heights. On Certainty was his last work. The final seven entries were inserted into the manuscript only two days before his death. A number of scholars now believe that On Certainty goes beyond anything contained in either the Tractatus or the Investigations. They thus see a post-Investigations stage in his philosophical development. Daniele Moyal-Sharrock has coined the phrase ‘The Third Wittgenstein’ to describe his final writings.

The most eminent philosophers of the past have had one significant idea. This is true of Plato, Aristotle, St. Augustine, Descartes, Spinoza, Locke, Berkeley, Hume and Kant. It is also true of many of the best philosophers of the twentieth century: Frege, Russell, Carnap, Ryle, and Quine, for instance. But Wittgenstein stands alone in having had three great ideas: they are found in the Tractatus, the Investigations, and On Certainty, respectively. Indeed, if we turn from philosophy to other creative endeavors of the highest order, it is difficult to find anyone other than Wittgenstein who has had three distinct and important ideas. Consider composers, for example. Bach’s polyphonic technique was already set when he was twenty and it never changed throughout his long career. Mozart’s style remained essentially the same from beginning to end. One can say comparable things about Schubert, Brahms and Berlioz. In contrast, Beethoven’s career had two distinct periods. His early compositions were very much like those of Haydn and Mozart; but by the end of his life his late quartets and piano sonatas soared beyond anything that he, or indeed any other composer, had previously accomplished. Wittgenstein’s intellectual growth is thus remarkable. There are huge differences between his early ideas and those of the Investigations, and huge differences between those of the Investigations and those of On Certainty. In agreement with Daniele Moyal-Sharrock, I will emphasize these three phases of his philosophical development in this book. Such an emphasis constitutes a second justification for writing it.

Many scholars have pointed out the revolutionary nature of Wittgenstein’s ideas. In a brief biographical sketch, G. H. von Wright, a distinguished Finnish scholar and philosopher, has expressed this point of view as eloquently as anyone. Here is how he states the matter:

The young Wittgenstein had learned from Frege and Russell. His problems were in part theirs. The later Wittgenstein, in my view, has no ancestors in the history of thought. His work signals a radical departure from previously existing paths of philosophy.

In a footnote, von Wright expands this remark:

I have seen this statement, and the one preceding it, contested. But I think they are substantially correct and also important. The Tractatus belongs in a definite tradition in European philosophy, extending back beyond Frege and Russell at least to Leibniz. Wittgenstein’s so called ‘later philosophy’, as I see it, is quite different. Its spirit is unlike anything I know in Western thought and in many ways opposed to aims and methods in traditional philosophy. This is not incompatible with the fact – about which more is known now than when this essay was first published – that many of Wittgenstein’s later ideas have seeds in works which he had read and conversations he had with others. It is interesting to note what Wittgenstein himself says about this in Vermischte Bemerkungen (Culture and Value) especially pp. 18ff and 36. In the latter place he says: ‘I believe my originality (if that is the right word) is an originality belonging to the soil rather than to the seed. (Perhaps I have no seed of my own.) Sow a seed in my soil and it will grow differently than it would in any other soil.’

In a later passage von Wright states, ‘As late as two days before his death he wrote down thoughts that are equal to the best he produced.’ In this passage Wright is indirectly referring to On Certainty. The quotation supports Moyal-Sharrock’s thesis that Wittgenstein’s final writings mark a third stage in his philosophical development.

Wittgenstein says that his originality belongs to the soil rather than to the seed. What is the difference between these two kinds of originality? The remark is eye-stopping and goes to the heart of what makes the later Wittgenstein different from anyone else in Western philosophy. A full answer is possible only after we have explored his three great ideas. But one can get a preliminary sense of his orientation by contrasting his philosophy with a flow of thought inherited from the Greeks. The later Wittgenstein stands at the end and outside of that tradition and can be thought of as turning it on its head. The tradition sees the ordinary person as confused and in need of philosophical therapy. Socrates is the paradigmatic philosopher on this view. He walked around Athens questioning his fellow citizens and quickly exposed the shallowness and inconsistencies of their thinking about fundamental issues. For Wittgenstein the emphasis is in the other direction. It is philosophers like Socrates and his successors who ‘tend to cast up a dust and then complain they cannot see’ and who need help. Therefore in order to explain why his ‘soil’ is different from anyone else’s, let us look briefly at the tradition we have inherited from the Greeks, and then contrast Wittgenstein’s approach with it. We shall find that what is true of the earliest of Greek thinkers, Thales, is generally true of his successors up to the later Wittgenstein.

Textbooks give Thales’ dates as 625–546 b.c., usually adding that these figures are only approximate. Thales was famous among his countrymen as an intellectual prodigy. He was a legislator, a mathematician, an astronomer (who predicted an eclipse of the sun in 585 b.c.) and of course a speculative thinker. Some of what is known about him comes from the historian Herodotus, who was born about fifty years after Thales died, and some from a still later author, Aristotle. In his Metaphysics, Aristotle wrote an account of his philosophical predecessors, beginning with Thales. He says that Thales believed that the fundamental stuff of reality was water. As Aristotle puts it, Thales saw that the ‘nourishment of all things is moist, and that warmth itself is generated from moisture and persists in it; and also that the seeds of all things are of a moist nature,’ and concluded that ‘water is the first principle’ of nature. As an inhabitant of a coastal city in Asia Minor, Thales was aware of the enormous stretch of water composing the Mediterranean Sea. It is also believed that he visited Egypt and saw the vast outpouring of water that flows into the Nile basin. In saying that the nourishment of all things is moist, he attempted to demonstrate that a simple theory will reveal a basic connection between seemingly diverse natural objects, processes and events – plants, soil, ice, and animals. The theory was designed to uncover the common characteristic (essence) that all things possess. His argument was that water was this characteristic.

Thales and his successors in the Greek tradition engaged in speculations about a spectrum of topics, ranging from moral and theological considerations to those that today we would call scientific. In each case they were attempting to show that certain basic principles explain a wide range of phenomena. They were interested in such questions as: What is the fundamental nature of reality? Is there some primal stuff from which all diversity emerges? What remains constant when something changes? What is the difference between mind and matter? Where did the universe come from? Is the sun a rock? Is it possible to obtain knowledge/certainty about nature? Is there any meaning or purpose in life and if so what is it? What is the nature of the good life for man? and so forth. Their ways of dealing with such questions emphasized reason, rather than experiment. They presupposed that rational inquiry would by itself answer all such questions. It was only two thousand years later that Galileo began a new tradition in which it gradually became apparent that reason would have to be supplemented by experiment in order to obtain an accurate picture of the workings of nature.

As a result of this new understanding, inquiries that had originally been treated as part of philosophy gradually separated themselves from the parent discipline. Even as late as the seventeenth century, the physicist Isaac Newton described himself as a ‘natural philosopher.’ But as a consequence of his work, physics soon became an autonomous discipline. In this respect, it was rapidly followed by chemistry and biology, and then in the twentieth century by psychology, anthropology, sociology, political science and linguistics.

Nonetheless, philosophy managed to survive, but not without feeling the effects of these defections. On the one hand, it recognized that the kinds of experimental/theoretical investigations that science conducted were of a different order from anything philosophers could or should do. There was thus a growing and explicit recognition that scientific exploration differed in kind from philosophical inquiry. Yet this acknowledgment did not mean that there were no commonalities among these differing activities. Both were committed to exploring, understanding, and thus ultimately to explaining the inanimate and animate aspects of the world, and both were committed to rigor in argumentation, to the same canons of evidence and proof, and to the use of reason and logic in arriving at knowledge and truth. The tradition thus envisioned its activities as running parallel to those of science. We might say that it saw itself as a kind of non-experimental science. In arguing that water was the basic stuff of reality, Thales was presupposing this parallelism and the tradition followed him in accepting its principles as central to philosophical inquiry.

These are sensible and compelling notions and it is hard to imagine that they could seriously be challenged by anyone whose commitment is to rational inquiry. Yet, in his later writings Wittgenstein explicitly disavowed the assumption that philosophy is and should be a kind of parallel science. In his view theory building by philosophers imposed a restricted conceptual scheme on a complex world and in so doing misrepresented it. Accordingly, the philosophical urge for a deeper explanation led not to understanding but to paradox and confusion. A new conception of the nature and purpose of philosophy was thus required. In Wittgenstein’s later writings this new approach rests on a method he invented for dealing with philosophical problems. Wittgenstein does not talk much about the method but applies it in a detailed way, thus showing by his practice how certain seemingly obdurate philosophical issues can be resolved. His assumption seems to be that the reader will pick up the method by seeing it in operation. The outcome of his work is to challenge the entire tradition that has come down to us from Thales. In a series of lectures he gave in 1939 on the foundations of mathematics, he said about his method:

You might, to be very misleading, call this investigation an investigation into the meaning of certain words. But this is apt to lead to misunderstandings.

  The investigation is to draw your attention to facts you know quite as well as I, but which you have forgotten, or at least which are not immediately in your field of vision. They will all be quite trivial facts. I won’t say anything which anyone can dispute. Or if anyone does dispute it, I will let that point drop and pass on to say something else.

Somewhat later he was to write:

Philosophy simply puts everything before us, and neither explains nor deduces anything. Since everything lies open to view there is nothing to explain. For what is hidden, for example, is of no interest to us.

  One might also give the name ‘philosophy’ to what is possible before all new discoveries and inventions … The work of the philosopher consists in assembling reminders for a particular purpose … If one tried to advance theses in philosophy, it would never be possible to debate them, because everyone would agree to them. (Philosophical Investigations, 126–128)

As these quotations make plain, Wittgenstein is denying that one of philosophy’s fundamental purposes is to explain anything. Indeed, he differs from the tradition and from science in stating that nothing needs to be explained because nothing is hidden. He means, of course, that nothing is hidden from philosophy – but that is just the difference between philosophy and science. As he says in the Investigations, ‘We want to understand something that is already in plain view. For this is what we seem in some sense not to understand.’ This is why ‘one might give the name “philosophy” to what is possible before new discoveries and inventions,’ and why the work of the philosopher ‘consists in assembling reminders for a particular purpose.’ Elsewhere he rejects the idea that philosophy should develop theories. As he says, ‘description should replace explanation,’ and by an explanation he means a theory. It is clear we are dealing with a revolutionary thinker here. To make these non-traditional conceptions plausible, indeed even to explain what they are, is the main purpose of this book and Chapters 2–4 will be dedicated to this endeavor. But before turning to that task I shall devote the rest of the chapter to his remarkable life and personality.

The young Wittgenstein and familial influence

Even though Wittgenstein’s thought has spilled beyond the boundaries of philosophy into other academic domains, he is not the kind of philosopher whose work is known to the general public. In this respect he differs from Bertrand Russell, for instance, who became famous for opposing Britain’s involvement in the First World War and who, along with Albert Einstein and Linus Pauling, protested against the development and deployment of nuclear weapons after the Second World War. There is a wonderful story in illustration of this point that involves the English philosopher, G. E. Moore. In 1951 Moore was awarded the Order of Merit, the highest honor that a man of letters could receive in the British Empire. The presentation was made by King George VI, who afterwards spoke with Moore for a short period and then arose, indicating that the ceremony was at an end. Moore returned to the taxicab where his wife was waiting and leaning over excitedly said: ‘Do you know that the king has never heard of Wittgenstein!’ It is probably true that the general reader, like the king, has never heard of Wittgenstein and it is even more probable that he or she has never read anything written by him. Nonetheless, Wittgenstein had a remarkable personality and led an interesting life. Russell’s four words capture much of the man: he was passionate, profound, intense, and dominating. To these we can also add that he was guilt ridden, insecure, and doubtful of his own abilities. He thus had the kind of personality that most of us think geniuses should have. And the kind of life he led was in perfect conformity with that personality. In nearly every way it deviated from the ordinary. It is thus not remarkable that there should be a spate of biographies about him.

His character and career were to a considerable extent determined by the unusual family in which he was reared. Wittgenstein was the youngest of eight children. Hermine, the eldest, was fifteen years older than Ludwig. Each parent and each sibling was a strong personality and as a group they were close-knit. The impact they made on Ludwig was profound and resonated throughout his life. A simple example: three of his four brothers committed suicide, and Ludwig on several occasions contemplated doing so as well. His brother Rudolf was driven to this action by homosexual guilt. I have mentioned that Wittgenstein was also guilt ridden. He was so for many reasons, but his homosexual impulses and practices were important among them (I shall have more to say about this later). The sisters, by way of contrast, were less emotional and played a stabilizing role in Wittgenstein’s life. This was especially true of Hermine, who consoled him in moments of depression and stress.

Moreover, the family was incredibly wealthy. Wittgenstein’s father, Karl, was an industrialist whose success in the iron and steel industry made him one of the richest men in Europe. In 1898, having accumulated a fortune, he decided to retire from business. But in a prescient move he transferred all of his securities into US equities. This had the benefit of protecting the family against the wild inflation in Austria and Germany that followed the First World War. Each of the children was to inherit a fortune. But Ludwig followed a wholly different course from the others. After returning from the war in 1919 he decided to dispose of his entire inheritance and insisted that it should be transferred to his sisters Helene and Hermine and to his brother Paul. He arranged with the family’s monetary adviser to make sure that none of these funds would be returned to him in any shape or form. The accountant reluctantly helped Wittgenstein to commit a less fatal form of suicide, namely ‘financial suicide.’ From then on his life was almost monk-like in its austerity. When Frank Ramsey visited Wittgenstein in Lower Austria, where he was teaching in 1923, Ramsey described his situation in these words: ‘He is very poor, at least he lives very economically. He has one tiny room whitewashed, containing a bed, washstand, small table, and one hard chair and that is all there is room for. His evening meal which I shared last night is rather unpleasant coarse bread, butter and cocoa.’ Despite the efforts of his siblings to subvert his desire for financial self-destruction, Wittgenstein refused to accept any assistance from them. Norman Malcolm tells an amusing story in this connection. When Wittgenstein visited Malcolm at Cornell in 1949, the Malcolms offered to make him an elegant dinner. Thanking them, he refused, stating that he preferred something simple. He then added that he liked food but it had to be the same thing for every meal.

Wittgenstein’s mother, Leopoldine, was a pianist with talents at the professional level. His brother Hans was a musical prodigy who at the age of four could play the piano and violin and compose original music. Another brother, Paul, was a touring pianist who lost his right arm in the First World War. He managed to have a distinguished subsequent career, playing special compositions for the left hand alone, written for him by Ravel and Scriabin. The three sisters all had strong artistic interests. Margarete (‘Gretl’), close in age to Ludwig, was considered the avante-garde intellectual of the family. She admired the philosophy of Schopenhauer, and was a revolutionary spirit prepared to entertain new developments in the arts, literature and science. She was also an early supporter of Sigmund Freud and was psychoanalyzed by him. She introduced Ludwig to the work of Karl Kraus, a witty, Voltaire-like journalist who was the rage among Viennese intellectuals for his stinging criticisms of the policies of the decaying Austro-Hungarian empire. Margarete agreed with Kraus and her attitudes affected the young Ludwig. Some resonances of Schopenhauerian influences are to be found in the mystical later sections of the Tractatus. The third sister, Helene, was also an accomplished pianist. She had four children and eight grandchildren. When the Nazis occupied Austria she was at first declared to be a Jew and thus subject to the severe racial laws they imposed. But after a complicated series of negotiations in which Ludwig participated, and in which a portion of the family fortune was given to the Nazis, she and her family were declared not to be Jews, or even to be of mixed blood, and accordingly she was able to survive the Nazi occupation. Hermine was especially close to Ludwig and stood in an almost maternal relationship to him. Her written recollections provide a revealing psychological portrait of Ludwig. After Ludwig’s disavowal of the fortune left to him by his father, Hermine wrote that ‘it is not easy to have a saint for a brother, and I would rather have a happy person for a brother than an unhappy saint.’

Wittgenstein was reared in an environment of wealth and culture that is rare today. Among the friends the family entertained were the musicians Johannes Brahms, Joseph Joachim, and Gustav Mahler, and various writers, artists and architects, such as Gustav Klimt and Adolf Loos. Klimt’s portrait of Margarete is a modern classic, and Loos directly influenced the architect Paul Engelmann, who designed her house. The Wittgenstein establishment was thus a cultural center in fin-de-siècle Vienna. Wittgenstein was to absorb these influences in ways that especially affected his personal life but, paradoxically enough, hardly his philosophy at all. All of his most important works deal with technical issues and have little cultural relevance. It is true that in Culture and Value, Lectures on Aesthetics, Conversations on Freud and other short essays he deals with such matters, but they are all minor pieces compared with his major contributions.

Ludwig and Margarete were the least gifted musically in the family. Ludwig only learned to play an instrument (the clarinet) when he was in his early thirties as part of his teaching duties in Lower Austria. His interests as a child and as a young man lay in technical and mechanical activities, such as working with lathes and various tools and instruments. When he was seventeen his parents decided that he should become an engineer and he spent two years in a vocational school in Berlin. After graduating he decided to become an aeronautical engineer, and so in 1908 at the age of nineteen he enrolled as a research student at the University of Manchester. His first experiments concerned the design of kites but eventually he became interested in the design of propellers and airplane engines. Plans still exist for some of his designs and show an inventive mind at at work. During his stay in Manchester a friend introduced him to Bertrand Russell’s Principles of Mathematics, first published in 1903. Wittgenstein was captivated by its argument. In this work Russell advanced what was later to be called ‘the logistic thesis.’ This is the contention that mathematics is a branch of logic.

When he began this treatise, Russell did not know that Gottlob Frege (1848–1925) had attempted a similar demonstration in his Begriffschrift of 1879. Frege is generally regarded as the inventor of mathematical logic, but his work was unknown even to his German contemporaries. It was Russell who first brought his contributions to the attention of the scholarly world. The Principles of Mathematics was virtually finished before Russell became acquainted with Frege’s writings. The Principles of Mathematics did not carry out the demonstration but rather suggested how it might be done. Russell and his collaborator, Alfred North Whitehead, were in fact to complete the task in their magisterial three-volume work, Principia Mathematica, which took about ten years to write and whose third volume was published in 1913. Despite this great achievement there is considerable dispute about whether they were successful or not. Their approach depended on principles that subsequent logicians have questioned, such as the Axiom of Reducibility and the Axiom of Infinity. They also employed notions that are now recognized to belong to what is called ‘set theory.’ Sets are collections of objects, and are abstractions having a peculiar status, being neither physical nor concrete. Set theory is thus generally distinguished from logic in a narrow sense of the term, i.e., as whatever concerns only rules for propositional connectives, quantifiers and nonspecific terms for individuals and predicates.

Furthermore, Principia employed the concept of identity (denoted by the symbol ‘=’). Though most logicians have assumed that it is part of logic in a narrow sense, even this is controversial. Accordingly, Whitehead and Russell’s attempt to prove the logistic thesis has been widely challenged and many logicians maintain that the thesis has not yet been proven. Nonetheless, their endeavor was a creation of the highest importance and has had a lasting effect on subsequent work in logic and some parts of mathematics. It totally eclipsed scholastic logic, a theory of inference which had existed since the time of Aristotle. This would have astounded Immanuel Kant, who at the end of the eighteenth century stated that logic was complete and beyond further development. In Principia the whole of scholastic logic occupies a few paragraphs in a work consisting of about fifteen hundred pages.

Their approach consisted in showing that what are called ‘Peano’s Postulates’ could be derived wholly within their system. The postulates were formulated by the Italian mathematician Giuseppe Peano in 1895, and are the basis of the natural number series. Natural numbers, such as the sequence 1, 2, 3 … … n are distinguished from integers which not only include the natural numbers, but also negative numbers, such as –1, –2, –3 … … –n. The two number systems have different logical bases, the integers being derived via ‘upper and lower bounds,’ or ‘Dedekind cuts,’ developed by the German mathematician Richard Dedekind (1831–1916), and the natural numbers from Peano’s postulates. In Principia Mathematica, Russell and Whitehead were able to derive Peano’s five postulates, showing them to be formulable in wholly logical terms. This entailed that mathematics was indeed a branch of logic and that logic was the more fundamental of the two disciplines. Here are the postulates:

1. Zero is a number.

2. The successor of any number is a number.

3. No two numbers have the same successor.

4. Zero is not the successor of any number.

5. If any property is possessed by zero, and also by the successor of any number having that property, then all numbers have that property.

The last of these is the principle of mathematical induction.

After the publication of Begriffschrift Frege continued to work at the logistic thesis and found, as Russell was to do later, that he had a monumental task on his hands. Volume 1 of his Grundgesetze der Arithmetik (Fundamental Laws of Arithmetic) was published in 1893 and a second volume in 1903. Russell had discovered the first volume of Grundgesetze just as he was completing the Principles of Mathematics. He realized that Frege’s system was susceptible to a paradox that showed its foundations to be inconsistent. This difficulty, called ‘Russell’s paradox,’ has become famous in the history of philosophy. In attempting to prove the logistic thesis, Frege had made use of the concept of a class and gave this notion a particular interpretation, namely that it was the Bedeutung or extension of a concept. Thus, the concept dog refers to the class of canines, and the concept aardvark to the class of aardvarks, and so forth. Russell pointed out that the principle that each concept denotes a class leads to a contradiction.

This follows from the fact that there are some classes that are members of themselves and some that are not. The class of all classes is itself a class, and therefore is a member of itself; but the class of dogs is not a dog and therefore is not a member of itself. It is thus possible to form a class, K, which is the class of all classes that are not members of themselves. And now a key question: Is K a member of itself? Either it is or it is not. Either answer leads to a contradiction. The basic problem can be explained in ordinary English. Let us assume that there is a village in which there is a barber who shaves all those and only those who do not shave themselves. The words ‘all’ and ‘only’ are key to the paradox. We can now ask: Who shaves the barber? Either he shaves or he does not shave. If he shaves himself, he shaves at least one person who shaves himself and accordingly does not shave only those who do not shave themselves. If he does not shave himself, then another must shave him, and accordingly he does not shave all those who do not shave themselves. It follows from the paradox that the fundamental principle of Fregean logic that describes a relationship between concepts and classes leads to a contradiction. Therefore, it cannot be used as a foundation for the reduction of mathematics to logic.

After discovering this difficulty, Russell wrote Frege who attempted to emend the second volume of Grundgesetze before its publication; but his rectification failed. The task of demonstrating the logistic thesis thus fell on Russell and Whitehead. The period between 1879 and 1913 was one of the most inventive and exciting periods in the history of philosophy. Wittgenstein was caught up in these challenging developments and decided that when he graduated from Manchester he should abandon engineering in favor of philosophy. In 1911 he went to Frege to discuss his future. Frege urged him to go to England to study with Russell, then, in Frege’s view, the premier figure in logic. And Wittgenstein followed his advice.

Wittgenstein and Russell, 1911–1914

Wittgenstein was twenty-one when in 1911 he began to work with Russell. For about three years he was an undergraduate at Cambridge and Russell was his supervisor. When they first met Wittgenstein was a neophyte in logic. By the end of Wittgenstein’s first year, Russell stated that he had nothing more to teach him and told Hermine that ‘we expect the next big step in philosophy to be taken by your brother.’ Russell was right on both counts. But even he did not anticipate how rapidly his prediction would come true. In 1918 Russell gave a series of lectures in London that were motivated by the principle that mathematical logic has significant philosophical implications. He called the resulting doctrine ‘Logical Atomism.’ What is particularly interesting is that Russell credited Wittgenstein with having originated this view while Wittgenstein was still his pupil. He begins the published version of the lectures by saying:

The following is the text of a course of eight lectures delivered in (Gordon Square) London, in the first months of 1918, which are very largely concerned with explaining certain ideas which I learnt from my friend and former pupil Ludwig Wittgenstein. I have had no opportunity of knowing his views since August 1914, and I do not even know whether he is alive or dead. He has therefore no responsibility for what is said in these lectures beyond that of having originally supplied many of the theories contained in them.

In the text, on page 205, there is a virtual duplicate of this comment. There Russell says:

A very great deal of what I am saying in this course of lectures consists of ideas which I derived from my friend Wittgenstein. But I have had no opportunity of knowing how far his ideas have changed since August 1914, nor whether he is alive or dead, so I cannot make anyone but myself responsible for them.

The ideas that Russell is referring to were developed by Wittgenstein in the period 1911–1914, and are precursors to the view we later find in the Tractatus. According to Russell, the logical system of Principia Mathematica ‘implied’ – though not in the strict sense of ‘imply’ – a certain metaphysical world view, and it was this, with his own variations, that Russell named ‘Logical Atomism.’ Wittgenstein was not to use this term in the Tractatus but his early notebooks indicate that Russell’s understanding of the main thrust of his thinking before he departed for Austria was correct. Here is how Russell’s account begins:

In the present lectures, I shall try to set forth in a sort of outline, briefly and unsatisfactorily, a kind of logical doctrine which seems to me to result from the philosophy of mathematics – not exactly logically, but what emerges as one reflects: a certain kind of logical doctrine, and on the basis of this a certain kind of metaphysics. The logic which I shall advocate is atomistic, as opposed to the monistic logic of the people who more or less follow Hegel. When I say that my logic is atomistic, I mean that I share the common-sense belief that there are many separate things: I do not regard the apparent multiplicity of the world as consisting merely in phases and unreal divisions of a single indivisible Reality.

This three-year period in which Wittgenstein’s genius exploded on the philosophical scene has fascinated intellectual historians. Given the complexity of the new logic, it seems impossible that Wittgenstein could have mastered it in such a short time. Today in almost every American university mathematical logic is taught to hundreds of undergraduates. It is much more advanced than the Russell/Whitehead system. But in its day it was understood only by a handful of specialists. Even in the late 1920s the only logic taught at Oxford was scholastic logic. Though philosophy was a popular subject at Cambridge, Russell’s lectures were often attended by only three or four students, and by the occasional colleague, like G. E. Moore. Wittgenstein was present at every session, and indeed became a kind of incubus who would not let any point drop. He dominated the discussions and continued to argue with Russell for hours afterwards. Russell described him as ‘my ferocious German.’

During a summer vacation in 1912 Ludwig wrote a paper that Russell decided was far better than anything his English pupils could do. On this basis he encouraged Wittgenstein, even suggesting that he might do great work in the future. Wittgenstein’s self-doubts about whether philosophy should be his life’s work immediately came to an end. As he said to a friend, Russell’s enthusiasm proved his salvation. It ended years of loneliness and mental turmoil, years during which he had thought of committing suicide and often felt ashamed that he had not done so. Yet, as Wittgenstein’s knowledge of logic deepened, his attitude toward Russell underwent a change. Wittgenstein began to feel that Russell was becoming a popularizer and was no longer interested in fundamental research. Russell in turn found Wittgenstein increasingly patronizing. There were frequently painful moments between them. Once Russell queried: ‘Are you thinking about logic or your sins?’ Wittgenstein continued to pace back and forth and finally replied: ‘Both.’ The final months before Wittgenstein left for Austria were especially difficult. Nonetheless, Russell never stopped admiring Wittgenstein’s abilities and even in periods of considerable tension felt that Ludwig was the only person he knew who could make real advances in logic.

In part Russell’s problem was one of psychological exhaustion. The intensive ten years he had devoted to writing Principia Mathematica had taken a terrible toll. In his three-volume autobiography he stated that he had never recovered from the labor required to write this work, and that ‘since finishing it I was definitely less capable of dealing with difficult abstractions than I was before.’ It should be stressed that the axiomatic system that he and Whitehead had created required that each theorem be constructively proved – a tremendous effort given the size of the project. Some four decades later, when I was a student at Berkeley, the instructor gave the class, as an exercise, the task of constructively proving various theorems in Principia. I spent a month grappling with one of the propositions in Chapter 20 and finally gave up. Today, using natural deduction, the task would be comparatively simple. But natural deduction was not to be invented until the 1930s so Russell had to use the only techniques then available to him. Though he was only thirty-nine in 1911 he felt that he would never again be able to do ground-breaking work in logic. He was thus looking for somebody who could carry on where he had left off. Once he became aware of Wittgenstein’s talent and deep commitment to the subject, he realized that he had found his protégé. Wittgenstein by now had such a command of the material that he was able to show that some of the proofs in Principia were flawed. When he pointed these out, Russell’s response was to hand him the torch. Russell admitted he did not have the energy to rework the material and told Ludwig that it was now up to him to revise Principia.

In 1913 Wittgenstein decided to take the year off and move to Norway to work out his developing ideas. He felt that he could not do creative work in the donnish and stuffy atmosphere of Cambridge. He found a tiny village in which he could isolate himself. It was called Skjolden, and was located in the mountains north of Bergen. There, almost without interruption, he devoted himself to logic. Later he was to say that in Skjolden ‘his mind was on fire.’ Wittgenstein was simultaneously working on a variety of topics. One of them consisted in trying to develop a method for showing in a mechanical way whether a well-formed string of symbols is a theorem. In this task he was successful and the procedure is now called ‘the truth table method.’ It works only for the propositional (sentential) calculus, to be sure, but there it works infallibly. It is still taught in courses in elementary logic and can be applied by machines. In a fully worked-out form it appears in the Tractatus. Since that work was finished at the end of 1918, Wittgenstein’s achievement preceded that of E. L. Post, who published a similar tabular method in 1920. As a decision procedure it is a brilliant creation. Yet it is only one of the many original ideas in the Tractatus.

At this time Wittgenstein was also developing a distinction that was to be central to the Tractatus, i.e., the difference between saying and showing. He regarded this notion as of the highest importance. He thought, among other things, that it would demonstrate that the Theory of Types was superfluous. The Theory of Types was Russell’s solution to the paradox he had originally found in Frege’s Grundgesetze. It held, in effect, that the paradox about K being the class of all classes that are not members of themselves could be neutralized if K was shown to belong to a different type or order from the propositions about the classes that were subsumed under it. The solution indeed blocked the paradox, but Russell himself realized that it was ad hoc and in the long run would have to be modified or abandoned. But nobody in the following decade had been able to improve on it. In Wittgenstein’s opinion he had now done so. In the next chapter I will discuss the distinction as it appears in the Tractatus, and in a subsequent chapter why it totally disappears in his later philosophy. It is an original and penetrating concept and yet it has been widely criticized. Whatever evaluation of it we eventually arrive at, the evidence is overwhelming that Wittgenstein’s year in Norway had indeed set his mind on fire.

In June of 1914 Wittgenstein left Norway for a brief vacation in Vienna. A month later the First World War broke out, and he enlisted in the Austrian army. It was to be an ‘extended vacation.’ He was not to resume his affiliation with Cambridge for another fifteen years.