WITTGENSTEIN, LUDWIG JOSEF JOHANN
(1889–1951)

Ludwig Josef Johann Wittgenstein, the Austrian-British philosopher, was born in Vienna, the youngest of eight children. Ludwig's paternal grandfather, a convert from Judaism to Protestantism, had been a wool merchant in Saxony before moving to Vienna. Ludwig's father, Karl Wittgenstein, had, as a strong-willed boy, rebelled against a classical education, running away to America when he was seventeen. After two years he returned to Vienna and underwent a brief training in engineering. He went to work as a draftsman, designed and largely directed the construction of a steel-rolling mill, became its manager, in ten years' time was the head of a large steel company, and subsequently organized the first cartel of the Austrian steel industry. Ludwig's mother was the daughter of a Viennese banker. She was a Roman Catholic, and Ludwig was baptized in the Catholic Church. Ludwig had four brothers and three sisters; all the children were generously endowed with artistic and intellectual talent. Their mother was devoted to music, and their home became a center of musical life. Johannes Brahms was a frequent visitor and a close friend of the family. One of Ludwig's brothers, Paul, became a distinguished pianist.

Ludwig was educated at home until he was fourteen. He was an indifferent student, and apparently his greatest interest was in machinery; a sewing machine that he constructed was much admired. His parents decided to send him to a school at Linz, in Upper Austria, that provided preparation in mathematics and the physical sciences rather than a classical education. After three years at Linz, Wittgenstein studied mechanical engineering for two years at the Technische Hochschule at Charlottenburg, in Berlin. He left this school in the spring of 1908 and went to England. In the summer of 1908 he experimented with kites at a kite-flying station in Derbyshire. That fall he registered as a research student of engineering at the University of Manchester. He engaged in aeronautical research for three years and designed a jet-reaction engine and a propeller.

Wittgenstein's interest began to shift to pure mathematics and then to the philosophical foundations of mathematics. He chanced upon Bertrand Russell's Principles of Mathematics and was greatly excited by it. He decided to give up engineering and to study with Russell at Cambridge. At the beginning of 1912 he was admitted to Trinity College, where he remained for the three terms of 1912 and the first two terms of 1913. Under Russell's supervision he applied himself intensively to logical studies and made astonishing progress. Soon he was engaged in the research that culminated in the logical ideas of the Tractatus.

Wittgenstein's most intimate friend during those early years at Cambridge was David Pinsent, a fellow student, to whom he later dedicated the Tractatus. When they met in the spring of 1912, Wittgenstein, in addition to studying logic, was doing experiments in the psychological laboratory on rhythm in music. He and Pinsent were united by strong musical interests. They had a repertoire of forty of Franz Schubert's songs, whose melodies Wittgenstein would whistle while Pinsent accompanied him on the piano. Wittgenstein could play the clarinet and had an excellent memory for music and an unusual gift for sight-reading. He retained a deep interest in music throughout his life; in his philosophical writings there are many allusions to the nature of musical understanding.

In 1912, Wittgenstein was doing his first extensive reading in philosophy, and according to Pinsent he expressed "naive surprise" that the philosophers whom he had "worshipped in ignorance" were after all "stupid and dishonest and make disgusting mistakes!" He and Pinsent made holiday junkets to Iceland and Norway, Wittgenstein paying all expenses. Pinsent found Wittgenstein a difficult companion: irritable, nervously sensitive, often depressed. But when he was cheerful he was extremely charming. Sometimes he was depressed by the conviction that his death was near at hand and that he would not have time to perfect his new ideas in logic, sometimes by the thought that perhaps his logical work was of no real value. Even so, his general frame of mind was less morbid than before he had come to Cambridge. For a number of years previously there had hardly been a day, he told Pinsent, in which he had not thought of suicide "as a possibility." Coming to study philosophy with Russell had been his "salvation."

Wittgenstein worked with fierce energy at his logical ideas. In the spring of 1913 he submitted to hypnosis with the hope that in the hypnotic trance he could give clear answers to questions about difficulties in logic. He entertained a plan of going to live in seclusion in Norway for some years, devoting himself to logical problems. The reasons he gave to Pinsent were that he could do better work in the absence of all distractions, but he also said that "he had no right to live in a world" where he constantly felt contempt for other people and irritated them by his nervous temperament. Wittgenstein acted on his plan and lived in Norway from the latter part of 1913 until the outbreak of World War I. He stayed on a farm at Skjolden and later built a hut, where he lived in complete seclusion.

During this period Wittgenstein corresponded with Russell. His letters were warmly affectionate and were full of the excitement of his logical discoveries. However, he expressed the conviction that he and Russell had such different "ideals" that they were not suited for true friendship. Two people can be friends, he said, only if both of them are "pure," so that they can be completely open with one another without causing offense. A relationship founded on "hypocrisy" is intolerable. He and Russell should break off entirely or else limit their communications to their logical work. Both of them have weaknesses, but especially himself: "My life is full of the most hateful and petty thoughts and acts (this is no exaggeration)." "Perhaps you think it is a waste of time for me to think about myself; but how can I be a logician if I am not yet a man! Before everything else I must become pure."

When war broke out Wittgenstein entered the Austrian Army as a volunteer. He served in an artillery group on a vessel on the Vistula and later in an artillery workshop at Kraków. He was ordered to an officers' training school and subsequently served on the eastern front and later with mountain artillery in the southern Tyrol. During these years he continued to work at his book, writing down his philosophical thoughts in notebooks that he carried in his rucksack. He completed the book in August 1918; when he was taken prisoner by the Italians in November, he had the manuscript with him. From his prison camp near Monte Cassino he wrote to Russell, to whom the manuscript was subsequently delivered by diplomatic courier through the offices of a mutual friend, J. M. Keynes.

While serving on the eastern front Wittgenstein bought at a bookshop in Galicia a copy of one of Lev Tolstoy's works on the Gospels, which apparently made a deep impression on him. In the prison camp in Italy he read a standard version of the Gospels, possibly for the first time, and is reported to have been disturbed by much that he found in it and to have questioned its authenticity, perhaps because of the differences from Tolstoy's version.

Wittgenstein was anxious to have his book, Logisch-Philosophische Abhandlung, published immediately. Shortly after his release from imprisonment and his return to Vienna, in August 1919, he offered it to a publisher. He believed that his book finally solved the problems with which he and Russell had struggled. From Russell's letters, however, he concluded that Russell had not understood his main ideas, and he feared that no one would. He and Russell met in Holland in December 1919 to discuss the book. Russell undertook to write an introduction for it, but the following May, Wittgenstein wrote to Russell that the introduction contained much misunderstanding and he could not let it be printed with his book. Subsequently the publisher with whom he had been negotiating rejected the book. Wittgenstein wrote to Russell, in July 1920, that he would take no further steps to have it published and that Russell could do with it as he wished. The German text was published in 1921 in Wilhelm Ostwald's Annalen der Naturphilosophie. The following year it was published in London with a parallel English translation, under the title Tractatus Logico-Philosophicus. A new and improved English translation was published in 1961.

Most of the notebooks used in the preparation of the Tractatus were destroyed on Wittgenstein's order. Three of them, however, from the years 1914–1916, were accidentally preserved and were published in 1961 with a parallel English translation. The notebooks present a vivid picture of the intensity of Wittgenstein's struggles with the problems of the Tractatus, and they sometimes help to show what the problems were.

Soon after his return to civilian life Wittgenstein decided to become a schoolteacher. He attended a teacher-training course in order to receive a certificate, and in the fall of 1920 he began teaching classes of children aged nine and ten in the village of Trattenbach in Lower Austria. He was an exacting teacher. He did not get on with his colleagues and was often depressed. When he was transferred to another village he was somewhat happier, for one of the teachers, Rudolf Koder, was a talented pianist. The two of them devoted many afternoons to music, Wittgenstein playing the clarinet or whistling. He remained a schoolteacher until 1926. In 1924 he prepared a dictionary of six thousand to seven thousand words for the use of pupils in the elementary schools of the Austrian villages; this small book was published in 1926.

When his father died, in 1913, Wittgenstein inherited a large fortune. In the summer of the following year he wrote to Ludwig von Ficker, editor of the literary review Der Brenner, proposing to send a large sum of money to be distributed among needy Austrian poets and artists. The poets Rainer Maria Rilke and Georg Trakl received sizable gifts of money from this anonymous source. Upon his return to civilian life after the war, Wittgenstein gave his fortune to two of his sisters. Part of the reason for this action was that he did not want to have friends for the sake of his money, but undoubtedly it was largely due to his inclination toward a simple and frugal life.

During his years as a teacher, until Frank Ramsey visited him in 1923, Wittgenstein probably gave no thought to philosophy. Ramsey, a brilliant young mathematician and philosopher at Cambridge, had just completed a review of the Tractatus and was eager to discuss the book with its author. He found Wittgenstein living in extreme simplicity in a small village. In explaining his book, to which he was willing to devote several hours a day for a fortnight or more, Wittgenstein would become very excited. He told Ramsey, however, that he would do no further work in philosophy because his mind was "no longer flexible." He believed that no one would understand the Tractatus merely by reading it but that some day some person would, independently, think those same thoughts and would derive pleasure from finding their exact expression in Wittgenstein's book.

After his resignation as a schoolteacher in 1926, Wittgenstein inquired at a monastery about the possibility of entering upon monastic life, but he was discouraged by the father superior. In the summer of that year he worked as a gardener's assistant with the monks at Hütteldorf, near Vienna. Meanwhile, one of his sisters had commissioned the architect Paul Engelmann to build a mansion for her in Vienna. Engelmann, a friend of Wittgenstein's, proposed to him that they undertake it jointly. Wittgenstein agreed and actually became the directing mind in the project, which occupied him for two years. The building has been described by G. H. von Wright as "characteristic of its creator. It is free from all decoration and marked by a severe exactitude in measure and proportion. Its beauty is of the same simple and static kind that belongs to the sentences of the Tractatus. " During the same period Wittgenstein did some work in sculpture.

Moritz Schlick, a professor in Vienna, had been deeply impressed by the Tractatus. He managed to establish contact with Wittgenstein and apparently prevailed upon him to attend one or two meetings of the group founded by Schlick, known as the Vienna circle. Subsequently Schlick and Friedrich Waismann paid visits to Wittgenstein, in which he expounded some ideas that were passed on to other members of the circle.

In January 1929 he returned to Cambridge to devote himself again to philosophy. What produced this renewal of interest is unknown, but it is said that it was provoked by a lecture he heard L. E. J. Brouwer give in Vienna in 1928 on the foundations of mathematics. Wittgenstein found he would be eligible to receive the Ph.D. degree from Cambridge if he submitted a dissertation, whereupon he submitted the Tractatus. Russell and G. E. Moore were appointed to give him an oral examination, which they did in June 1929. Moore found the occasion "both pleasant and amusing." Trinity College granted Wittgenstein a research fellowship. At this time he published a short paper, "Some Remarks on Logical Form," which he soon came to think was weak and confused. This paper and the Tractatus were the sole philosophical writings of his that were published in his lifetime.

Wittgenstein began to give lectures in January 1930. He remained at Cambridge until the summer of 1936, when he went to live for a year in his hut in Norway and to begin writing the Philosophical Investigations. In 1937 he returned to Cambridge and two years later succeeded Moore to the chair of philosophy.

Wittgenstein's lectures made a powerful impression on his auditors. They were given without notes or preparation. Each lecture was new philosophical work. Wittgenstein's ideas did not come easily. He carried on a visible struggle with his thoughts. At times there were long silences, during which his gaze was concentrated, his face intensely alive, and his expression stern, and his hands made arresting movements. His hearers knew that they were in the presence of extreme seriousness, absorption, and force of intellect. When he spoke his words did not come fluently, but they came with force and conviction. His face was remarkably mobile and expressive when he talked. His eyes were often fierce, and his whole personality was commanding. His lectures moved over a wide range of topics and were marked by great richness of illustration and comparison. Wittgenstein attacked philosophical problems energetically, even passionately. Unlike many other philosophers, who really want to retain the problems rather than to solve them, Wittgenstein's desire was to clear them up, to get rid of them. He exclaimed to a friend: "My father was a business man and I am a business man too!" He wanted his philosophical work to be businesslike, to settle things.

When he was not working at philosophy Wittgenstein could sometimes, with a friend, put on a charming mood of mock seriousness in which he said nonsensical things with utmost gravity. These lighthearted moments were, however, comparatively infrequent. Most commonly his thoughts were somber. He was dismayed by the insincerity, vanity, and coldness of the human heart. He was always troubled about his own life and was often close to despair. Human kindness and human concern were for him more important attributes in a person than intellectual power or cultivated taste. He had an acute need for friendship, and his generosity as a friend was striking. At the same time it was not easy to maintain a friendly relationship with him, for he was easily angered and inclined to be censorious, suspicious, and demanding.

In World War II Wittgenstein found it impossible to remain a spectator. He obtained a porter's job at Guy's Hospital in London and worked there from November 1941 to April 1943. He was then transferred to the Royal Victoria Infirmary in Newcastle, where he served as a "lab boy" in the Clinical Research Laboratory until the spring of 1944. He impressed the doctors for whom he worked by the prolonged and concentrated thought he gave to their medical problems. This hard thinking would often result in a new way of looking at the problems. At Newcastle, Wittgenstein devised a simple technique for estimating the area of war wounds that proved of value in determining their treatment.

In 1944 he resumed his lectures at Cambridge. But he became increasingly dissatisfied with his role as a teacher. He feared that his influence was positively harmful. He was disgusted by what he observed of the half understanding of his ideas. "The only seed I am likely to sow is a jargon," he said. He strongly disliked universities and academic life. He felt an increasing need to live alone, perhaps occasionally seeing a friend, and to devote his remaining energies (for several years he had been repeatedly unwell) to finishing the Investigations.

In the fall of 1947 he finally resigned his chair. He sought a secluded life, first in the Irish countryside near Dublin, then in an isolated cottage on the west coast of Ireland. He worked hard when his health permitted it. In the summer of 1949 he went to spend three months with a friend in the United States. Upon his return to England, in the fall, he was discovered to have cancer. He wrote that he was not shocked by this news because he had no wish to continue living. During part of 1950 he visited his family in Vienna, then went to Oxford to live with a friend, and afterward made a trip to Norway. In 1951 he moved to the home of his physician in Cambridge. Wittgenstein had expressed an aversion to spending his last days in a hospital, and his doctor had invited him to come to his own home to die. Wittgenstein was deeply grateful for this offer. Knowing that death was imminent, he continued hard at work. The philosophical thoughts that he wrote in his notebooks at this time are of the highest quality.

On April 27 he was taken violently ill. When his doctor informed him that the end had come he said, "Good!" His last words, before he lost consciousness, were "Tell them I've had a wonderful life!" He died on April 29, 1951.

The Tractatus

The Tractatus is a comprehensive work of extreme originality, yet it is less than eighty pages long. It is arranged as a series of remarks numbered in decimal notation. The following propositions are distinguished by their numbering as the primary theses of the book:

1. The world is everything that is the case.
2. What is the case, the fact, is the existence of states of affairs.
3. A logical picture of facts is a thought.
4. A thought is a sentence with a sense.
5. A sentence is a truth-function of elementary sentences.
6. The general form of a truth-function is [p̄, ξ̄,N(ξ̄) ].
7. Whereof one cannot speak, thereof one must be silent.

Erik Stenius has perceptively remarked that the book has a "musical" structure and that the numbering brings out a "rhythm of emphasis": these seven main propositions are "forte" places in the rhythm.

the picture theory

In a notebook Wittgenstein wrote (Notebooks, p. 39): "My whole task consists in explaining the nature of sentences." (The German Satz will be translated sometimes as "sentence," sometimes as "proposition.") What makes it possible for a combination of words to represent a fact in the world? How is it that by producing a sentence I can say something—can tell someone that so-and-so is the case?

Wittgenstein's explanation consists in the striking idea that a sentence is a picture. He meant that it is literally a picture, not merely like a picture in certain respects. Apparently this thought first occurred to him during the war, when he saw in a magazine an account of how a motorcar accident was represented in a law court by means of small models (see Notebooks, p. 7). So he said: "A proposition is a picture of reality. A proposition is a model of reality as we think it to be" (Tractatus, 4.01). The dolls and toy cars could be manipulated so as to depict different ways in which the accident might have taken place. They could be used to construct different propositions about the accident—to put forward different accounts, different models of what took place. Wittgenstein's general conception was that when we put a sentence together we construct a model of reality. "In a proposition a situation is, as it were, put together experimentally" (4.031).

One would not normally think that a sentence printed on a page is a picture. According to the Tractatus it really is a picture, in the ordinary sense, of what it represents. Wittgenstein conceived the proof of this to be that although words we have not previously encountered have to be explained to us, when we meet for the first time a sentence that is composed of familiar words, we understand the sentence without further explanation. "I understand a sentence without having had its sense explained to me" (4.021). This can appear to one as a remarkable fact. If it is a fact, the only possible explanation would be that a sentence shows its sense. It shows how things are if it is true (4.022). This is exactly what a picture does. A sentence composed of old words is able to communicate a new state of affairs by virtue of being a picture of it.

In any picture, according to the Tractatus, there has to be a one-to-one correspondence between the elements of a picture and the things in the state of affairs its represents. If one element of a picture stands for a man and another for a cow, then the relationship between the picture elements might show that the man is milking the cow. A picture is a fact, namely the fact that the picture elements are related to one another in a definite way. A picture fact shows that the things the picture elements stand for are related in the same way as are the picture elements.

Since a sentence is held to be a picture, there must be as many elements to be distinguished in it as in the state of affairs it portrays. The two must have the same logical or mathematical multiplicity. Again, this does not seem to be true of our ordinary sentences. For Wittgenstein this meant not that it is not true but that our sentences possess a concealed complexity that can be exhibited by analysis.

According to the Tractatus a picture must have something in common with what it pictures. This common thing is the picture's "form of representation." There are different kinds of pictures, different pictorial notations, different methods of projection. But all pictures must have in common with reality the same logical form in order to be able to picture reality at all, either truly or falsely. This logical form, also called "the form of reality," is defined as the possibility that things in the world are related as are the elements of the picture (2.18, 2.151). Sentences, since they are pictures, have the same form as the reality they depict.

what cannot be said

A picture can depict reality, but it cannot depict its own form of representation. It depicts (represents) its subject from "outside," but it cannot get outside itself to depict its own form of representation. A picture of another form might depict the representational form of a given picture; for instance, a picture in sound might depict the representational form of a picture in color. But in order for the one to represent the form of the other, there must be something that is the same in both. "There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all" (2.161). Therefore, logical form, the form of reality, which all pictures must possess, cannot be depicted by any picture.

This consideration must apply to sentences, too. We make assertions by means of sentences. With a sentence we say something. We say how things are. Things in the world are related in a certain way, and we try to describe that. But we cannot describe how our sentences succeed in representing reality, truly or falsely. We cannot say what the form of representation is that is common to all sentences and that makes them pictures of reality. We cannot say how language represents the world. We cannot state in any sentence the pictorial form of all sentences. "What can be said can only be said by means of a sentence, and so nothing that is necessary for the understanding of all sentences can be said" (Notebooks, p. 25).

This doctrine implies that in a sense one cannot say what the meaning of a sentence is. With regard to the sentence "a is larger than b, " one can explain to a person what "a " and "b " each refer to and what "larger" means, but there is not a further explanation to give him, namely what "a is larger than b " means. We understand the elements of a sentence, and we see how they are combined. But we cannot say what this combination means. Yet we grasp its meaning. In some sense we know what it means, because the sentence shows its meaning. Anything that can be said can be said clearly, but not everything that is understood can be said. In a letter to Russell, Wittgenstein remarked that his "main contention" was this distinction between what can be said in propositions—that is, in language—and what cannot be said but can only be shown. This, he said, was "the cardinal problem of philosophy."

the nature of thought

The picture theory of propositions is at the same time an account of the nature of thought. Wittgenstein said: "A thought is a sentence with a sense" (Tractatus, 4). This implies that thinking is impossible without language. Since a thought is a sentence and a sentence is a picture, a thought is a picture. The totality of true thoughts would be a true picture of the world.

The view that a thought is a sentence seems to imply that the words of a sentence could be the constituents of a thought. But in a letter written to Russell shortly after the Tractatus was completed, Wittgenstein explicitly denied this. A thought consists not of words "but of psychical constituents that have the same sort of relation to reality as words. What those constituents are I don't know." "I don't know what the constituents of a thought are but I know that it must have such constituents which correspond to the words of Language" (Notebooks, pp. 130, 129). It would appear from these remarks that Wittgenstein's view was not that a thought and a sentence with a sense are one and the same thing but that they are two things with corresponding constituents of different natures. Each of these two things is a picture. "Thinking is a kind of language. For a thought too is, of course, a logical picture of a sentence, and therefore it just is a kind of sentence" (Notebooks, p. 82).

To say that a state of affairs is conceivable (thinkable) means that we can make a picture of it (Tractatus, 3.001). A thought "contains" the possibility of a state of affairs, for the logical form of the thought is the possibility that things in the world are combined in the way the constituents of the thought are combined. Whatever is conceivable is possible. In a spoken or written sentence a thought is "made perceptible to the senses." All thoughts can be stated in sentences; what cannot be stated cannot be thought.

A consequence of these views is that the form of representation of propositions (the form of reality, logical form), which cannot be stated, also cannot be thought. Language shows us something we cannot think. A function of philosophy is to indicate (bedeuten ) what cannot be said (or thought) by presenting clearly what can be said. According to the Tractatus, therefore, there is a realm of the unthinkable that, far from being a mere wind egg, is the foundation of all language and all thought. In some way we grasp this foundation of thought (what we do here cannot really be said); it is mirrored in our thoughts, but it cannot be an object of thought.

Obviously the Tractatus is a thoroughly metaphysical work; this is not a minor tendency of the book. Yet it was once widely regarded as being antimetaphysical in its outlook. There is some excuse for this interpretation, since at the end of the book Wittgenstein said that the correct philosophical method would be to prove to anyone who wants to say something metaphysical that he has failed to give a meaning to certain signs in his sentences (6.53). But Wittgenstein did not reject the metaphysical; rather, he rejected the possibility of stating the metaphysical.

names and objects

The conception of propositions, and therefore of language, in the Tractatus rests on the notion of a name. This is defined as a "simple sign" employed in a sentence. A simple sign is not composed of other signs, as, for example, the phrase "the king of Sweden" is. The word John would satisfy this requirement of a simple sign. But a further requirement of a name is that it should stand for a simple thing, which is called an "object." According to the Tractatus the object for which a name stands is the meaning of the name (3.203). It is easy to determine whether a sign is composed of other signs but not whether it stands for something simple.

Wittgenstein conceived of objects as absolutely simple and not merely as simple relative to some system of notation. "Objects make up the substance of the world. That is why they cannot be composite.… Substance is what exists independently of what is the case.… Objects are identical with the fixed, the existent.… The configuration of objects is the changing, the mutable" (2.021, 2.024, 2.027, 2.0271).

A name is not a picture of the object it stands for, and therefore a name does not say anything. A picture in language—that is, the sentence—can be formed only by a combination of names. This combination pictures a configuration of objects. The combination of names is like a tableau vivant (4.0311). (One might think here, for example, of a group of people posed to represent The Last Supper ). A name is a substitute for an object, and a combination of names portrays a configuration of objects—that is, a state of affairs (Sachverhalt ).

A reader of the Tractatus will be perplexed to know what examples of names and of objects would be. No examples are given. It is said that names occur only in "elementary" propositions, but there are no examples of the latter notion. Wittgenstein was not able to come to any conclusion about examples. The Notebooks show that he was very vexed by this problem. He struggled with the question of whether "points of the visual field" might be simples (see, for example, p. 45). Sometimes he wondered whether any ordinary name whatsoever might not be a "genuine" name. And he wondered whether his watch might not be a "simple object" (Notebooks, pp. 60–61). His final conviction that there are absolutely simple objects was purely a priori. He wrote in his notes:

It seems that the idea of the simple is already to be found contained in that of the complex and in the idea of analysis, and in such a way that we come to this idea quite apart from any examples of simple objects, or of propositions which mention them, and we realize the existence of the simple object—a priori —as a logical necessity. (Notebooks, p. 60)

The "logical necessity" arises from the requirement that propositions have a definite sense. "The demand for simple things is the demand for definiteness of sense" (Notebooks, p. 63). As it is put in the Tractatus, "The requirement that simple signs be possible is the requirement that sense be definite" (3.23). An indefinite sense would be no sense at all. A proposition might be ambiguous, but the ambiguity would be between definite alternatives: either this or that.

The sentences of everyday language are in perfect logical order. This order rests on the simples—that which is fixed, unchangeable, hard (das Harte: Notebooks, p. 63). The simples and their configurations—that is what order is. Wittgenstein said: "Our problems are not abstract, but perhaps the most concrete that there are" (Tractatus, 5.5563).

elementary propositions

A combination of genuine names is an elementary proposition. It is not analyzable into other propositions. "It is obvious that the analysis of propositions must bring us to elementary propositions which consist of names in immediate combination" (4.221). An elementary proposition shows (represents) a certain configuration of simple objects.

The picture theory is meant to hold for all genuine propositions, not merely for elementary propositions. Wittgenstein said without qualification: "A proposition is a picture of reality" (4.01, 4.021). Elementary and nonelementary propositions are equally pictures: the difference is that in an elementary proposition the pictorial nature is manifest. "It is evident that we perceive (empfinden ) an elementary proposition as the picture of a state of affairs" (Notebooks, p. 25). But Wittgenstein admitted that most sentences do not seem to be pictures.

At first sight a sentence—one set out on the printed page, for example—does not seem to be a picture of the reality with which it is concerned. But no more does musical notation at first sight seem to be a picture of music, nor our phonetic notation (letters) to be a picture of our speech. And yet these sign-languages prove to be pictures, even in the ordinary sense, of what they represent. (Tractatus, 4.011)

All genuine propositions, according to the Tractatus, are analyzable into elementary propositions. This analysis of our ordinary propositions, with their complicated modes of symbolizing—their various "methods of projection"—will make manifest their concealed pictorial nature. In his introduction to the Tractatus, written for the first English edition, Russell said:

Mr. Wittgenstein is concerned with the conditions for a logically perfect language—not that any language is logically perfect, or that we believe ourselves capable, here and now, of constructing a logically perfect language, but that the whole function of language is to have meaning, and it only fulfils this function in proportion as it approaches to the ideal language which we postulate.

That this is an incorrect account of the Tractatus is sufficiently shown by Wittgenstein's remark "All the propositions of our everyday language are actually in perfect logical order, just as they are" (5.5563). The analysis achieved by the philosophical logician will not create order where previously there was no order; instead, it will make evident what is already there.

Every genuine proposition has one and only one complete analysis into elementary propositions (3.25). This is so even if every fact consists of infinitely many states of affairs and every state of affairs is composed of infinitely many simple objects (4.2211). The completely analyzed proposition will consist of simple names; the meaning of each simple name will be a simple object; the particular way in which the names are combined in the proposition will say that the simple objects in the world are related in the same way. To understand the completely analyzed proposition one need only understand the names—that is, know what objects they stand for. What their combination means will be immediately evident. Understanding a proposition requires merely understanding its constituents (4.024).

As Rush Rhees has remarked, the idea that there are elementary propositions is not an arbitrary assumption. Wittgenstein was trying to solve the question of how language and thought can be related to reality. His basic intuition was that language pictures reality. If this is so, then among the sentences of language there must be some that show their sense immediately, which, of course, does not mean that their truth is self-evident. Wittgenstein had no criteria for identifying elementary propositions and could give no general account of their subject matter. But if his intuition was right, then there must be elementary propositions—that is, propositions that show their sense immediately and of which all other propositions are "truth-functions." If this were not so, no sentence could say anything or be understood (Rush Rhees, "The Tractatus : Seeds of Some Misunderstandings," pp. 218–219).

theory of truth-functions

A truth-function of a single proposition p is a proposition whose truth or falsity is uniquely determined by the truth or falsity of p ; for example, not-p (p is false) is a truth-function of p. A truth-function of two propositions p, q is a proposition whose truth or falsity is uniquely determined by the truth or falsity of p, q ; for instance, "p, q are both true" is a truth-function of p, q. According to the Tractatus (5) every genuine proposition is a truth-function of elementary propositions. (It is an interesting and difficult question whether this doctrine follows from the picture theory or, on the other hand, is even compatible with it.) If two nonelementary propositions r and s are truth-functions of some of the same elementary propositions, then r and s will be internally related: For instance, one of them may logically follow from the other, or they may be contradictories or contraries of each other. If we see the internal structure of two propositions, we know what logical relations hold between them. We do not need, in addition, a knowledge of logical principles. We can actually do without the formal principles of logic, "for in a suitable notation we can recognize the formal properties of propositions by mere inspection of the propositions themselves" (6.122).

Wittgenstein employed a technique (known as the method of truth tables) for making manifest the truth conditions of a proposition that is a truth-function of other propositions—that is, for exhibiting the relation between the truth or falsity of the latter and the truth or falsity of the former.

There are two limiting cases among the possible groupings of truth conditions of propositions. One case would be when a proposition was true for all truth possibilities of the elementary propositions; this proposition is called a tautology. The other would be when a proposition was false for all the truth possibilities; this proposition is called a contradiction. Although it is convenient to refer to tautologies and contradictions as "propositions," they are actually degenerate cases, not genuine propositions. They are not pictures of reality. They do not determine reality in any way. They have no truth conditions, since a tautology is un conditionally true and a contradiction un conditionally false. Wittgenstein compared a genuine proposition, a picture, to "a solid body that restricts the freedom of movement of others." In contrast a tautology (for example, "He is here, or he is not here") "leaves open to reality the whole of logical space." No restriction is imposed on anything. A contradiction (for example, "He is here, and he is not here") "fills the whole of logical space and leaves no point of it for reality" (4.461, 4.462, 4.463).

According to the Tractatus the so-called propositions of logic, logical truths, principles of logic are all tautologies. They express no thoughts. They say nothing. We could do without them. But they are not nonsense, for the fact that a certain combination of propositions yields a tautology reveals something about the structures of the constituent propositions. "That the propositions of logic are tautologies shows the formal—logical—properties of language, of the world" (6.12).

necessity

Wittgenstein's picture theory and his explanation of logical truth lead to an interesting doctrine of necessity and also to a denial of any knowledge of the future. Genuine propositions say only how things are, not how things must be. The only necessity there can be is embodied in tautologies (and the equations of mathematics). Neither tautologies nor equations say anything about the world. Therefore, there is no necessity in the world. "Outside of logic everything is accidental" (6.3). One proposition can be inferred from another proposition only if there is an internal, structural connection between them. The existence of one state of affairs cannot be inferred from the existence of another, entirely different, state of affairs (5.135). But that is what an inference to a future state of affairs would have to be. Thus Wittgenstein declared that we do not know whether the sun will rise tomorrow (6.36311).

will and action

If we conceive of an act of will (a volition) as one occurrence and the transpiring of what is willed as an entirely different occurrence, it follows from the foregoing doctrines that there can be, at most, a merely accidental correlation between one's will and what happens in the world. I cannot make anything happen—not even a movement of my body. "The world is independent of my will" (6.373). In his notes Wittgenstein gave this idea dramatic expression: "I cannot bend the happenings of the world to my will: I am completely powerless" (Notebooks, p. 73).

ethics

According to the picture theory a proposition and its negation are both possible; which one is true is accidental. Wittgenstein drew the conclusion that there can be no propositions of ethics. His thought here was that if anything has value, this fact cannot be accidental: the thing must have that value. But everything in the world is accidental. Therefore there is no value in the world. "In the world everything is as it is, and everything happens as it does happen: in it no value exists—and if it did, it would have no value" (Tractatus, 6.41).

This view is an absolute denial not of the existence of value but of its existence in the world. Propositions can state only what is in the world. What belongs to ethics cannot be stated; it is "transcendental" (6.421). The world, and what is in the world, is neither good nor evil. Good and evil exist only in relation to the subject (the ego). But this "subject" to which Wittgenstein referred is also "transcendental." It is not in the world but is a "limit" of the world (5.5632).

the mystical

In the view of the Tractatus there are a variety of things that cannot be stated: the form of representation of propositions, the existence of the simple objects that constitute the substance of the world, the existence of a metaphysical subject, of good and evil—these things are all unsayable. Wittgenstein seems to have believed that we have thoughts on these matters only when we view the world as a limited whole. This latter experience is what he called "the mystical" (6.45).

Although one cannot say anything on these metaphysical topics included in the mystical, this is not because they are absurd but because they lie beyond the reach of language. "Unsayable things do indeed exist" (Es gibt allerdings Unaussprechliches : 6.522). This itself is something unsayable. It is one of those sentences of his own of which Wittgenstein declared that although they can produce philosophical insight, they are actually nonsensical and eventually must be "thrown away" (6.54). The final proposition of the book ("Whereof one cannot speak, thereof one must be silent") is not the truism one might take it to be, for it means that there is a realm about which one can say nothing.

the tractatus and logical positivism

The Tractatus exerted a considerable influence on the so-called Vienna circle of logical positivism. Moritz Schlick, the leader of this movement, declared that the Tractatus had brought modern philosophy to a "decisive turning point." It is true that there is some agreement between the predominant views of the Vienna circle and the positions of the Tractatus —for example, that all genuine propositions are truth-functions of elementary propositions, that logical truths are tautologies and say nothing, and that philosophy can contain no body of doctrine but is an activity of clarifying thoughts.

But there are fundamental differences. The Vienna circle did not adopt the picture theory of propositions, which is the central idea of the Tractatus. A conspicuous doctrine of the circle was that all genuine propositions are reducible to propositions that report "direct perception" or what is "immediately given in experience." This doctrine is not found in the Tractatus. A corollary to it is the famous positivist thesis "The meaning of a statement is its method of verification." But the topic of verification is not even brought into the Tractatus. The only proposition there that seems to resemble this thesis is the following: "To understand a proposition means to know what is the case if it is true" (4.024). Even here nothing is explicitly said about verification, and a comment immediately following this remark shows that Wittgenstein was not thinking about verification. A proposition, he said, "is understood by anyone who understands its constituents." That is to say, if you understand the words in a sentence, you thereby understand the sentence. There is no mention of a requirement that you must know how to verify what it says.

As previously noted, Wittgenstein was tempted by the suggestion that "points in the visual field" are examples of the simples out of which all meaning is composed. But the final view of the Tractatus is that the simples are fixed, immutable things, which exist "independently of what is the case." If so, they cannot be described by propositions and cannot be given in experience. The Tractatus does not contain, therefore, an empiricist theory of meaning. What it holds is that to understand any sentence one must know the references of the names that compose it; that is all. When you understand a sentence you know how reality is constituted if the sentence is true, regardless of whether you know how to verify what it says. The picture theory is not a verification theory of meaning. It is ironical that the role of verification in meaning and understanding receives much attention in Wittgenstein's later philosophy, which obviously is not positivistic, but none at all in the reputedly positivistic Tractatus.

Logical positivism and the author of the Tractatus were both opposed to metaphysics, but in different ways. For positivism there is nothing at all behind metaphysical propositions except possibly their authors' emotions. "Metaphysicians are musicians without musical ability," said Rudolf Carnap. In the view of the Tractatus one may gain insights into the presuppositions and limits of language, thought, and reality. These metaphysical insights cannot be stated in language, but if they could be, they would be true insights and not mere muddles or expressions of feeling.

The foregoing sketch of the Tractatus has omitted many of its important topics. Wittgenstein wrote in his notes, "My work has extended from the foundations of logic to the nature of the world." In his preface to the Tractatus he expressed the opinion that he had obtained the final solution of the problems treated in the book, but he added that one value of his work is that "it shows how little is achieved when these problems are solved."

The "New" Philosophy

In 1929, Wittgenstein returned to Cambridge, after an absence of more than fifteen years, to resume philosophical research and to lecture. From then until his death he did a huge amount of writing. Among the first works of this period were two large typescript volumes. One, which was composed in the period 1929–1930, has been published under the title Philosophische Bemerkungen. The other is a systematic work of nearly 800 typewritten pages written between 1930 and 1932. In both of these volumes Wittgenstein reexamined the problems of the Tractatus and revised what he had written there. This led him to questions he had not previously considered. Perhaps it can be said that he found that the logical investigations of the Tractatus and its supreme problem of the relation of language to reality had drawn him more and more into questions in the philosophy of psychology. These volumes seem to show that the change from the Tractatus to the Philosophical Investigations was an intensive but continuous development rather than a sudden revolution.

In 1933–1934, Wittgenstein dictated to his students a set of notes that came to be called the Blue Book, and in 1934–1935 he dictated another set, later known as the Brown Book. (Although Wittgenstein always wrote in German, the Blue Book and the Brown Book were dictated in English.) Both circulated widely in typescript, and Wittgenstein's new ideas began to create a stir. The Blue Book is clear and lively and is perhaps the beginner's best introduction to Wittgenstein. Nevertheless, it is a comparatively superficial work; Wittgenstein never regarded it as more than a set of class notes. The Brown Book, on the other hand, he regarded for a short time as a draft of something that might be published. He worked at a revision but gave it up in 1936, when he began to write the Philosophical Investigations. Wittgenstein refrained from publishing the Investigations during his lifetime, but his explicit wish was that it be published posthumously, a wish that he probably did not have with respect to any of the rest of the voluminous work he produced between 1929 and 1951.

The Philosophical Investigations was published in 1953 in two parts. Part I was written in the period 1936–1945 and Part II between 1947 and 1949. Concurrently with the Investigations, Wittgenstein did other writing, which was closely related to the topics of the Investigations or even overlapped it. From the years 1937 to 1944 there are extensive manuscripts on the philosophy of logic and mathematics. Remarks on the Foundations of Mathematics, published in 1956, consists of selections, made by the editors, from this material. A quantity of writing in the form of loose notes, probably from the years 1947 to 1949, is of the same subject matter and quality as the latter part of Part I of the Investigations. Wittgenstein's last manuscript notebooks, from the years 1949 to 1951, treating questions about belief, doubt, knowledge, and certainty, also contain much material that should eventually be published.

Philosophical Investigations

Wittgenstein believed that the Investigations could be better understood if one saw it against the background of the Tractatus. A considerable part of the Investigations is an attack, either explicit or implicit, on the earlier work. This development is probably unique in the history of philosophy—a thinker producing, at different periods of his life, two highly original systems of thought, each system the result of many years of intensive labors, each expressed in an elegant and powerful style, each greatly influencing contemporary philosophy, and the second being a criticism and rejection of the first.

Apparently it is possible for a serious student of Wittgenstein to form the impression that "the Investigations basically contains an application of the main ideas of the Tractatus to several concrete problems, the only difference being the use of language-games instead of the language of the natural sciences which formed the theoretical background of the Tractatus. " This view is thoroughly mistaken, as will be seen.

the whole of language

It is held in the Tractatus that any proposition presupposes the whole of language. "If objects are given, then at the same time we are given all objects. If elementary propositions are given, then at the same time all elementary propositions are given" (5.524). "If all objects are given, then at the same time all possible states of affairs are also given" (2.0124). An elementary proposition is a combination of names, and in order to understand the proposition one must in some sense "know" the objects for which the names stand. In understanding any proposition at all one must know some objects, and therefore, as stated, one must know all objects and all possibilities. Any proposition whatsoever carries with it the whole of "logical space." This view is connected with the idea that there is an essence of propositions. The essence of propositions is "the essence of all description, and thus the essence of the world" (5.4711). The essence of propositions is the same as "the universal form of proposition" (Die allgemeine Satzform ). That there is a universal form of proposition is proved by the fact that all possibilities—i.e., all forms of proposition—"must be foreseeable " (Notebooks, p. 89; Tractatus, 4.5).

The Investigations emphatically rejects the idea that each proposition carries with it the whole of language. A sentence does presuppose a "language game," but a language game will be only a small segment of the whole of language. An example of a language game is the following, which appears at the beginning of the Investigations (Sec. 2): There are a builder and his helper. The building materials are blocks, pillars, slabs, and beams. The two men have a language consisting of the words block, pillar, slab, beam. The builder calls out one of the words and the helper brings the building material that he has learned to bring at that call. Wittgenstein called the words and the actions with which they are joined a language game (Sprachspiel ). He said that it is complete in itself and could even be conceived to be the entire language of a tribe. If we think it is incomplete we are only comparing it with our more complex language. In the Brown Book there is the analogy of someone's describing chess without mentioning pawns. As a description of chess it is incomplete, yet we can also say that it is a complete description of a simpler game (Blue and Brown Books, p. 77). This simpler game does not presuppose chess, nor does the part played, for example, by the word block in the game of Sec. 2 imply its use in descriptions or questions.

According to the Tractatus every form of proposition can be anticipated because a new form of proposition would represent a new combination of simple objects in logical space. It would be like grouping the pieces on a chessboard in a new way. It would be a different arrangement of what you already have. But in Wittgenstein's later philosophy a new language game would embody a new "form of life," and this would not merely be a rearrangement of what was there before. Suppose the people of a certain tribe use language to describe events that are occurring or have occurred (such as men walking, running, or fighting, or the weather), or that they believe have occurred, but they do not have any imaginative use of language. They do not lie, pretend, make supposals, or engage in any imaginative play. Nor does any behavior of pretending occur: the children do not ever, for example, walk on all fours and growl as if they were lions. These people would not understand kidding. If one of us said to them something obviously false and then laughed, they would not know how to take it. (We should remember that among ourselves we differ greatly in our responsiveness to joking and pretense.) What these people lack is not words but the behavior and reactions that enter into the language games of imagination. Are they capable of foreseeing a use of language to convey a play of imagination? They do not even understand it when they encounter it. A new use of language embedded in a new form of life could not be anticipated, any more than could the rise of nonobjective painting.

the essence of language

The Tractatus assumes that there is a universal form of language, just as it assumes (6.022) that there is a universal form of number—that which is common to all numbers. The Investigations rejects this assumption. There is nothing common to the various forms of language that makes them language. There is not something common to all language games, just as there is not something common to all games. We are asked to consider the various kinds of games there are (for example, board games, card games, ball games) and the variety within each kind. If we pick out a feature common to two games we shall find that it is absent from some other place in the spectrum of games. Not all games are amusing, not all involve winning or losing, not all require competition between players, and so on. What makes all of them games, what gives unity to those activities, is not some feature present in all games but a multitude of relationships "overlapping and criss-crossing." Wittgenstein employed the analogy of a family resemblance. One can often see a striking resemblance between several generations of the same family. Studying them at close hand one may find that there is no feature common to all of the family. The eyes or the build or the temperament are not always the same. The family resemblance is due to many features that "overlap and criss-cross." The unity of games is like a family resemblance. This is also the case with sentences, descriptions, and numbers.

Why do we call something a "number": Well, perhaps because it has a—direct—relationship with several things that have hitherto been called number; and this can be said to give it an indirect relationship to other things we call the same name. And we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of the fibres. (Sec. 67)

One of the remarkable features of the Investigations is the detail and ingenuity of Wittgenstein's examination of some sample concepts (reading, deriving, being guided : Secs. 156–178) in order to bring out the variety of cases that fall under them and to prove that they are not united by an essence. If these concepts do not have an essential nature, then neither do the concepts of description, proposition, and language. The Tractatus was wrong in a most fundamental assumption.

absolute simples

The Tractatus held that the ultimate elements of language are names that designate simple objects. In the Investigations it is argued that the words simple and complex have no absolute meaning. It has to be laid down, within a particular language game, what is to be taken as simple and what composite. For example, is one's visual image of a tree simple or composite? The question makes no sense until we make some such stipulation as that if one sees merely the trunk, it is simple, but if one sees trunk and branches, it is composite.

But isn't a chess board, for instance, obviously, and absolutely composite?——You are probably thinking of the composition out of thirty-two white and thirty-two black squares. But could we not also say, for instance, that it was composed of the colours black and white and the schema of squares? And if there are quite different ways of looking at it, do you still want to say that the chessboard is absolutely "composite"? … Is the colour of a square on a chessboard simple, or does it consist of pure white and pure yellow? And is white simple, or does it consist of the colours of the rainbow?——Is this length of 2 cm. simple, or does it consist of two parts, each 1 cm. long? But why not of one bit 3 cm. long, and one bit 1 cm. long measured in the opposite direction? (Sec. 47)

By such examples Wittgenstein tried to show that the ideas of "simple" and "complex" are necessarily relative to a language game. The notion of a simplicity that is not relative but absolute, because all of language is based on it, is a philosophical "super-concept." We have an image but we do not know how to apply it: we do not know what would be an example of an absolute simple.

In the Tractatus the existence of simple objects was conceived as following from the requirement that the sense of sentences be definite. In the Investigations this requirement is regarded as another philosophical illusion. We have imagined an "ideal" of language that will not satisfy actual needs. A sharp boundary has not been drawn between, for example, games and activities that are not games. But why should there be one in general? Precision and exactness are relative to some particular purpose. The guests are to arrive exactly at one o'clock, but this notion of exactness would not employ the instruments and measurements of an observatory. "No single ideal of exactness has been laid down; we do not know what we should be supposed to imagine under this head" (Sec. 88). Losing sight of the fact that there are different standards of exactness for different purposes, we have supposed that there is a certain state of complete exactness underneath the surface of our everyday speech and that logical analysis can bring it to light. We have supposed, therefore, that a proposition would have one and only one complete analysis.

In searching for the ideal of perfect exactness we become dissatisfied with ordinary words and sentences. We do not find in actual language the pure and clear-cut structure that we desire. The more closely we examine actual language, the sharper becomes the conflict between it and our philosophical ideal. The latter now begins to seem empty. We do not even understand how it could be realized in actual language. We have been bewitched by a picture. Instead of trying to perceive in our language a design too fine to grasp, we need to see more clearly what is really there. We should abandon preconceived ideas and hypotheses and turn to description, the purpose of which will be to remove our philosophical perplexities. The substitution of description for analysis, and the new conception that nothing is hidden, is a major change from the Tractatus.

meaning as use

If the picture theory is the central feature of the Tractatus, it is important to see how Wittgenstein's new thinking judged that theory. Surprisingly, there is not much explicit discussion of it, and the remarks that do occur are usually enigmatic. But if we take a long view of the new philosophy, there can be no question that it rejects the picture theory. In the later work as well as the earlier, Wittgenstein was concerned with the question, How can a sentence say something; how can language represent reality? The first sentence of the Blue Book is "What is the meaning of a word?" and it might equally well have been "What is the meaning of a sentence?" Both philosophical systems are centered on the same question, but the answer given in the second is entirely different. Instead of holding that a sentence has meaning or sense because it is a picture, the Investigations says that the meaning of a sentence is its "use" (Gebrauch ) or "employment" (Verwendung ) or "application" (Anwendung ).

Some readers of Wittgenstein have doubted that he spoke of the use of a sentence, and others have thought that in any case it is wrong to speak this way. There is no question on the first point. Wittgenstein spoke of the "use" of a sentence in many passages. For example: "But doesn't the fact that sentences have the same sense consist in their having the same use ?" (Investigations, Sec. 20); there are "countless different kinds of use of what we call 'symbols,' 'words,' 'sentences'" (Sec. 23).

The other objection may be important. Some philosophers want to say that a sentence cannot have a use. Words have a use; we learn the use of words, not of sentences. We understand sentences without having their sense explained to us, because we understand the use of the words that compose them.

What is espoused here is really the ground of the picture theory of the Tractatus (cf. Tractatus, 4.021, 4.026, 4.027). In the Investigations there is more than one objection to the above argument. Wittgenstein denied that we always understand a sentence, even if it is a grammatically correct sentence whose words we do understand. If someone says, for example, that the sentence "This is here" (saying which, he points to an object in front of him) makes sense to him, "then he should ask himself in what special circumstances this sentence is actually used. There it does make sense" (Sec. 117). "A philosopher says that he understands the sentence 'I am here,' that he means something by it, thinks something—even when he doesn't think at all how, on what occasions, this sentence is used" (Sec. 514). Wittgenstein was saying that these sentences have sense only in special circumstances; in other circumstances we do not understand them—that is, we do not know what to do with them.

The view of the Tractatus is entirely different. An elementary sentence is a combination of names, and if we know what the names refer to, then we understand the sentence, for it shows its sense. "Circumstances" have nothing to do with it. The Investigations regards this view as absurd. What does the sentence "I am here" show? Certainly it does not show its use. What can it mean to say that it shows its sense? A significant sentence is a tool with which a certain job is done. By looking at a sentence you cannot always tell whether it is a tool and, if it is, what job it is used for. The Investigations denies the claim that was the basis of the picture theory, namely that "we understand the sense of a propositional sign without its having been explained to us" (Tractatus, 4.02).

In holding that (in many cases) the meaning of an expression is its use, Wittgenstein was not declaring that the words meaning and use are general synonyms. By the "use" of an expression he meant the special circumstances, the "surroundings," in which it is spoken or written. The use of an expression is the language game in which it plays a part. Some readers have arrived at the mistaken idea that by the "use" of an expression Wittgenstein meant its ordinary or its correct use: They have thought that he was an "ordinary-language philosopher." But Wittgenstein studied any use of language, real or imaginary, that may illuminate a philosophical problem. Often he invented language games that corresponded to no actual use of language (see, for example, Blue and Brown Books, pp. 103–104, 110). The language games are "objects of comparison which are meant to throw light on the facts of our language by way not only of similarities, but also of dissimilarities" (Investigations, Sec. 130).

The Tractatus holds that language is ultimately composed of names, that the meaning of a name is a simple object, and that the sense of a sentence arises from the names that compose it. One name stands for one thing, another for another thing, and the combination pictures a state of affairs (4.0311). Thus, naming is prior to the sense of sentences (although it is also said that a name has meaning only in a sentence: 3.3). A sentence says something because it is composed of names that stand for things. In the Investigations two objections are made against this notion of the priority of names. First, the meaning of a word is never the thing, if there is one, that corresponds to the word (Sec. 40). Second, before one can find out what a name stands for one must already have mastered the language game to which the name belongs. In order to learn the name of a color, a direction, a sensation, one must have some grasp of the activities of placing colors in an order, of reading a map, of responding to the words, gestures, and behavior that are expressions of sensation. Merely pointing at something and saying a word achieves nothing. The kind of use the word will have, the special circumstances in which it will be said, must be understood before it can even be a name.

One could say that the Tractatus conceives of a significant sentence as having the nature of a mechanism. If the parts fit, then the whole thing works: you have a picture of reality. If the parts do not fit, they are like cogwheels that do not mesh. There is, as it were, a clash of meanings. But in the Investigations we read: "When a sentence is called senseless, it is not as it were its sense that is senseless" (Sec. 500). If someone said to us, for example, "My head is asleep," we should be perplexed. It would be no help if he said: "You know what it is for an arm or a leg to be asleep. I have the same thing, except that it is my head." Here we do not know what the "same" is. It is not that we see that the meaning of "head" is incompatible with the meaning of "asleep." We do not perceive a clash of meanings. But we do not know what behavior and circumstances go with this sentence. It is not that we see that it cannot have a use (because the words do not fit together). The fact is that it does not have a use: we do not know in what circumstances one should say it. "Look at the sentence as an instrument, and at its sense as its employment!" (Sec. 421). Instead of the fundamental notion being the right combination of words and the sense of the sentence being explained in terms of it, it is the other way around: whether the sentence has an "employment" (Verwendung ) is what is fundamental. This would be our only criterion for whether there is a sense-making combination of parts.

One additional criticism of the picture theory will be noted. Suppose that a sentence were a picture. There would still be a question of how we should apply the picture. If someone showed you a drawing of a cube and told you to bring him one of those things, you might in good faith bring him a triangular prism instead of a cube. More than one way of taking the drawing was possible. It suggests a cube, but it is possible to interpret the drawing differently. A picture represents an old man walking up a steep path leaning on a stick. But could it not also represent him as sliding down the hill in that position? For us it is more natural to take it in the first way, but the explanation of this does not lie in anything intrinsic to the picture. A picture of a green leaf might be understood to be a representation of the color green, or of a specific shade of green, or of leaf shape in general, or of a particular shape of leaf, or of foliage in general, and so on. How a picture is used will determine what it is a picture of. It cannot, therefore, be a fundamental explanation of the sense of sentences to say that they are pictures. Wittgenstein hinted that the picture theory is plausible because we tend to think of portraits that hang on our walls and are, as it were, "idle." If we consider instead an engineer's machine drawing or an elevation with measurements, then the activity of using the picture will be seen to be the important thing (Sec. 291).

logical compulsion

Our discussion may suggest the following view: How a word, sentence, or picture is interpreted determines what use is made of it. How a man responds to an order, for example, depends on how he understands it, and whether the one who gave the order will be satisfied with that response will depend on what he meant by it. If someone understands the algebraic formula determining a numerical series, then he will know what numbers should occur at various places in the expansion of the series. What a person deduces from a proposition will depend entirely on his understanding of the proposition. Wittgenstein once wrote (in a pre-Tractatus notebook): "What propositions follow from a proposition must be completely settled before that proposition can have a sense" (Notebooks, p. 64). By virtue of grasping the meaning or sense of an expression we know how to employ it: we know when to say it and what action it calls for. Instead of meaning being identical with use, it comes before use, and use is based on it. When you hear a sentence and understand it or give an order and mean it, the action required in responding to the sentence or obeying the order is already, in a queer sense, taken in your mind. In your act of meaning or understanding, "your mind as it were flew ahead and took all the steps" before they were taken physically (Investigations, Sec. 188). In taking, or accepting, those physical steps, you would be ratifying what has already transpired in your mind. To do differently would be inconsistent with the previous mental act. Consistency, rationality, requires you to take these steps or draw these conclusions. Understanding carries compulsion with it.

This idea of "logical compulsion" is vigorously attacked in the Investigations and in Wittgenstein's writings on the foundations of mathematics. Was Wittgenstein rejecting deductive reasoning and logical necessity? No. He was rejecting this picture of logical necessity, namely that when I have understood a proposition and there is a question of what follows from it, I have to deduce such-and-such consequences because it was already settled in my understanding of the proposition that it would have those consequences. Wittgenstein's criticism of this imagery creates a continuity between his philosophy of psychology and his philosophy of logic. A part of his criticism could be put as follows: Suppose that two people, A and B, have received the same instruction in elementary arithmetic. They have been given the same rules and illustrations and have worked through the same examples. Later, when they are required to perform some arithmetical operation, A does it right and B wrong, although B thinks he has done it correctly. We shall say that A understood the problem and B did not. What does this come to? It could have been that the sole difference between them was that A wrote down correct numbers and B incorrect ones. If this fact is our criterion of a difference of understanding, then it is wrongheaded to postulate a difference of understanding to explain the fact that A and B wrote down different answers.

The inclination to insert an act or state of understanding as an intermediary between, for example, hearing an order and executing it is an example of what is called in the Brown Book (Blue and Brown Books, p. 143) "a general disease of thinking." It consists in always looking for (and "finding") mental states and acts as the sources of our actions. Other examples of this inclination are thinking that one must know where one's pain is before one can point to the place, thinking that we call various shades of red by the name "red" because we see something in common in all of them, thinking that we speak of "looking in our memory for a word" and of "looking in the park for a friend" because we have noticed a similarity between the two cases.

The assumption of mental states to explain our actions comes from a "one-sided diet." If we let our view range over the family of cases of "differences of understanding," we shall discover some in which the only difference between two people who understood a certain proposition differently consists in their having drawn different conclusions from it.

Must we believe, then, that our understanding does not reach beyond the particular training we received and the examples we studied? No. There is a good sense in which it reaches beyond, for we do go on to apply rules in new cases in what we agree is the same way we were taught. Does this agreement have to be explained by the fact that our understanding has penetrated to the essence of the examples? No. This agreement is one of the "extremely general facts of nature" (Investigations, pp. 56, 230) that underlie our concepts. We do handle new cases in the same way. If this strikes us as mysterious, it is a symptom of our confusion. We are trying to imagine that the future steps are taken in the mind, "in a queer sense," before they are taken in reality—as if the mind were a machine that already contained its future movements (Investigations, Secs. 193–195).

Wittgenstein was saying that our understanding of a rule is not a state that forces us to apply the rule in a particular way. Someone who has received the ordinary instruction in arithmetic or chess and has applied it normally in the past could go on in the future in a different way but still be a rational person. Perhaps he could even give a reasonable defense of his divergence.

If this is true, it makes it seem that there are no rules, for a rule forbids some things and requires others. It appears that anything goes, anything can be justified. But then understanding, meaning, language itself all crumble away because they imply rules.

Wittgenstein was not denying, however, that there are rules and that we follow them. He held that the way a rule is applied in particular cases determines its meaning. A rule, as it is formulated in a sentence, "hangs in the air" (Investigations, Sec. 198). What puts it on the ground, gives it content, is what we say and do in actual cases. And on this there is overwhelming agreement: we nearly always say and do the same. It is this agreement that determines whether a particular action is in accordance with a rule. Rather than to say that we agree because we follow rules, it is more perceptive to say that our agreement fixes the meaning of the rules, defines their content. In a sense the content of the rules grows as our practice grows. Instead of thinking of humankind as coerced by the rules of logic and mathematics, we should consider that human practice establishes what the rules are.

private rules

The idea that the content of a rule can be fixed only by a practice provides a transition to one of the most subtle topics of the Investigations, namely the treatment of "private language." The conception that a significant sentence is a picture was replaced in Wittgenstein's thought by the conception that the sense of a sentence is determined by the circumstances in which it is uttered. Swinging a stick is a strike and pushing a piece of wood is a move—in the circumstances of games. Likewise, saying some words is making a decision—in certain circumstances. In one set of circumstances saying a particular sentence would be asserting something; in other circumstances saying those same words would be asking a question; in still others it would be repeating what someone had said.

This is a difficult conception to grasp. We feel a strong inclination to say that the only thing that determines the sense of what someone says is what goes on in his mind as he says it. As John Locke put it, "Words, in their primary or immediate signification, stand for nothing but the ideas in the mind of him that uses them. " Whether some words you uttered expressed a question or an assertion is solely a matter of whether there was a question or an assertion in your mind. What the occasion was, what happened before and after, what persons were present—those circumstances are irrelevant to the sense of your words. The only "circumstance" that matters is the mental occurrence at the time of utterance.

Wittgenstein fought hard and resourcefully against this objection. One technique he used was to describe different cases of deciding, asserting, intending, expecting, and so on. The purpose of this was to show that when one utters some words that express, for instance, a decision, one cannot pick out anything that occurred (for example, a thought, an image, some spoken words, a feeling) such that one wants to call that the act of deciding.

This technique, although powerful, may provoke the response that the only thing proved is the intangibility, the indescribability, of the mental phenomenon in question. William James remarked about the intention of saying a thing before one has said it: "It is an entirely definite intention, distinct from all other intentions, an absolutely distinct state of consciousness, therefore; and yet how much of it consists of definite sensorial images, either of words or of things? Hardly anything!" This intention has "a nature of its own of the most positive sort, and yet what can we say about it without using words that belong to the later mental facts that replace it? The intention to-say-so-and-so is the only name it can receive" (Principles of Psychology, New York, 1890, Vol. I, p. 253). Likewise, the decision to stay an hour longer cannot be expressed in any other words than those, yet it is a quite definite mental occurrence; one knows it is there!

Wittgenstein opposed this conception not with further description but with an argument. It is the following: If a decision or expectation or sensation were a state or event that was logically independent of circumstances, then no one, not even the subject of the supposed event, could ever determine that it had occurred. First, how would one learn what, for example, deciding is? Since circumstances are supposed to be irrelevant, one could not learn it by observing other people. Apparently one would have to learn what deciding is from one's own case. But as Wittgenstein remarked: "If I know it only from my own case, then I know only what I call that, not what anyone else does" (Investigations, Sec. 347). Thus it would be unverifiable whether two people refer to the same phenomenon by the word deciding. But worse is to come. One could not even take comfort in the thought "At least I know what I call 'deciding.'" You might believe that you have always called the same thing by that name. Yet nothing could determine that this belief was right or wrong. Perhaps the private object constantly changes but you do not notice the change because your memory constantly deceives you (Investigations, p. 207)! The idea that you might have a language with logically private rules—that is, rules that only you could understand because only you could know to what the words refer—is a self-contradictory idea. Following a rule implies doing the same, and what "the same" is can only be defined by a practice in which more than one person participates.

Wittgenstein's rejection of the intrinsically private, inner object is a consequence of his new conception of meaning. Language requires rules, and following a rule implies a customary way of doing something. It could not be that only once in the history of humankind was a rule followed (Sec. 199). An expression has a meaning only if there is a regular, a uniform, connection between saying the expression and certain circumstances. When we call something measuring, for example, a part of the uniformity we require is a constancy in the results of measurement (Sec. 242). A person can be guided by a signpost only if there is a regular way of responding to signposts. The meaning of an expression is its use—that is to say, the language game in which it occurs—that is to say, the uniform relation of the expression to certain circumstances. Wittgenstein made explicit the connection between this view of the nature of meaning and his attack on "private" mental contents when he said that following a rule is a practice and therefore one cannot follow a rule "privately" (Sec. 202).

See also Brouwer, Luitzen Egbertus Jan; Existence; James, William; Keynes, John Maynard; Language; Logical Positivism; Logic, History of; Mathematics, Foundations of; Moore, George Edward; Number; Ostwald, Wilhelm; Proper Names and Descriptions; Propositions; Ramsey, Frank Plumpton; Rilke, Rainer Maria (René); Rules; Russell, Bertrand Arthur William; Schlick, Moritz; Thinking; Tolstoy, Lev (Leo) Nikolaevich; Volition; Wright, Georg Henrik von.

Bibliography

works by wittgenstein

Tractatus Logico-Philosophicus. London: Routledge, 1922. Contains the German text of Logisch-Philosophische Abhandlung, with English translation on facing pages, and an introduction by Bertrand Russell. Republished with a new translation by D. F. Pears and B. F. McGuinness. London: Routledge and Paul, 1961.

"Some Remarks on Logical Form." PAS supp. 9 (1929): 162–171.

Philosophical Investigations. Edited by G. E. M. Anscombe, Rush Rhees, and G. H. von Wright, translated by G. E. M. Anscombe. Oxford: Blackwell, 1953. Contains German text of Philosophische Untersuchungen, with English translation on facing pages.

Remarks on the Foundations of Mathematics. Edited by G. E. M. Anscombe, Rush Rhees, and G. H. von Wright, translated by G. E. M. Anscombe. Oxford: Blackwell, 1956. Parallel German and English texts.

The Blue and Brown Books: Preliminary Studies for the Philosophical Investigations. Oxford: Blackwell, 1958. With a preface by Rush Rhees.

Notebooks 1914–1916. Edited by G. E. M. Anscombe and G. H. von Wright, translated by G. E. M. Anscombe. Oxford: Blackwell, 1961. Parallel German and English texts.

Philosophische Bemerkungen. Frankfurt, 1964.

"A Lecture on Ethics." Philosophical Review 74 (1965). A paper delivered at Cambridge in 1929 or 1930.

works on wittgenstein

Biography

Gasking, D. A. T., and A. C. Jackson. "Ludwig Wittgenstein," memorial notice. Australasian Journal of Philosophy 29 (1951).

Malcolm, Norman. Ludwig Wittgenstein: A Memoir. London: Oxford University Press, 1958.

Russell, Bertrand. "Ludwig Wittgenstein," memorial notice. Mind 60 (1951).

Ryle, Gilbert. "Ludwig Wittgenstein," memorial notice. Analysis 12 (1951).

Von Wright, G. H. "Ludwig Wittgenstein: A Biographical Sketch," Malcolm, op. cit.

Wisdom, John. "Ludwig Wittgenstein, 1934–1937." Mind 61 (1952).

Tractatus

Anscombe, G. E. M. An Introduction to Wittgenstein's Tractatus. London: Hutchinson University Library, 1959.

Black, Max. A Companion to Wittgenstein's Tractatus. Ithaca, NY: Cornell University Press, 1964.

Colombo, G. C. M. Critical introduction and notes to the Italian translation of the Tractatus. Milan and Rome, 1954.

Daitz, E. "The Picture Theory of Meaning." In Essays in Conceptual Analysis, edited by Antony Flew. London: Macmillan, 1956.

Griffin, James. Wittgenstein's Logical Atomism. Oxford: Clarendon Press, 1964.

Hartnack, Justus. Wittgenstein og den moderne Filosofi. Copenhagen, 1960. Translated into German as Wittgenstein und die moderne Philosophie. Stuttgart, 1962.

Hintikka, Jaakko. "On Wittgenstein's Solipsism." Mind 67 (1958).

Keyt, David. "A New Interpretation of the Tractatus Examined." Philosophical Review 74 (1965).

Keyt, David. "Wittgenstein's Notion of an Object." Philosophical Quarterly 13 (1963).

Maslow, Alexander. A Study in Wittgenstein's Tractatus. Berkeley: University of California Press, 1961.

Pitcher, George. The Philosophy of Wittgenstein. Englewood Cliffs, NJ: Prentice-Hall, 1964.

Ramsey, F. P. Critical notice of the Tractatus. In The Foundations of Mathematics, edited by R. F. Braithwaite. London: K. Paul, Trench, Trubner, 1931.

Rhees, Rush. "Miss Anscombe on the Tractatus." Philosophical Quarterly 10 (1960).

Rhees, Rush. "The Tractatus : Seeds of Some Misunderstandings." Philosophical Review 72 (1963).

Russell, Bertrand. "The Philosophy of Logical Atomism." In Logic and Knowledge, edited by R. C. Marsh, London: Allen and Unwin, 1956.

Schlick, Moritz. "The Turning Point in Philosophy." In Logical Positivism, edited by A. J. Ayer. Glencoe, IL: Free Press, 1959.

Stenius, Eric. Wittgenstein's Tractatus. Ithaca, NY: Cornell University Press, 1960.

Wienpahl, Paul D. "Wittgenstein and the Naming Relation." Inquiry 7 (1964).

Blue and Brown Books, Investigations, Remarks on the Foundations of Mathematics

Albritton, Rogers. "On Wittgenstein's Use of the Term 'Criterion.'" Journal of Philosophy 56 (22) (1959).

Ayer, A. J. "Privacy." Proceedings of the British Academy 45 (1959).

Ayer, A. J., and Rush Rhees. "Can There Be a Private Language?" PAS supp. 28 (1954). Symposium.

Bambrough, Renford. "Universals and Family Resemblances." PAS 61 (1960–1961).

Bouwsma, O. K. "The Blue Book." Journal of Philosophy 58 (6) (1961).

Buck, R. C. "Non-other Minds." In Analytical Philosophy, edited by R. J. Butler. Oxford: Blackwell, 1962.

Carney, J. D. "Private Language: The Logic of Wittgenstein's Argument." Mind 69 (1960).

Cavell, Stanley. "The Availability of Wittgenstein's Later Philosophy." Philosophical Review 71 (1962).

Chihara, C. S. "Mathematical Discovery and Concept Formation." Philosophical Review 72 (1963).

Chihara, C. S. "Wittgenstein and Logical Compulsion." Analysis 21 (1961).

Cook, J. W. "Wittgenstein on Privacy." Philosophical Review 74 (1965).

Cowan, J. L. "Wittgenstein's Philosophy of Logic." Philosophical Review 70 (1961).

Dummett, Michael. "Wittgenstein's Philosophy of Mathematics." Philosophical Review 68 (1959).

Feyerabend, Paul K. "Wittgenstein's Philosophical Investigations. " Philosophical Review 64 (1955).

Fodor, J. A., and J. J. Katz. "The Availability of What We Say." Philosophical Review 72 (1963).

Gasking, D. A. T. "Avowals." In Analytical Philosophy, edited by R. J. Butler. Oxford: Blackwell, 1962.

Hardin, C. L. "Wittgenstein on Private Languages." Journal of Philosophy 56 (1959).

Hartnack, Justus. Wittgenstein og den moderne Filosofi, see above.

Kreisel, Georg. "Wittgenstein's Remarks on the Foundations of Mathematics. " British Journal for the Philosophy of Science 9 (1958).

Kreisel, Georg. "Wittgenstein's Theory and Practice of Philosophy." British Journal for the Philosophy of Science 11 (1960).

Malcolm, Norman. "Behaviorism as a Philosophy of Psychology." In Behaviorism and Phenomenology, edited by T. W. Wann. Chicago: William Marsh Rice University by the University of Chicago Press, 1964.

Malcolm, Norman. Dreaming. New York: Humanities Press, 1959.

Malcolm, Norman. Knowledge and Certainty. Englewood Cliffs, NJ: Prentice-Hall, 1963. See "Wittgenstein's Philosophical Investigations " and "Knowledge of Other Minds."

Moore, G. E. "Wittgenstein's Lectures in 1930–1933." In Philosophical Papers. New York: Macmillan, 1959.

Nell, E. J. "The Hardness of the Logical 'Must.'" Analysis 21 (1961).

Pitcher, George. The Philosophy of Wittgenstein. Englewood Cliffs, NJ: Prentice-Hall, 1964.

Rhees, Rush. Preface to The Blue and Brown Books. Oxford: Blackwell, 1958.

Rhees, Rush. "Some Developments in Wittgenstein's View of Ethics." Philosophical Review 74 (1965).

Rhees, Rush. "Wittgenstein's Builders." PAS 60 (1959–1960).

Strawson, P. F. Critical notice of Philosophical Investigations. Mind 63 (1954).

Thomson, Judith J. "Private Languages." American Philosophical Quarterly 1 (1964).

Waismann, Friedrich. "Notes on Talks with Wittgenstein." Philosophical Review 74 (1965).

Wellman, Carl. "Our Criteria for Third-Person Psychological Sentences." Journal of Philosophy 58 (1961).

Wellman, Carl. "Wittgenstein and the Egocentric Predicament." Mind 68 (1959).

Wellman, Carl. "Wittgenstein's Conception of a Criterion." Philosophical Review 71 (1962).

Wisdom, John. "A Feature of Wittgenstein's Technique." PAS supp. 35 (1961).

Wisdom, John. Philosophy and Psychoanalysis. Oxford, 1953.

Norman Malcolm (1967)