Simply Wittgenstein Read online

  So far we have learned something of the household in which Ludwig grew up. From here we will pick up the story of his life along the way, as it becomes relevant and provides the context for understanding his writings. But it is the writings—his two great books—that made Wittgenstein famous. So they will be our focus.

  James C. Klagge

  Blacksburg, Virginia

  The Tractatus

  Despite its long title, the Tractatus Logico-Philosophicus is a short book. In fact, it was originally published in German in 1921 as a 67 page-long article entitled “Logisch-Philosophische Abhandlung,” which means a treatise or essay on logical philosophy, or philosophy done in a logical way. Wittgenstein wrote it while he was a soldier in the First World War, and completed it in 1918. It took a few years to find a publisher, and no wonder: This work is a series of 526 decimally-numbered passages, each ranging from a single sentence to several paragraphs, running from 1 to 7, with an eight-paragraph long preface. For the most part, the language is simple and straightforward, though there are a number of logical and mathematical symbols used towards the end.

  The book’s seven main propositions are as follows:

  The world is all that is the case.

  What is the case—a fact—is the existence of states of affairs.

  A logical picture of facts is a thought.

  A thought is a proposition with sense.

  A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)

  The general form of a truth-function is [p̄, ξ̄, N(ξ̄)]. This is the general form of a proposition.

  What we cannot speak about we must pass over in silence.

  The other 519 passages are arranged decimally as commentaries on the above points. Yet, one of Wittgenstein’s mentors, the German logician Gottlob Frege (1848-1925), told him: “I find it difficult to understand. You place your propositions one after the other mostly without giving reasons for them, or without giving enough detailed reasons.” Based on this assessment, we should not expect the Tractatus to be easy going.

  Its publication as a book, in 1922, included an English translation and a new title. The Latin title has roughly the same meaning as the German one, but gives the work a lofty, quasi-biblical tone. Wittgenstein took the decimal numbering of the passages to be quite important, but the reader needn’t take it too seriously, apart from the general sense of organization it provides.

  The World

  The Tractatus opens with a sort of cosmic creation story: “The world is everything that is the case” (TLP 1). Philosophers like to ask big questions—like, what is the world made up of? And then offer a theory. René Descartes thought the world was made up of minds and bodies. Minds included God and human minds; bodies comprised human bodies and everything else made of matter. Bishop George Berkeley thought the world was made up only of minds—human minds and the mind of God. What we think of as physical objects were just a bunch of mental experiences or possibilities for experiences. Aristotle thought the world was made up of substances, and living beings were the best examples of substances. Another Greek philosopher, Democritus, believed the world was made up of only physical atoms and void—empty space. Mind was just a complicated arrangement of physical atoms. And Plato thought so little of the physical world that he believed the abstract realm of the Forms was what mattered most. In each case, the answer to the big question was one or two kinds of thing.

  But Wittgenstein saw it differently: “The world is the totality of facts, not of things” (TLP 1.1). He wasn’t so much interested in what the basic things were, but in how they were. To him, the fundamental nature of the world was structural: Facts have a structure and are arrangements of things. Things do not exist except in arrangements.

  To understand Wittgenstein’s thinking, let’s go back for a moment to his days as a student. Before getting interested in philosophy, Wittgenstein had trained, from 1906 to 1908, as an engineer at a renowned technical college near Berlin. His father would have liked him to study business, but this course was practical enough to prove acceptable. Then, from 1908 to 1911, the period that coincided with the beginnings of engine-powered flights, Wittgenstein studied aeronautical engineering at the University of Manchester in England. In November of 1910, he submitted a patent application for “Improvements in Propellers Applicable for Aerial Machines.” The patent was granted in August of the next year.

  The patent application made no mention of what the propeller would be made of; it only explained how it would be structured. Engineers are interested in structures and models that can abstract away from the specific material that makes up a system.

  Engineering work sparked Wittgenstein’s interest in mathematics, and then in the foundations of mathematics, or logic. After asking around, he determined that the best place to study his newfound interest in logic was with Bertrand Russell (1872-1970) at the University of Cambridge, in England. So he went there in October of 1911 and sought out Russell.

  Russell wrote to a friend on that day: “…an unknown German appeared, speaking very little English, but refusing to speak German. He turned out to be a man who had learned engineering at Charlottenburg, but during his course had acquired, by himself, a passion for the philosophy of mathematics & he has now come to Cambridge on purpose to hear me” (DG, pp. 38-39).

  It was Wittgenstein’s work with Russell that got him thinking about the nature of the world. In fact, Russell’s interests in many ways became Wittgenstein’s too, as it often happens in a teacher-student relationship. Russell called his own theory “logical atomism,” and that was an apt name for the view Wittgenstein propounded as well. Scientists see the physical world as built up out of arrangements of physical atoms. In parallel, Russell and Wittgenstein saw the world in general as constructed out of arrangements of logical atoms, or basic facts. We can see Wittgenstein as asking the question: “How might the world be engineered out of basic facts?”

  Analysis

  Let’s begin by thinking about a fact that is familiar to us—Obama won the US Presidential election in 2008. This may come across as a simple fact, but it is immediately clear that it is not. It is not even as simple as that he received the most votes in the 2008 US Presidential election. That is because the US Presidential election is determined by an Electoral College election, which, in turn, is determined by the popular votes in each state. So the Presidential electoral victory amounts to a set of electoral outcomes in each state and a set of rules for the Electoral College. Therefore, we might say that the familiar fact, which can be analyzed or broken down into more basic facts, is really a complex structure of other facts. Wittgenstein thought this held generally: “Every statement about complexes can be resolved into a statement about their constituents and into the propositions that describe the complexes completely” (TLP 2.0201).

  It is plausible to suppose that many of the kinds of facts we are familiar with are actually complex in this sense. Take, for instance, this sentence: “John is a bachelor.” This implies that John is a male, of marrying age, who is currently not married. Another example: “The cat is on the mat,” could also be further analyzed. We might analyze what it is to be a cat or a mat. We might even analyze what it is to be “on” something, though that seems pretty basic.

  Where does such analysis lead? Some might think this is a hopeless process, that most things cannot be analyzed in this way. Others may believe this is an endless exercise. Numbers, for example, seem endlessly divisible. Between these two extremes, Wittgenstein and Russell thought that the process would lead to a single and complete analysis, breaking facts down into their most basic constituents: “A proposition has one and only one complete analysis” (TLP 3.25). Wittgenstein called facts at this most basic level—the endpoint of a complete analysis—“atomic facts” or “states of affairs.”

  Russell had his own view about what the basic things were that got structured into facts at the basic level of analysis. He thoug
ht they were tiny bits of experience—what philosophers call “sense data.” Russell was, around the time Wittgenstein studied with him, an “idealist” (meaning, in this context, that to him everything was made up out of ideas or experiences). But Wittgenstein did not seem interested in answering the question of what the things were. He just called them “objects”: “Objects are simple” (TLP 2.02); “Objects make up the substance of the world” (TLP 2.021).

  Many years later, a friend asked Wittgenstein whether, when he wrote the Tractatus, he had ever decided on anything as an example of a “simple object.” His reply was that his thought at that time had been that he was a logician and, as such, it was not his business to try to decide “whether this thing or that was a simple thing or a complex thing” (MM, p. 70).

  While Wittgenstein did not conjecture about what the objects might turn out to be, his commitment to the existence of such objects constituted a sort of conceptual scheme: Any world, real or imagined, is object-ual, or object-based (TLP 2.022, 2.023). The differences between possible worlds are just differences in the arrangement of basic objects (TLP 2.0271). Objects are the metaphysical building blocks of any world, and any world can be engineered out of them.

  Language

  Wittgenstein took it for granted that we talk about the world. We can be right or wrong when we say, for example, “The cat is on the mat.” If a sentence can be an accurate description of the world, then there must be some explanation of how that can be. What is it about a sentence that accounts for its being about the world, and what is it about a true sentence that accounts for its being an accurate portrayal of the world? Wittgenstein focused on the fact that a sentence has structure, just as the part of the world that the sentence is about has structure too. He assumed that this parallelism of structure—mathematicians call it “isomorphism”—accounted for the ability of language to be about, and to accurately portray, facts in the world. This structure is what Wittgenstein called “logical form” (TLP 2.18).

  When Wittgenstein introduced this concept in the Tractatus, he approached it as an issue, not about language specifically, but about representation more generally. He spoke of a picture and what it pictures: “A picture is a model of reality. In a picture objects have the elements of the picture corresponding to them. In a picture the elements of the picture are the representatives of the objects” (TLP 2.12-2.131). An accurate visual picture will look like reality. “The fact that the elements of the picture are related to one another in a determinate way represents that things are related to one another in the same way” (TLP 2.15).

  This way of looking at things came to Wittgenstein while he was stationed at the front during the First World War: “At one time I was brought to the picture theory of language through a newspaper notice which said that in Paris at a legal proceeding about a traffic accident, the accident was presented through dolls and a little bus” (WA2, p. 279). This was a three-dimensional model or picture.

  But there are other kinds of representation, such as thought and language. Just as there can be an accurate picture of the cat on the mat, so too there can be a thought that the cat is on the mat, or a statement “The cat is on the mat,” that is accurate, or true as well.

  When Wittgenstein asserted: “A logical picture of facts is a thought” (TLP 3), I think he really meant to state the reverse: A thought is a logical picture of facts. That is, a thought, like a proposition or a model or a picture, is also representational.

  In the case of a statement, there is no obvious similarity between the statement and the fact, even when the statement is true. But there will still be a similarity nevertheless—a more abstract structural similarity. “In a proposition a name is a representative of an object. The configuration of objects in a situation corresponds to the configuration of simple signs in a propositional sign” (TLP 3.22, 3.21). The representation and the fact share a logical form.

  Just as Wittgenstein used “object” for whatever is reached at the deepest level of analysis of the world, so too he used “name” for what refers to an object at the deepest level of analysis of language. But a sentence cannot be just a bunch of names: “A proposition is not a blend of words…. A proposition is articulate” (TLP 3.141). The words must be structured together; they must go together in a certain way: “An elementary proposition consists of names. It is a nexus, a concatenation, of names” (TLP 4.22). And this mirrors the situation with facts. A fact is not just a collection of objects: “In a state of affairs objects fit into one another like the links of a chain” (TLP 2.03). The objects are structured together in a certain way. I think you’ll agree: “The cat is on the mat” is a sentence; “cat The on mat is the” is not.

  We know a good deal about the structure of language. Sentences have a grammar, which we study in school. For example, there is the subject-predicate structure: John is tall. “John” is the name or subject, and “is tall” is the predicate. This can be extended to more complex structures: John loves Mary, or The cat is on the mat. In these cases, the verbs connect two names. It is natural to speak of a “relation,” or in this case “two-place relation,” to describe the grammatical structure. Giving would be a three-place relationship: John gives to Mary a ring. Wittgenstein exhibits the structure of sentences like these logically as:

  T(j) abbreviates: Tall (john), which stands for: John is tall

  O(c, m) abbreviates: On(cat, mat), which stands for: The cat is on the mat, and

  G(j, m, r) abbreviates: Gives to(john, mary, ring), which stands for: John gives to Mary the ring

  In school, students (used to) learn how to do a grammatical diagram of a sentence. You might call what Wittgenstein offers here a “logical diagram” of a sentence. Logical diagrams show the different logical structures that sentences might have.

  But this familiar subject-predicate structure is not always what it seems. The grammatical subject of “Nobody is home” would be “nobody.” But in Chapter 7 of Through the Looking Glass, Lewis Carroll shows us the humor in supposing, as the king does, that “Nobody” is a name of something:

  “I see nobody on the road,” said Alice.

  “I only wish I had such eyes,” remarked the king in a fretful tone. “To be able to see Nobody! And at that distance, too! Why, it’s as much as I can do to see real people, by this light.”

  And a bit later the king asks the messenger whom he passed on the road:

  “Nobody,” said the messenger.

  “Quite right,” said the king: “this young lady saw him too. So of course Nobody walks slower than you.”

  “I do my best,” the messenger said in a sulky tone. “I’m sure nobody walks much faster than I do!”

  “He can’t do that,” said the king, “or else he’d have been here first.”

  Cases like this led Wittgenstein, following Russell, to warn that sometimes “Language disguises thought” (TLP 4.002). He went on to liken language to clothing, “which is not designed to reveal the form of the body, but for entirely different purposes.” Much as some might wish it, language does not develop with the desires of logical philosophers in mind. Sometimes the surface grammar of a sentence conceals its real structure.

  So language can be an avenue to understanding the structure of reality, but it can also be a blind alley. Language must first be analyzed into its proper logical form. Then it can indicate the structure of reality.

  When language is analyzed far enough—to the basic level—it will turn out that the basic sentences are logically independent of one another: “It is a sign of a proposition’s being elementary that there can be no [other] elementary proposition contradicting it” (TLP 4.211). And so, too, the atomic facts are independent of one another (TLP 1.2). How things stand over here is independent of how they stand over there.

  What’s More Basic?

  I have just said that language can be an avenue to understanding the structure of reality. But if you remember, the Tractatus began by telling us that the structure of reality is made up of
facts, not things (TLP 1.1), and only later got around to discussing language. Even though the book starts by characterizing the world, it seems that we only understand this characterization from a more basic understanding of the structure of language. So, in our understanding of reality, language comes first. Language has a sentential subject-predicate form, so reality must have a factual object-property form.

  Understanding the structure of language is the key to understanding the structure of reality. Wittgenstein did not make this clear initially, but it became clear later when he wrote: “The limits of my language mean the limits of my world” (TLP 5.6). We understand reality through the conceptualization of language, not independently of it. Insofar as the basic sentences are true, they will mirror the basic facts. But we conceptualize the basic facts as we do because language has the structure it has.

  This has reminded some people of the later Sapir-Whorf Hypothesis in linguistics, which claims that the structure of a language determines the way a person behaves and thinks. But Wittgenstein, following Russell’s lead, did not at this time question the fact that the language he spoke and wrote, German (or, in Russell’s case, English), was not representative of the structure of all languages. Russell, however, spent a year living and lecturing in China in 1920-1921. Of this experience, mathematician John Edensor Littlewood reported that, “He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica [Russell’s account of logic] was an Indo-European one” (LM, p. 130).

  The contemporary linguist Noam Chomsky argued that there is a universal grammar underlying all languages. If so, that would provide support for the position that Russell and Wittgenstein took after all, but it continues to be a matter for debate.