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wittgenstein-ludwig.blogspot.com/2010/07/tractatus.html


Ludwig Josef Johann Wittgenstein (1889-1951)

(The Tractatus Logico-Philosophicus)

I am going to use K. T. Fann's book Wittgenstein's Conception of Philosophy as a guide, because I think it is one of the best summaries written on Wittgenstein's philosophy. If you want to study Wittgenstein I would suggest getting Fann's book. You can get it on Alibris (used) for just a few dollars.

Second, I think it is important to understand the background to Wittgenstein's works or notes in order to better understand his thinking. I am not going to be able to give those of you who are interested a complete background of what was going on in philosophy at the time, vis-a-vis Bertrand Russell, A. N. Whitehead, and Gottlob Frege. I will only give you bits and pieces, and hopefully this will inspire you to do your own thinking, and come to your own conclusions about the nature of Wittgenstein's work; and not only the nature of his work, but to come to understand how his thinking should influence the way we think about language, and in particular - propositions.

As much as I enjoy Wittgenstein's philosophy, and thinking about what he said concerning the nature of a proposition, it is important to understand that no philosopher no matter how brilliant - is perfect. Hence, we have to be careful about getting tunnel vision, and we have to be careful about being too dogmatic about a certain philosopher, philosophy, or theory.

I have come to the conclusion after reading several biographies, and studying Wittgenstein on my own for many years, that in the 20th century Wittgenstein is to philosophy what Einstein is to physics; and just as a physicist would not neglect Einstein's theories, I think philosophers should also not neglect the study of Wittgenstein's methods. His works are some of the most original in all of philosophy. The power of his intellect is truly amazing, and this is seen not only in his philosophy, but in other areas of his life.

Wittgenstein was born in Vienna, and he was the youngest of eight children. He came from a very rich industrialist family. In fact, Brahm's would come to the Wittgenstein home and play his music. He was educated at home until the age of 14, when his parents decided to send the young Wittgenstein to Linz to prepare him in mathematics and the physical sciences. It seems that the young Wittgenstein wanted to study with the physicist Boltzmann, but Boltzmann died in 1906.

After being educated in Linz for three years, he then went to Berlin to study mechanical engineering at the Technische Hochscule at Charlottenburg. After two years in Berlin, he then went to England where he became a research student of engineering at the University of Manchester. During this time he engaged in aeronautical research, and went from experimenting with kites, to the construction of a jet reaction propeller for aircraft. The design of the propeller was a mathematical endeavor, which eventually led the young Wittgenstein into pure mathematics, and then, to the foundation of mathematics. Apparently his interest in the foundation of mathematics led him to Russell and Whitehead's work called the Principles of Mathematics. This book greatly affected the young Wittgenstein, and his interest in mathematics also led him to the works of Frege, who is the founder of modern mathematical logic. So it was through Russell, Whitehead, and Frege's works that Wittgenstein entered into the study of philosophy.

According to G. H. Von Wright, Wittgenstein had read Schopenhauer's Die Welt als Wille und Vorstellung, and this brought him face-to-face with Schopenhauer's idealism. Later Wittgenstein apparently abandoned his Schopenharuerian idealistic views in favor of Frege's conceptual realism; and it seems that after a talk with Frege, Wittgenstein decided to go to Cambridge and study philosophy with Russell (G. H. Von Wright, A Biographical Sketch, p. 6).

The Tractatus (part 2)

It is important to understand that the Philosophical Investigations has to be seen in the light of his former work - the Tractatus. Therefore, I will begin by briefly outlining the Tractatus before I move on to a brief outline of the Philosophical Investigations.

The Tractatus is one of the most difficult works of philosophy to understand, and therefore, many of the interpretations of the Tractatus have been deficient. Even Russell and Frege misinterpreted the Tractatus according to Wittgenstein.

In the preface to the Tractatus Wittgenstein tells us what the aim of the Tractatus is, "The book deals with the problems of philosophy, and shows, I believe, that the reason why these problems are posed is that the logic of our language is misunderstood. The whole sense of the book might be summed up in the following words: what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence.

"Thus the aim of the book is to draw a limit to thought, or rather--not to thought, but to the expression of thoughts: for in order to be able to draw a limit to thought, we should have to find both sides of the limit thinkable (i.e. we should have to be able to think what cannot be thought).

"It will therefore only be in language that the limit can be drawn, and what lies on the other side of the limit will simply be nonsense(Tractatus, p. 3)."

Keep in mind that even in the Philosophical Investigations Wittgenstein is still thinking in terms of the logic of language; however, his method is different. The Tractatus is an a priori investigation of language, and the Philosophical Investigations is more of an a posteriori or pragmatic approach to language. My personal belief is that both works have something important to say.

The a priori approach in the Tractatus is due to Wittgenstein's belief that the structure of language is revealed by logic (P.I. para. 107). Also Wittgenstein believed that the function of language is essentially to describe the world. Therefore, we can see that the three main issues of the Tractatus are logic, language, and the world. And this is clearly pointed out in Wittgenstein's picture theory of language, which is directly related to his theory of truth-functions.

"These two theories are designed to answer the questions: 'What is the function of language?' and 'What is the structure of language?' Since language is conceived as 'the totality of propositions' (T. 4.001), the two questions are transformed into the following: 'How are propositions related to the world?' and 'How are propositions related to one another?' This is why Wittgenstein wrote in his Notebook, 'My whole task consists in explaining the nature of the proposition' (Nb p. 39). Wittgenstein assumes that if we can use language to talk about the world there must be some propositions directly connected with the world, so that their truth or falsity are not determined by other propositions but by the world: these he called 'elementary propositions' (K. T. Fann, p. 8)."

The Tractatus (part 3)

Elementary propositions are the constituent parts of complex or ordinary propositions. That is to say, ordinary propositions can be analyzed into more basic kinds of propositions, which can be further analyzed into the most fundamental parts, until no further analysis is possible. Once we reach the point where no further analysis is possible, then we have what Wittgenstein calls the elementary proposition. The elementary proposition puts us into direct contact with the world. Elementary propositions are logical pictures of atomic facts. Atomic facts are the smallest constituent parts of more complex facts. We are in direct contact with the world, because the smallest analyzable proposition, the elementary proposition, puts us in contact with the smallest analyzable fact - the atomic fact (facts exist in the world).

An elementary proposition is the simplest kind of proposition, and it is made up of names (T. 4.22). What is a name? "A name cannot be dissected any further by means of a definition: it is a primitive sign (T. 3.26)." Names refer to objects in the world, and objects are simple (T. 3.203, 2.02). While it is true that elementary propositions are the simplest kind of proposition, they can be analyzed or broken into smaller parts; however, these parts are no longer called propositions, they are called names. Hence, a complete analysis of a proposition is the following: Complex proposition -------> elementary proposition -------> and finally, names.

Nowhere does Wittgenstein come up with an example of elementary propositions or names. According to Norman Malcolm, when he asked Wittgenstein about this, Wittgenstein said that it was not his job as a logician to decide whether this thing or that was a simple or complex thing. His thinking was that this was an empirical matter, and it was not up to him. However, to be fair Wittgenstein understood the problem, and makes reference to it in the Notebooks on page 68 (Fann, p. 12).

So what we have then is the following: Complex propositions can be analyzed into the most basic kind of proposition - called elementary propositions. Elementary propositions are made up of simple terms called names. He concludes that names must refer to objects in the world, that is, the object is its referent. If the referent does not exist, then the proposition is senseless.

The idea that names must refer to objects, is a view that goes all the way back to Augustine, and this is the view of Wittgenstein in the Tractatus; and it's this view that he criticizes in the Philosophical Investigations. However, remember that language in part does name objects, but it does more than just name objects - much more. This can be seen (the naming of objects) in the primitive language-game that Wittgenstein describes in paragraph 2 of the Investigations. Moreover, we observe the use of ostensive definitions when we teach a child the use of words like pencil, cow, car, cat, etc. Therefore, we want to be careful in making the claim that language does not use the ostensive definition model - it does, or that Wittgenstein completely abandons this idea, he doesn't. It is just that this view (the view that language names objects) is a very narrow description of language.

The Tractatus (part 4)

So what we have then is the following: Complex propositions can be analyzed into the most basic kind of propositions - called elementary propositions. Elementary propositions are made up of simple terms called names. He concludes that names must refer to objects in the world, that is, the object is its referent. If the referent does not exist, then the proposition is senseless. But how can this be, since we often make reference to things that do not exist, and yet we understand the sense of the proposition. We refer to Hobbits, witches, little green monsters, and yet they do not exist. We understand, because we understand the concepts - not because they point to some thing; and we understand because propositions present a picture, and these pictures either mirror reality or they do not.

These objects, which are the simplest elements in reality, that is, they are what reality is composed of; and they are what the names in elementary propositions refer too. Objects are indestructible, they are the constituent parts that remain the same over time. We use them to construct a picture of reality (PI, para. 59). Furthermore, objects make up atomic facts, which are then used to construct any fact or state of affairs portrayed in complex propositions.

Again, we have the world (T. 1), and the world is composed of objects, atomic facts, and finally the facts themselves, or states of affairs (T. 2, 2.01). Each of these (objects, atomic facts, and facts) has its corresponding component in language (names, elementary propositions, and complex propositions). Wittgenstein is constructing an ontology in the Tractatus: "Objects make up the substance of the world (T. 2.021)." "Empirical reality is limited by the totality of objects. The limit also makes itself manifest in the totality of elementary propositions (T. 5.5561)."

How do the names in elementary propositions say anything? And if they are pictures of atomic facts - what does that mean? It apparently means that they reflect or mirror reality, but this seems to beg-the-question. In the Notebooks Wittgenstein says the following: "In the proposition a world is as it were put together experimentally (Nb. p. 7)." This idea apparently occurred to Wittgenstein when he observed or read about a model of a car accident that was used in a Paris court of law, that is, they used dolls and other objects to represent the facts of the case. The model was a picture of reality; and so it is with the proposition, it is a model of reality as we imagine or picture it (T. 4.01).

Before I end this post, I just want to say that I believe that many of our propositions are pictures of reality, but again this is not the only way propositions state the facts. Many people think that Wittgenstein repudiated this idea, but I think he merely was saying that language does more than this. Just as language does more than refer to objects ostensively.

The Tractatus (part 5)

Earlier I talked about names being the simplest component of elementary propositions, and that the names referred to objects, which then compose atomic facts. The question came up about how we could make sense of a proposition if there were no corresponding objects, and thus, no corresponding facts. According to my understanding of the Tractatus a proposition pictures reality, so if we are to understand a proposition like "There are unicorns." it is because the proposition displays a picture, and that picture either matches up with reality, or it does not. If it correctly mirrors reality, then it is true, if it does not mirror reality, then it is false. Hence, to understand the sense of the proposition is a matter of picturing the proposition, and this occurs quite apart from there being a corresponding fact in reality.

A picture presents a fact from a position outside of it. Just as a picture of the White House presents the White House from a position outside it, or quite separate from the reality of the situation or state-of-affairs. Any picture either accurately or inaccurately presents a certain state of affairs (T. 2.1). Propositions then are pictures according to the Tractatus.

"The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way. Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture (T. 2.15)."

The pictorial form is the form a picture shares with a fact. "What a picture must have in common with reality, in order to be able to depict it--correctly or incorrectly--in the way it does, is its pictorial form. A picture can depict any reality whose form it has. A spacial picture can depict anything spacial, a colored one anything coloured, etc. A picture cannot, however, depict its pictorial form: it displays it (T. 2.17 - 2.172)."

There is a shared logic between the picture and the fact (T. 2.18).

How does a proposition correspond with reality? "Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture.

"That is how a picture is attached to reality; it reaches right out to it.

"It is laid against reality like a measure (T. 2.151-2.1512)."

Each person, truck, bridge, house in the picture represents those things in the world.

So how do we tell if a proposition is true or false? We must compare it with reality (T. 2.223).

The sense of a picture is the arrangement of the things in the picture, which supposedly correspond to the arrangement of things in the world (T. 2.221).

The way one verifies the correctness of a proposition is by inspecting the proposition to see if it indeed reflects reality (T. 2.223).

According to Wittgenstein a thought is a logical picture (Wittgenstein does not believe that we can think illogically), it uses the form of logic to represent a fact (T. 3 and 3.03).

"In a proposition a thought finds an expression that can be perceived by the senses (T. 3.1)." So the logical picture is made by logical units, such as, visual marks or auditory marks.

Therefore, a proposition says that a is in a certain relation to b, i.e., aRb. For instance, Sam is standing next to Jane.

If language was indeed like Wittgenstein describes here, then it would be possible to construct an ideal language, since each name in a proposition would correspond to each object in a fact. Hence, given every possible elementary proposition, we could in theory describe all the atomic facts in the world - the world would be completely described.

The Tractatus (part 6)

So how are we able to understand a new proposition? We understand it because it presents a picture of reality to us. Hence, we understand a proposition like "I saw ten dogs flying over my house today," because it gives us a picture, and that picture either matches reality, or it does not match reality. This is how we can understand propositions that are false (T. 4.024), because even false propositions present a picture.

A picture shows its sense, i.e., it shows how things stand if it is true. The fact that propositions show a particular sense is something that I believe was carried over into the Philosophical Investigations.

Another central idea presented in the Tractatus is the truth-function theory. This theory goes hand-in-hand with the picture theory. "A proposition is a truth-function of elementary propositions (T. 5)." Therefore, if you are given all elementary propositions, then you can construct every possible proposition, which fixes their limits (T. 4.51). My understanding is that this sets the limit of language, or sets a limit to what can be said.

"A full appreciation of this thesis requires an understanding of truth-functional logic. It suffices for our purpose to point out merely that a compound proposition, compounded of the propositions P1, P2,....,Pn, is a truth-functional compound of P1, P2,..., Pn if and only if its truth or falsity is uniquely determined by the truth or falsity (the truth-values) of P1,..., Pn. In other words, the truth-value of a compound proposition is completely determined by the truth-values of its components--once the truth-values of is components are given, the truth-value of the compound proposition can be calculated. Wittgenstein claims that all propositions are related to elementary propositions truth-functionally (K.T. Fann, p. 17)."

Therefore, what follows is the following: "If all true elementary propositions are given, the result is a complete description of the world. The world is completely described by giving all elementary propositions, and adding which of them are true and which false (T. 4.26)."