This is an unusual book, both in content and in style. In content it is about logic, though Ludwig Wittgenstein, in discussing this subject, manages to say much about the theory of signs, epistemology, metaphysics, and philosophy in general. Furthermore, Wittgenstein indicates that there are many things that we cannot say about logic, not because we do not know them or because we cannot find words by which to express them, but because they are literally inexpressible by means of any language. Consequently, we must remain silent about them.

The sentences (or sometimes groups of sentences) in this work are all numbered in accordance with a plan. For example, a certain sentence has the number 3; this follows sentences 1 and 2 in the order of the natural numbers. However, between 2 and 3 are sentences numbered, for example, 2.0122 and 2.151. Sentence 2.0122 is a statement referring to statement 2. Statement 2.151 follows statement 2.1 and is a comment on it; statement 2.1, in turn, is another comment on 2, and follows it. All statements are in this way arranged in a unique, linear order based on the decimal notation, and the reader is able to determine by the number attached to each sentence what general topic is being considered, what special aspect of this general subject is involved, and so on, sometimes to a fourth level of specialization.

Furthermore, because of the unusual meanings associated with many of the terms employed by the author, the editor chose to publish, on facing pages, the original German text and its parallel English translation. This design permits those who are familiar with German to improve their understanding of the text by comparing the English version with its German original, thereby in many cases detecting fine shades of meaning. In a book where such common words as “fact,” “object,” “meaning,” and “truth” occur in great abundance and are employed with somewhat unusual connotations, the parallel translation is of great help. The book also contains a valuable introduction, written by Wittgenstein’s mentor Bertrand Russell, that both summarizes the text and criticizes it on some important points.

Atomic Facts

For convenience of discussion, one can combine Wittgenstein’s discussion of proposition 1 and the remarks on it with proposition 2 and all of the remarks contained in propositions numbered 2.0. Proposition 1 states that the world is everything that is the case; proposition 2 asserts that what is the case, or the fact, is the existence of atomic facts. The world, then, is made up of atomic facts and is constituted by them. Atomic facts are facts that are incapable of analysis into more elemental facts. This does not mean that atomic facts cannot be analyzed, but only that they cannot be analyzed into other atomic facts. An atomic fact is itself a combination of objects (entities, things), each of whose essence lies in its being a constituent of an atomic fact. However, the objects that are elements of atomic facts cannot themselves be analyzed because they form the substance of the world. If we take advantage of the illustration of an atomic fact that Russell gives in his introduction (Wittgenstein does not give illustrations of atomic facts), we may say that it is what is asserted by the proposition “Socrates is wise.” This contains two objects, Socrates and wise, each of which, in its own unique way, unites with the other to form the atomic fact. Traditional philosophy would call these objects “substances” and “qualities.”

Wittgenstein states that however different from the real world an imaginary world might be, it must have something, its form, in common with the real world. Because the form is given by the objects, we may presume Wittgenstein to be saying that any imaginable world would have to contain substances and qualities, however these might differ from those in the real world. The world is the totality of atomic facts; it also determines the nonexistence of atomic facts, for the nonexistence of an atomic fact is a kind of fact. Reality, therefore, is the totality of atomic facts plus the fact that these are all the atomic facts.


Beginning with proposition 2.1, continuing more or less explicitly through proposition 4, and extending implicitly through the rest of the book, Wittgenstein examines what is meant by saying that a proposition is a picture of a fact. He describes this picturing relation variously as “modeling,” “standing for,” “representing,” “corresponding with,” “depicting,” and “projecting.” Note, however, that a proposition is itself a fact. By this is not meant the propositional sign that expresses the fact, though Wittgenstein admits that propositions can be expressed perceptibly through the senses, but rather the sense of the proposition. The point is, of course, that the proposition is a logical picture of the fact, not a visual one or an audible one. He says that it represents the fact in “logical space”—a metaphor that he uses repeatedly throughout the book. Its representative character lies in its form or structure, which means a coordination of the elements in the picture with the objects in the fact, and an identity of logical form exhibited by both the picture and the fact.

Thus the proposition “Socrates is wise” pictures the fact of Socrates’ wisdom because “Socrates” represents Socrates, and “wise” represents wisdom, and the form exhibited by “Socrates” and “wise” in the propositional relation is the same as that exhibited by Socrates and wisdom in the fact. That this is a logical form rather than a spatial form is to be seen in the fact that while the...

(The entire section is 636 words.)

A Logical Language

In the language of everyday life, the same word often signifies in two different ways, and different words signify in the same way. For example, the verb “to be” appears sometimes as the sign of equality, sometimes as the expression of existence, sometimes as an intransitive verb, and sometimes as a sign of identity. Words of this kind are the cause of some of the most fundamental confusions in thought, especially in philosophical thought. The only way to avoid these difficulties is to invent a special symbolism—a symbolism that obeys the rules of logical grammar (logical syntax). Such rules follow of themselves if we know how every sign signifies. Russell and the mathematician Gottlob Frege have invented such logical symbolisms, but even these do not exclude the possibility of error.

The great advantage of a logical language is that it calls our attention to formal properties of objects and facts. This is not because propositions express the form of facts, but because they “show it” and do not state it. No proposition is capable of representing its form of representation, for this would require something that is impossible—the picture would have to place itself outside its form of representation. “The proposition shows how things stand, if it is true.” The existence of a structure in a possible state of affairs is not expressed by the proposition that presents the state of affairs; it is shown in the proposition by means of its structure. The identity of form that is exhibited by the proposition and by the fact accounts for the representation of the fact by the proposition, but this does not give the proposition a formal property of representing the fact. It would be as meaningless to ascribe a formal property to a...

(The entire section is 737 words.)

Types of Propositions

The simplest proposition, the elementary proposition, asserts the existence of an atomic fact. Such a proposition is a concatenation of names and is incapable of analysis into further propositions. One of Wittgenstein’s important theses is that all propositions are truth-functions of elementary propositions and can be built up from them. (An elementary proposition is a truth-function of itself.) Truth-functions are obtained in the following way: Suppose all elementary propositions were given. Each of these could be either true or false. Therefore a proposition containing three elementary propositions p, q, r could have a truth-function T, T, F or T, F, T, and there would be eight such possible truth-functions. If there were four elementary propositions, there would be sixteen truth-functions. Starting with any group of elementary propositions, the truth-functions formed from them may be arranged in a series.

Of the propositions, two kinds are particularly important. One of them, a “tautology,” is a type of proposition that is true for all the truth-possibilities of the elementary propositions. The other, a “contradiction,” is a proposition that is false for all the truth-possibilities of the elementary propositions. The truth of a tautology is certain; the truth of a contradiction is impossible; the truth of all other propositions is possible. Here we have the serial arrangement of...

(The entire section is 474 words.)


Language cannot express anything that contradicts logic. Wittgenstein now resumes discussion of this topic and points out that we cannot say what we cannot think. We cannot say that there is this in the world but there is not that, for such a statement would imply that logic can exclude certain possibilities from the world; but in such a case, logic would have to “get outside the limits of the world”; that is, it would have to consider these limits from both within and without the world. However, logic cannot go beyond itself: “Logic fills the world: the limits of the world are also its limits.” This principle also has applications for solipsism. Solipsism is correct but cannot be asserted; it can only be...

(The entire section is 310 words.)

The Role of Philosophy

What, then, is philosophy? It seems to have two tasks. One is to show that every proposition is a picture of a fact. This cannot be said, for no proposition can say anything about itself. That a proposition has, for example, the subject-predicate form cannot be said in a proposition, and that a proposition has the form “p or q” cannot be said in a proposition. Nor can it be said how a proposition pictures reality. A sentence has no apparent pictorial character. However, neither does a musical score or a phonograph record; nor does a pattern of sound waves obviously picture the sound themselves. Yet all of these stand to that which they represent in a relation that can be seen in the...

(The entire section is 393 words.)


Additional Reading

Fann, K. T., ed. Ludwig Wittgenstein: The Man and His Philosophy. New York: Dell, 1967. A collection of articles by friends, students, and scholars of Ludwig Wittgenstein. Included are articles on Wittgenstein as a person, a teacher, and a philosopher, and treatments of various aspects of Wittgenstein’s philosophical work.

Hacker, P. M. S. Wittgenstein. New York: Routledge, 1999. An excellent biographical introduction to the thoughts of the philosopher, clearly presented and requiring no special background. Bibliography.

Hacker, P. M. S. Wittgenstein’s Place in...

(The entire section is 496 words.)