PREFACE

Perhaps this book will be understood only by someone who has himself already had the thoughts that are expressed in it - or at least similar thoughts. - So it is not a textbook. - Its purpose would be achieved if it gave pleasure to one person who read and understood it. The whole sense of the book might be summed up 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.

If this work has any value, it consists in two things: the first is that thoughts are expressed in it, and on this score the better the thoughts are expressed - the more the nail has been hit on the head - the greater will be its value. - Here I am conscious of having fallen a long way short of what is possible. Simply because my powers are too slight for the accomplishment of the task. - May others come and do it better.

L.W. Vienna, 1918

PROPOSITIONS UNDER 1

1 The world is all that is the case.
1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by their being all the facts.
1.12 For the totality of facts determines what is the case, and also whatever is not the case.
1.13 The facts in logical space are the world.
1.2 The world divides into facts.
1.21 Each item can be the case or not the case while everything else remains the same.

PROPOSITIONS UNDER 2

2 What is the case - a fact - is the existence of states of affairs.
2.01 A state of affairs (a state of things) is a combination of objects (things).
2.02 Objects are simple.
2.03 In a state of affairs objects fit into one another like the links of a chain.
2.033 Form is the possibility of structure.
2.04 The totality of existing states of affairs is the world.
2.05 The totality of existing states of affairs also determines which states of affairs do not exist.
2.063 The sum-total of reality is the world.
2.1 We picture facts to ourselves.
2.11 A picture presents a situation in logical space, the existence and non-existence of states of affairs.
2.12 A picture is a model of reality.
2.14 What constitutes a picture is that its elements are related to one another in a determinate way.
2.141 A picture is a fact.
2.15 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.
2.172 A picture cannot, however, depict its pictorial form: it displays it.
2.181 A picture whose pictorial form is logical form is called a logical picture.
2.19 Logical pictures can depict the world.
2.2 A picture has logico-pictorial form in common with what it depicts.
2.221 What a picture represents is its sense.
2.223 In order to tell whether a picture is true or false we must compare it with reality.
2.224 It is impossible to tell from the picture alone whether it is true or false.
2.225 There are no pictures that are true a priori.

PROPOSITIONS UNDER 3

3 A logical picture of facts is a thought.
3.01 The totality of true thoughts is a picture of the world.
3.03 Thought can never be of anything illogical, since, if it were, we should have to think illogically.
3.0321 Though a state of affairs that would contravene the laws of physics can be represented by us spatially, one that would contravene the laws of geometry cannot.
3.1 In a proposition a thought finds an expression that can be perceived by the senses.
3.2 In a proposition a thought can be expressed in such a way that elements of the propositional sign correspond to the objects of the thought.
3.203 A name means an object. The object is its meaning. ('A' is the same sign as 'A'.)
3.221 Objects can only be named. Signs are their representatives. I can only speak about them: I cannot put them into words. Propositions can only say how things are, not what they are.
3.3 Only propositions have sense; only in the nexus of a proposition does a name have meaning.
3.326 In order to recognize a symbol by its sign we must observe how it is used with a sense.
3.328 If a sign is useless, it is meaningless. That is the point of Occam's maxim.
3.332 No proposition can make a statement about itself, because a propositional sign cannot be contained in itself.
3.4 A proposition determines a place in logical space. The existence of this logical place is guaranteed by the mere existence of the constituents - by the existence of the proposition with a sense.
3.411 In geometry and logic alike a place is a possibility: something can exist in it.
3.42 A proposition can determine only one place in logical space
3.5 A propositional sign, applied and thought out, is a thought.

PROPOSITIONS UNDER 4

4 A thought is a proposition with a sense.
4.001 The totality of propositions is language.
4.022 Man possesses the ability to construct languages capable of expressing every sense, without having any idea how each word has meaning or what its meaning is - just as people speak without knowing how the individual sounds are produced. It is not humanly possible to gather immediately from it what the logic of language is. Language disguises thought.
4.003 Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language. And it is not surprising that the deepest problems are in fact not problems at all.
4.0031 All philosophy is a 'critique of language'. The apparent logical form of a proposition need not be its real one.
4.01 A proposition is a picture of reality as we imagine it.
4.014 A gramophone record, the musical idea, the written notes, and the sound-waves, all stand to one another in the same internal relation of depicting that holds between language and the world. There is a general rule by means of which the musician can obtain the symphony from the score. That is what constitutes the inner similarity between these things.
4.022 A proposition shows its sense. A proposition shows how things stand if it is true. And it says that they do so stand.
4.024 To understand a proposition means to know what is the case if it is true.
4.05 Reality is compared with propositions.
4.06 A proposition can be true or false only in virtue of being a picture of reality.
4.063 An analogy to illustrate the concept of truth: imagine a black spot on white paper: you can describe the shape of the spot by saying, for each point on the sheet, whether it is black or white. To the fact that a point is black there corresponds a positive fact, and to the fact that a point is white (not black), a negative fact.
4.1 Propositions represent the existence and non-existence of states of affairs.
4.11 The totality of true propositions is the whole of natural science
4.111 Philosophy is not one of the natural sciences.
4.112 Philosophy aims at the logical clarification of thoughts. Philosophy is not a body of doctrine but an activity. A philosophical work consists essentially of elucidations. Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries.
4.1122 Darwin's theory has no more to do with philosophy than any other hypothesis in natural science.
4.113 Philosophy sets limits to the much disputed sphere of natural science.
4.121 Propositions cannot represent logical form: it is mirrored in them.
4.1212 What can be shown, cannot be said.
4.2 The sense of a proposition is its agreement and disagreement with possibilities of existence and non-existence of states of affairs.
4.21 The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.
4.211 It is a sign of a proposition's being elementary that there can be no elementary proposition contradicting it.
4.22 An elementary proposition consists of names. It is a nexus, a concatenation, of names.
4.242 Expressions of the form 'a = b' are, therefore, mere representational devices. They state nothing about the meaning of the signs 'a' and 'b'.
4.243 Can we understand two names without knowing whether they signify the same thing or two different things? - Can we understand a proposition in which two names occur without knowing whether their meaning is the same or different? Suppose I know the meaning of an English word and of a German word that means the same: then it is impossible for me to be unaware that they do mean the same; I must be capable of translating each into the other. Expressions like 'a = a', and those derived from them, are neither elementary propositions nor is there any other way in which they have sense.
4.25 If an elementary proposition is true, the state of affairs exists: if an elementary proposition is false, the state of affairs does not exist.
4.26 If all true elementary propositions are given, the result is a complete description of the world.
4.3 Truth-possibilities of elementary propositions mean Possibilities of existence and non-existence of states of affairs.
4.31 We can represent truth-possibilities by schemata of the following kind ('T' means 'true', 'F' means 'false'; the rows of 'T's' and 'F's' under the row of elementary propositions (pqr, pq, p) symbolize their truth-possibilities in a way that can easily be understood):


4.4 A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions.
4.41 Truth-possibilities of elementary propositions are the conditions of the truth and falsity of propositions.
4.46 Among the possible groups of truth-conditions there are two extreme cases. In one of these cases the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological. In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory. In the first case we call the proposition a tautology; in the second, a contradiction.
4.461 Propositions show what they say; tautologies and contradictions show that they say nothing. (For example, I know nothing about the weather when I know that it is either raining or not raining.)
4.46211 Tautologies and contradictions are not, however, nonsensical. They are part of the symbolism, much as '0' is part of the symbolism of arithmetic.
4.462 Tautologies and contradictions are not pictures of reality. They do not represent any possible situations.
4.464 A tautology's truth is certain, a proposition's possible, a contradiction's impossible.
4.5 The general form of a proposition is: This is how things stand.

PROPOSITIONS UNDER 5

5 A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)
5.1 Truth-functions can be arranged in series. That is the foundation of the theory of probability.
5.101 The truth-functions of a given number of elementary propositions can always be set out in a schema of the following kind:



5.3 All propositions are results of truth-operations on elementary propositions.
5.5 Every truth-function is a result of successive applications to elementary propositions of the operation
5.5571 If I cannot say a priori what elementary propositions there are, then the attempt to do so must lead to obvious nonsense.
5.6 The limits of my language mean the limits of my world.
5.61 We cannot think what we cannot think; so what we cannot think we cannot say either.
5.62 This remark provides the key to the problem, how much truth there is in solipsism. For what the solipsist means is quite correct; only it cannot be said, but makes itself manifest. The world is my world: this is manifest in the fact that the limits of language (of that language which alone I understand) mean the limits of my world.
5.621 The world and life are one.
5.63 I am my world. (The microcosm.)

PROPOSITIONS UNDER 6

6 The general form of a truth-function is (p,ξN(ξ)). This is the general form of a proposition.
6.1 The propositions of logic are tautologies.
6.11 Therefore the propositions of logic say nothing. (They are the analytic propositions.)
6.1251 Hence there can never be surprises in logic.
6.13 Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.
6.2 Mathematics is a logical method. The propositions of mathematics are equations, and therefore pseudo-propositions.
6.21 A proposition of mathematics does not express a thought.
6.211 Indeed in real life a mathematical proposition is never what we want. Rather, we make use of mathematical propositions only in inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics.
6.22 The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.
6.2331 The process of calculating serves to bring about that intuition. Calculation is not an experiment.
6.234 Mathematics is a method of logic.
6.3 The exploration of logic means the exploration of everything that is subject to law. And outside logic everything is accidental.
6.4 All propositions are of equal value.
6.41 The sense of the world must lie outside the world.
6.42 So too it is impossible for there to be propositions of ethics. Propositions can express nothing that is higher.
6.423 It is impossible to speak about the will in so far as it is the subject of ethical attributes. And the will as a phenomenon is of interest only to psychology.
6.43 If the good or bad exercise of the will does alter the world, it can alter only the limits of the world, not the facts - not what can be expressed by means of language. The world of the happy man is a different one from that of the unhappy man.
6.431 At death the world does not alter, but comes to an end.
6.4311 Death is not an event in life: we do not live to experience death.
6.4312 Not only is there no guarantee of the temporal immortality of the human soul but this assumption completely fails to accomplish the purpose for which it has always been intended. Or is some riddle solved by my surviving for ever? Is not this eternal life itself as much of a riddle as our present life? The solution of the riddle of life in space and time lies outside space and time.
6.44 It is not how things are in the world that is mystical, but that it exists.
6.45 To view the world sub specie aeterni ["from the viewpoint of eternity"] is to view it as a whole - a limited whole. Feeling the world as a limited whole - it is this that is mystical.
6.5 When the answer cannot be put into words, neither can the question be put into words. The riddle does not exist. If a question can be framed at all, it is also possible to answer it.
6.51 Scepticism is not irrefutable, but obviously nonsensical, when it tries to raise doubts where no questions can be asked. For doubt can exist only where a question exists, a question only where an answer exists, and an answer only where something can be said.
6.52 We feel that even when all possible scientific questions have been answered, the problems of life remain completely untouched. Of course there are then no questions left, and this itself is the answer.
6.521 The solution of the problem of life is seen in the vanishing of the problem.
6.522 There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical.
6.53 The correct method in philosophy would really be the following: to say nothing except what can be said, i.e., propositions of natural science - i.e., something that has nothing to do with philosophy - and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions.
6.54 My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up it.)

PROPOSITIONS UNDER 7

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