Will Stokes

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.

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.

2.04 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.

2.06 The existence and non-existence of states of affairs is reality.

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.

2.13 In a picture objects have the elements of the picture corresponding to them.

2.14 What constitutes a picture is that its elements are related to one another in a determinate way.

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.

2.16 If a fact is to be a picture, it must have something in common with what it depicts.

2.17 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.

2.18 What any picture, of whatever form, must have in common with reality, in order to be able to depict it—correctly or incorrectly—in any way at all, is logical form, i.e. the form of reality.

2.19 Logical pictures can depict the world.

2.2 A picture has logico-pictorial form in common with what it depicts.

2.21 A picture agrees with reality or fails to agree; it is correct or incorrect, true or false.

2.22 What a picture represents it represents independently of its truth or falsity, by means of its pictorial form.

2.221 What a picture represents is its sense.

2.222 The agreement or disagreement of its sense with reality constitutes its truth or falsity.

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.

3 A logical picture of facts is a thought.

3.01 The totality of true thoughts is a picture of the world.

3.02 A thought contains the possibility of the situation of which it is the thought. What is thinkable is possible too.

3.03 Thought can never be of anything illogical, since, if it were, we should have to think illogically.

3.04 If a thought were correct a priori, it would be a thought whose possibility ensured its truth.

3.05 A priori knowledge that a thought was true would be possible only if its truth were recognizable from the thought itself (without anything to compare it with).

3.1 In a proposition a thought finds an expression that can be perceived by the senses.

3.11 We use the perceptible sign of a proposition (spoken or written, etc.) as a projection of a possible situation.

3.12 A sign is what can be perceived of a symbol.

3.13 A proposition belongs all that belongs to the projection; but not what is projected.

3.14 What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another.

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.

3.21 The configuration of objects in a situation corresponds to the configuration of simple signs in the propositional sign.

3.22 In a proposition a name is the representative of an object.

3.23 The requirement that simple signs be possible is the requirement that sense be determinate.

3.24 A proposition about a complex stands in an internal relation to a proposition about a constituent of the complex.

3.25 A proposition has one and only one complete analysis.

3.26 A name cannot be dissected any further by means of a definition: it is a primitive sign.

3.3 Only propositions have sense; only in the nexus of a proposition does a name have meaning.

3.31 I call any part of a proposition that characterizes its sense an expression (or a symbol).

3.32 A sign is what can be perceived of a symbol.

3.33 In logical syntax the meaning of a sign should never play a role. It must be possible to establish logical syntax without mentioning the meaning of a sign: only the description of expressions may be presupposed.

3.34 A proposition possesses essential and accidental features.

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.

3.41 The propositional sign with logical coordinates—that is the logical place.

3.42 A proposition can determine only one place in logical space: nevertheless the whole of logical space must already be given by it.

4 A thought is a proposition with a sense.

4.01 A proposition is a picture of reality.

4.02 We can see this from the fact that we understand the sense of a propositional sign without its having been explained to us.

4.03 A proposition must use old expressions to communicate a new sense.

4.04 In a proposition there must be exactly as many distinguishable parts as in the situation that it represents.

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.

4.1 Propositions represent the existence and non-existence of states of affairs.

4.11 The totality of true propositions is the whole of natural science (or the whole corpus of the natural sciences).

4.12 Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it—logical form.

5 A proposition is a truth-function of elementary propositions.

5.01 Elementary propositions are the truth-arguments of propositions.

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

6.1 The propositions of logic are tautologies.

6.11 Therefore the propositions of logic say nothing. (They are the analytic propositions.)

6.12 The fact that the propositions of logic are tautologies shows the formal—logical—properties of language and the world.

6.2 Mathematics is a logical method.

6.21 A proposition of mathematics does not express a thought.

6.22 The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.

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. In the world everything is as it is, and everything happens as it does happen: in it no value exists—and if it did exist, it would have no value.

6.42 So too it is impossible for there to be propositions of ethics.

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.

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 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.

6.51 Scepticism is not irrefutable, but obviously nonsensical, when it tries to raise doubts where no questions can be asked.

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.

6.53 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 serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)

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