Wittgenstein,

From Tractatus Logico-Philosophicus

From the Introduction:

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.

From the Text:

1. The world is everything that is the case.

1.1 The world is the totality of facts, not of things.

1.2 The world divides into facts.

2. What is the case, a fact, is the existence of atomic facts (states of affairs).

2.01 A state of affairs 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 (positive facts) and non-existence (negative facts) of states of affairs is reality.

2.1 We make to ourselves pictures of facts. (We picture facts to ourselves.)

2.2 The picture has the logical (logico-pictorial) form of representation in common with what it pictures (depicts).

3. A logical picture of facts is a thought.

3.1 In the proposition the thought is expressed perceptibly through the

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

3.2 In propositions thoughts can be so expressed that to the objects of the

thoughts correspond the elements of the propositional sign.

3.3 Only the proposition has sense; only in the context of a proposition has a

name meaning.

3.4 A proposition determines a place in logical space. The existence of that place is

guaranteed by the mere existence of the constituents—by the existence of the proposition.

3.5 The applied, thought, propositional sign is the thought. (A propositional sign, applied and

thought out, is a hought.

4. A thought is a proposition with a sense.

4.003-4.0031: [Most philosophical propositions are nonsensical. We cannot answer such questions, we can only point out that they are nonsense. The deepest problems are not really problems. Philosophy is a “critique of language”. Apparent logical form need not be the real logical form (as shown by Russell).]

4.01 A proposition is a picture (model) of reality.

4.014: [The written notes of a musical score and the sound waves

stand in the same internal relation of depiction that holds between language and the world.]

4.0141: [There is a general rule by means of which the

musician obtains the symphony from the score. That rule is what constitutes the inner similarity between these things.]

4.022 [A proposition shows its sense (i.e., how things stand if it is

true), and says that things do so stand.]

4.1 A proposition presents the existence and non-existence of atomic facts. (Propositions represent the existence and non-existence of states of affairs.)

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 proposition, the elementary proposition, asserts the

existence of an atomic fact.

4.3 Truth possibilities of elementary propositions mean possibilities of existence and non-existence of states of affairs.

4.4 A proposition is an expression of agreement and disagreement with truth possibilities of elementary propositions.

4.46 Among the possible groups of truth-conditions there are two extreme

cases.

In the one case the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth 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 self-contradictory.

4.5 …The general form of a proposition is: This is how things stand.

5. Propositions are truth-functions of elementary propositions.

5.1 Truth functions can be arranged in a series.

5.2 The structure of propositions stand in internal relations to one another.

5.3 All propositions are the result of truth-operations on elementary propositions.

5.4 There are no ‘logical objects’ or ‘logical constants’.

5.5 Every truth-function is a result of successive applications to elementary propositions of the operation ‘ (…..T)(x….)’

5.6 The limits of my language are the limits of my world.

6. The general form of a truth-function is: [p, x, N(x )]

6.1 The propositions of logic are tautologies.

6.2 Mathematics is a logical method. The propositions of mathematics

are equations, and therefore pseudo-propositions.

6.3 Exploration of logic means the exploration of everything that is subject to law—outside

of logic everything is accidental.

6.4 All propositions are of equal value.

6.41 [The sense and value of the world must lie outside the world.]

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

6.423 It is impossible to speak about the will insofar as it is the subject of ethical attributes

6.43 If the good or bad exercise of the will alters the world, it can only alter 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 an answer cannot be put into words, neither can the question—riddle does not

exist.

6.51 Skepticism is not irrefutable, but obviously nonsensical, when it tries to raise

doubts where no questions can be asked. For doubt can only exist 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.

6.53 The correct method of philosophy would really be the following: to say nothing except what can be said—i.e., propositions of natural science—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 to climb up beyond them.

7. Whereof one cannot speak, thereof one must be silent.