Notes from Tractatus Logico-Philosophicus by Ludwig Wittgenstein

Page 13

The fact that nothing can be deduced from an atomic proposition has interesting applications, for example, to causality. There cannot, in Wittgenstein’s logic, be any such thing as a causal nexus. “The events of the future,” he says, “cannot be inferred from those of the present. Superstition is the belief in the causal nexus.” That the sun will rise to-morrow is a hypothesis. We do not in fact know whether it will rise, since there is no compulsion according to which one thing must happen because another happens.

Page 14

The rejection of identity removes one method of speaking of the totality of things, and it will be found that any other method that may be suggested is equally fallacious: so, at least, Wittgenstein contends and, I think, rightly. This amounts to saying that “object” is a pseudo-concept. To say “x is an object” is to say nothing. It follows from this that we cannot make such statements as “there are more than three objects in the world,” or “there are an infinite number of objects in the world.” Objects can only be mentioned in connexion with some definite property. We can say “there are more than three objects which are human,” or “there are more than three objects which are red,” for in these statements the word object can be replaced by a variable in the language of logic, the variable being one which satisfies in the first case the function “x is human”; in the second the function “x is red.” But when we attempt to say “there are more than three objects,” this substitution of the variable for the word “object” becomes impossible, and the proposition is therefore seen to be meaningless.

Page 15

According to this view we could only say things about the world as a whole if we could get outside the world, if, that is to say, it ceased to be for us the whole world. Our world may be bounded for some superior being who can survey it from above, but for us, however finite it may be, it cannot have a boundary, since it has nothing outside it. Wittgenstein uses, as an analogy, the field of vision. Our field of vision does not, for us, have a visual boundary, just because there is nothing outside it, and in like manner our logical world has no logical boundary because our logic knows of nothing outside it.

Page 24

In order to be a picture a fact must have something in common with what it pictures.

2.161

In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.

2.17

What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.

Page 25

The picture agrees with reality or not; it is right or wrong, true or false.

2.22

The picture represents what it represents, independently of its truth or falsehood, through the form of representation.

2.221

What the picture represents is its sense.

2.222

In the agreement or disagreement of its sense with reality, its truth or falsity consists.

2.21

The picture agrees with reality or not; it is right or wrong, true or false.

2.22

The picture represents what it represents, independently of its truth or falsehood, through the form of representation.

2.221

What the picture represents is its sense.

2.222

In the agreement or disagreement of its sense with reality, its truth or falsity consists.

Page 26

Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is.

Page 27

An expression is thus presented by a variable, whose values are the propositions which contain the expression.

Page 34

Every proposition must already have a sense; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc.

Page 35

Philosophy is not one of the natural sciences.

(The word “philosophy” must mean something which stands above or below, but not beside the natural sciences.)

4.112

The object of philosophy is the logical clarification of thoughts.

Philosophy is not a theory but an activity.

A philosophical work consists essentially of elucidations.

The result of philosophy is not a number of “philosophical propositions”, but to make propositions clear.

Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred.

Page 44

The events of the future cannot be inferred from those of the present.

Superstition is the belief in the causal nexus.

5.1362

The freedom of the will consists in the fact that future actions cannot be known now. We could only know them if causality were an inner necessity, like that of logical deduction.—The connexion of knowledge and what is known is that of logical necessity.

Page 45

Probability is a generalization.

It involves a general description of a propositional form. Only in default of certainty do we need probability.

If we are not completely acquainted with a fact, but know something about its form.

Page 53

Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing.

Page 63

We cannot compare any process with the “passage of time”—there is no such thing—but only with another process (say, with the movement of the chronometer).

Hence the description of the temporal sequence of events is only possible if we support ourselves on another process.

It is exactly analogous for space. When, for example, we say that neither of two events (which mutually exclude one another) can occur, because there is no cause why the one should occur rather than the other, it is really a matter of our being unable to describe one of the two events unless there is some sort of asymmetry. And if there is such an asymmetry, we can regard this as the cause of the occurrence of the one and of the non-occurrence of the other.