Tractatus Logico-Philosophicus

by Ludwig Wittgenstein

Here it becomes clear that there are no such things as “logical objects” or “logical constants” (in the sense of Frege and Russell).

That however is the general form of proposition. 5.471 The general form of proposition is the essence of proposition.

We cannot give a sign the wrong sense. 5.47321 Occam’s razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that unnecessary elements in a symbolism mean nothing.

p” is true if “p” is false. Therefore in the true proposition “~p” “p” is a false proposition. How then can the stroke “~” bring it into agreement with reality? That which denies in “~p” is however not “~”, but that which all signs of this notation, which deny p, have in common.

This is the place to solve all the problems which arise through Russell’s “Axiom of Infinity”. What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings.

The limits of my language mean the limits of my world.

What we cannot think, that we cannot think: we cannot therefore say what we cannot think.

Where in the world is a metaphysical subject to be noted?

Here we see that solipsism strictly carried out coincides with pure realism. The I in solipsism shrinks to an extensionless point and there remains the reality co-ordinated with it.

The theory of classes is altogether superfluous in mathematics.

This method could be called a zero-method.

The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations.

The method by which mathematics arrives at its equations is the method of substitution.

Logical research means the investigation of all regularity.

A right-hand glove could be put on a left hand if it could be turned round in four-dimensional space.

That the sun will rise to-morrow, is an hypothesis; and that means that we do not know whether it will rise.

So people stop short at natural laws as at something unassailable, as did the ancients at God and Fate. And they both are right and wrong. But the ancients were clearer,

Even if everything we wished were to happen, this would only be, so to speak, a favour of fate, for there is no logical connexion between will and world, which would guarantee this, and the

Let us consider how this contradiction presents itself in physics. Somewhat as follows: That a particle cannot at the same time have two velocities, i.e. that at the same time it cannot be in two places, i.e. that particles in different places at the same time cannot be identical.

The sense of the world must lie outside the world. In the world everything is as it is and happens as it does happen. In it there is no value—and if there were, it would be of no value.

Hence also there can be no ethical propositions. Propositions cannot express anything higher.

It is clear that ethics cannot be expressed. Ethics are transcendental. (Ethics and æsthetics are one.)

The first thought in setting up an ethical law of the form “thou shalt . . . ” is: And what if I do not do it.

There must be some sort of ethical reward and ethical punishment, but this must lie in the action itself.

Of the will as the bearer of the ethical we cannot speak. And the will as a phenomenon is only of interest to psychology.

If good or bad willing changes the world, it can only change the limits of the world, not the facts; not the things that can be expressed in language.

Death is not an event of life. Death is not lived through.

If by eternity is understood not endless temporal duration but timelessness, then he lives eternally who lives in the present.

The temporal immortality of the soul of man, that is to say, its eternal survival also after death, is not only in no way guaranteed, but this assumption in the first place will not do for us what we always tried to make it do. Is a riddle solved by the fact that I survive for ever? Is this eternal life not as enigmatic as our present one? The solution of the riddle of life in space and time lies outside space and time.

Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked.

We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer.

The solution of the problem of life is seen in the vanishing of this problem.

6.53 The right method of philosophy would be this. To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other—he would not have the feeling that we were teaching him philosophy—but it would be the only strictly correct method.

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 on it.) He must surmount these propositions; then he sees the world rightly. 7 Whereof one cannot speak, thereof one must be silent.