6.361
In the terminology of Hertz we might say: Only uniform connections are thinkable.
6.3611
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 nonoccurrence of the other.
6.36111
The Kantian problem of the right and left hand which cannot be made to cover one another already exists in the plane, and even in one-dimensional space; where the two congruent figures a and b cannot be made to cover one another without
moving them out of this space. The right and left hand are in fact completely congruent. And the fact that they cannot be made to cover one another has nothing to do with it.
A right-hand glove could be put on a left hand if it could be turned round in four-dimensional space.
6.362
What can be described can happen too, and what is excluded by the law of causality cannot be described.
6.363
The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience.
6.3631
This process, however, has no logical foundation but only a psychological one. It is clear that there are no grounds for believing that the simplest course of events will really happen.
6.36311
That the sun will rise tomorrow, is an hypothesis; and that means that we do not know whether it will rise.
6.37
A necessity for one thing to happen because another has happened does not exist. There is only logical necessity.
6.371
At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena.
6.372
So people stop short at natural laws as something unassailable, as did the ancients at God and Fate.
And they are both right and wrong. But the ancients were clearer, in so far as they recognized one clear terminus, whereas the modern system makes it appear as though everything were explained.
6.373
The world is independent of my will.
6.374
Even if everything we wished were to happen, this would only be, so to speak, a favour of fate, for there is no logical connection between will and world, which would guarantee this, and the assumed physical connection itself we could not again will.
6.375
As there is only a logical necessity, so there is only a logical impossibility.
6.3751
For two colours, e.g. to be at one place in the visual field, is impossible, logically impossible, for it is excluded by the logical structure of colour.
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.
It is clear that the logical product of two elementary propositions can neither be a tautology nor a contradiction. The assertion that a point in the visual field has two different colours at the same time, is a contradiction.
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 happens as it does happen. In it there is no value—and if there were, it would be of no value.
If there is a value which is of value, it must lie outside all happening and being-so. For all happening and being-so is accidental.
What makes it non-accidental cannot lie in the world, for otherwise this would again be accidental.
It must lie outside the world.
6.42
Hence also there can be no ethical propositions.
Propositions cannot express anything higher.
6.421
It is clear that ethics cannot be expressed.
Ethics is transcendental.
(Ethics and aesthetics are one.)
6.422
The first thought in setting up an ethical law of the form “thou shalt …” is: And what if I do not do it? But it is clear that ethics has nothing to do with punishment and reward in the ordinary sense. This question as to the consequences of an action must therefore be irrelevant. At least these consequences will not be events. For there must be something right in that formulation of the question. There must be some sort of ethical reward and ethical punishment, but this must lie in the action itself.
(And this is clear also that the reward must be something acceptable, and the punishment something unacceptable.)
6.423
Of the will as the subject of the ethical we cannot speak.
And the will as a phenomenon is only of interest to psychology.
6.43
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.
In brief, the world must thereby become quite another, it must so to speak wax or wane as a whole.
The world of the happy is quite another than that of the unhappy.
6.431
As in death, too, the world does not change, but ceases.
