Laws, like the law of causation, etc., treat of the network and not what the network describes.
If there were a law of causality, it might run: “There are natural laws.”
But that can clearly not be said: it shows itself.
In the terminology of Hertz we might say: Only uniform connections are thinkable.
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.
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.
What can be described can happen too, and what is excluded by the law of causality cannot be described.
The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience.
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.
That the sun will rise tomorrow, is an hypothesis; and that means that we do not know whether it will rise.
A necessity for one thing to happen because another has happened does not exist. There is only logical necessity.
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.
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.
The world is independent of my will.
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.
As there is only a logical necessity, so there is only a logical impossibility.
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.
All propositions are of equal value.