The relative position of logic and science.

That an image can be described using a grid with a given form tells us nothing about the image. (A grid works for all such images.) But what does characterize the image is that it can be completely described by a particular grid with a particular mesh size. So too, it tells us nothing about the world that it can be described by Newtonian mechanics or whatever. That it can be described at all, and in a particular way, does tell us something indeed. That one method of theoretical description is simpler than another also tells us something about the world.

Theoretical physics is an attempt to construct all the true propositions that we need to describe the world using a single plan. Throughout their whole logical apparatus, the laws of physics still speak about the objects of the world. We ought not forget that any theoretical description of the world will always be completely general. In mechanics, for example, one never speaks of particular point-masses, but only about any whatsoever.

Although the spots in our image are geometrical figures, it is obvious that geometry can say nothing at all about their actual form and position. The grid, however, is purely geometrical; all its properties can be given a priori. Laws like the principle of sufficient reason, etc. deal with the grid and not with what the grid describes.

If there were a law of causality, one might state it as: "There are laws of nature." But of course that cannot be said: it can be seen. Using Hertz's terminology, one might say: "Only regular correlations are thinkable. Hence the only way we can describe the lapse of time is to rely on some process such as the movement of a chronometer."

Something entirely analogous applies to space. Wherever one says that neither of two exclusive events can occur because there is no reason one should occur rather than the other, one is really dealing with the fact that one cannot describe either without some sort of asymmetry between them. And if such an asymmetry is found, we can regard it as the cause that made one occur and not the other.

Kant's problem about the right hand and the left hand, which cannot be made to coincide, exists already in two dimensions; indeed, even in one-dimensional space. The two congruent figures, a and b, cannot be made to coincide unless they are moved out of this space.


The right hand and the left hand are in fact completely congruent. It is quite irrelevant that they cannot be made to coincide. A right-hand glove could be put on the left hand, if it could be turned round in four-dimensional space.

The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences. But this procedure has no logical, only a psychological, justification. There is no reason to believe that the simplest case will in fact be realized. That the sun will rise tomorrow is a hypothesis; we do not know whether it will rise. There is nothing to compel one thing to happen because something else has. There is only logical necessity.

The whole modernist world view is based on the illusion that the laws of nature actually explain natural phenomena. Thus they stand before the laws of nature as something inviolable, just as the ancients did before God and Fate. Both, in fact, are both right and wrong. Nevertheless, the view of the ancients is clearer in so far as they acknowledge it as closure, while the modern system tries to make it seem as if everything were explained.