Books on Amazon
A theoretical fact has nothing indefinite, nothing fluctuating. The body being studied is geometrically defined. Its edges are real lines, without thickness, its corners are real points without dimensions.
Each point of a body corresponds to a temperature, and this temperature is, for each point, a number which is sharply distinguished from every other.
This theoretical fact is opposed to the practical fact which is the translation of it. There is nothing more to see of precision here.
The body is no longer a geometric one, but a concrete block, its edges jagged ridges, its points more or less broad, its temperature a medium one in a certain volume. It is also not that definite number, distinctly distinguished from any other number.
Nor could we explain that the temperature is exactly 10°, but only that it does not exceed a certain fraction of the degree which depends on the accuracy of the instrument.
An infinite number of different theoretical facts can serve as a translation of the same practical fact.
A law of the ordinary mind is a simple general judgment that is right or wrong. E.g. the sun rises every day in the east. Here we have a real law, without condition, without restriction. On the other hand, e.g. the moon is always full. Here we have a wrong law.
This does not apply to physical laws; they are always symbolic. A symbol is not correct or wrong, but more or less well chosen. The logician would not understand if one asked whether a certain physical law is right or wrong.
The degree of indeterminacy of the symbol is the error limit of the law in question. > Indeterminacy.
For the physicist, the discovery of the law of analogous facts means the discovery of a formula containing the symbolic representation of each of these facts. The indeterminacy of the symbols involves the indeterminacy of the formula.
Each of these laws, in order to be accepted, must not correspond to any fact, not the symbol, but any of the symbols from the infinite number which can represent this fact. This is what is meant when one explains that the laws of physics are only approximated.
E.g. Let us imagine that we cannot be content with the law: "The sun is rising in the east": the sun will be replaced by a huge sphere despite its unevenness.
If we want to find the law of motion of the sun, we can apply not only a single formula, but an infinite number of different formulas, to represent a change in length as a function of time. All these laws are equally acceptable to the physicist. The motives by which he chooses between different possibilities are not the same, which force him to prefer truth over error.
Ziel und Struktur der physikalischen Theorien Hamburg 1998