6.341 Newtonian mechanics, e.g., brings the description of the world to a unified form. Let us think of a white surface with irregular black spots on it. Now we say: Whatever kind of picture these spots produce, I can always describe it as closely as you like by covering the spots with a suitably fine square netting and now say of every square that it is white or black. In this way, I will have brought the description of the spots to a unified form. This form is arbitrary, since I could have used with the same success a net with triangular or hexagonal holes. It is possible that the description would have been simpler with the help of a triangular net; meaning that we could have described the spots more closely with a bigger triangular net than with a finer square one (or vice versa), and so on. Different systems of world description correspond to different nets. Mechanics defines a form of world description by saying: All propositions of the description of the world must be obtained from a number of given propositions – the axioms of mechanics – in a given way. In this way it supplies the building stones for the construction of the scientific edifice and says: Whatever edifice you want to build, you must somehow put together with these and only these building stones.
(With the system of mechanics, one must be able to write down any arbitrary proposition of physics, as one can [write down] any arbitrary number with the number system.)
A priori axioms are normative, then, and might make our lives easier or harder, but they cannot make them possible or impossible. Nor can they tell us anything synthetic.