Often that representation involves interpreting some part of that manifold as representing a region of physical spacetime, such as a set of points containing the orbit of Mercury. In general relativity we use Lorentzian manifolds to represent certain aspects of space and time. Thus, for even our best mathematical models, WeatherallвЂ™s dictum can dramatically fail. On the contrary, even our best mathematical models in physics are invariably incomplete, and so typically fail to distinguish between distinct physical situations. And it would mean that the only legitimate way to have a good mathematical representation of is to have one that is an absolutely complete description of the world.

It would prohibit the human activity of freely choosing how mathematical language represents the world. I would like to point out that if WeatherallвЂ™s dictum were strictly enforced, then it would be a crippling limitation on mathematical modelling. But Weatherall goes on to assert that in any legitimate mathematical representation, one must presume that mathematical structures represent a given physical scenario вЂњequally well, for all purposesвЂќ if and only if they are isomorphic, where the standard of isomorphism is the one that is вЂњgivenвЂќ by the standard formulation of a theory.

Earman and norton 1999