Most scholars of the problem of the incommensurabilty of scientific theories share the following two attitudes:
- the historical cases taken in account are those of the theories extending classical physics; in other terms it is a common opinion that inside classical physics there is no incommensurability problems
- the mathematics concerning physical theories is the rigorous mathematics founded by Cauchy - Weierstrass - Dedekind and furtherly developed in the last century; any other possibility is included in it as a particular improvement.
On the contrary, the following arguments about incommensurability will concern classical physics theories; we will find out a lot of incommensurability problems whose analysis may introduce to study those in modern physics theories. Furthermore, owing to the "Gesthalt phenomenon" elicited by constructive mathematics in the last two decades, we will take in account the several foundations of mathematics (and, in particular, of infinitesimal analysis); they lead us to recognize among the several formulations of a given theory of classical physics some formulations as essentially different. At last we will recognize one more option or basic choice for the foundations of a physical theory, i.e. the kind of organization of the theory itself.
