"Continuum versus Discrete" Physics: brief note on Endo- and exo-observer of a physical system

We argue about the following concepts:(i)introduction of endo and exo-observer of a physical system (ii) possible relation between endo, exo-observer and continuum/discrete nature of the same system (iii)the distinction about two categories of observers do not help to solve the basic nature(continuum/discrete)of the system considered. We argue that discrete math tool utilized to describe behavior of a physical system is to ascribe to the exo-observer description. In other words, discreteness nature of a system is due at the presence of an external observer description, the observation act. Vice versa, we retain, that endo-observer description give us a continuum nature of the system but only in a Platonic realm. Finally, we retain that a real theory of the state of matter could to build a real independence from the observer. These brief considerations open a discussion on the foundations of discrete math tools and their relation with the observation act, included the possible extension to foundations of the quantum mechanics.