Why there is no concept of “const-correctness” for class's static member functions?

Question

Use case:

class A {
  static int s_common;
public:
  static int getCommon () const { s_common; };
};

Typically this results in an error as:

Answer 1

cv-qualifiers affect the function's signature. So you could have:

class A {
  static int s_common;
public:
  static void getCommon () const {  };
  static void getCommon () {  };
};

Now... how would you call the const one? There's no const object to call it on (well, you could call it on a const object, but that's not the point).

I'm just guessing here, there probably are other reasons. :)