Lets do this example in Java (but it should be simple enough that C#, Python, Javascript and other programmers would understand it).

    public void myFunction(FooObject o){
        o.doSomething();
    }

How does the compiler know if "FooObject o" is a singleton or not? That's the thing about the "Singleton" pattern, you have an effective "global-ish" variable, but all of your code is written with normal pass-the-object style.

EDIT: If you're not aware, the way this works is that you call myFunction(getTheSingleton());, where "getTheSingleton()" fetches the Singleton object. myFunction() has no way of "knowing" its actually interacting with the singleton. This is a useful pattern, because you can create unit-tests over the "global" variable by simply mocking out the Singleton for a mock object (or maybe an object with preset state for better unit testing). Among other benefits (but also similar downsides to using a global variable: difficult to reason because you have this "shared state" being used all over the place)