I was going to add this as a comment to my previous question about type theory, but I felt it probably deserved its own exposition:
If you have a dynamic typing system and you add a “type” member to each object and verify that this “type” is a specific value before executing a function on the object, how is this different than static typing? (Other than the fact that it is run-time instead of compile-time).
static typing happens at compile-time, not at run-time! And that difference is essential!!
See B.Pierce’s book Types and Programming Languages for more.