I am trying to understand a bit more about the mechanics of the definite article. Normally, we are taught that "the" picks out the object with certain properties or is used when we want to refer to a unique thing.
Examples of the first: The big book, the tall man etc
Example of the second: The Bible, The Earth's moon
It seems to me that this example of the first type are actually like that of second type but with restricted domain of discourse. For instance, if we consider all the people "who look tall" in the world, "the tall man" may not tell us much, and, if we consider "the tall man" in the set of men who are tall(*), it tells us nothing, however, if we have a set of people, with one outstandingly greater in height than others, than "the tall man" does achieve the second purpose once we restrict the domain of discourse (in sense of Boole).
So, my question, is there a name for this phenomena where we implicitly constrict the domain of discourse in usage of definite articles?
Or, is there a totally different conceptual starting point to understand this phenomena from?
*: It doesn't even make grammatic sense since the set of men who are tall is many in number