"Counting can be exact?"
Yes. It *can* be. Some people would say that it *must* be. AND that what astronomers do when "counting" galaxies is actually "estimating." In either case, it at least *can* be exact as when I count the number of people in a room or the number of marbles in a sack.

baggage = assumptions about what a thing is or what properties it manifests that aren't explicit in the revised definition. These assumptions are due to the natural tendency of a person to conflate the properties of things that are similarly named. You do this when, for example, you think of the universe as everything and then use it only to describe those things which are desirable.