An interesting phenomenon I've noticed recently is that sometimes words do have short exact definitions that exactly coincide with common usage and intuition. For example, after Gettier scenarios ruined the definition of knowledge as "Justified true belief", philosophers found a new definition:

"A belief in X is knowledge if one would always have that belief whenever X, and never have it whenever not-X".

(where "always" and "never" are defined to be some appropriate significance level)

Now it seems to me that this definition completely nails it. There's not one scenario I can find where this definition doesn't return the correct answer. (EDIT: Wrong! See great-grandchild by Tyrrell McAllister) I now feel very silly for saying things like "'Knowledge' is a fuzzy concept, hard to carve out of thingspace, there's is always going to be some scenario that breaks your definition." It turns out that it had a nice definition all along.

It seems like there is a reason why words tend to have short definitions: the brain can only run short algorithms to determine whether an instance falls into the category or not. All you've got to do to write the definition is to find this algorithm.