The problem isn't that we can't define intelligence, the problem (IMHO) is that people aren't comfortable of the implications of any given definition.
I like to play a game whenever I meet a new group of programmers/lawyers/board gamers/pedants. I ask them to define a sandwich, then I point out all of the edge cases until we get to the point where I can either say their definition is bad because it e.g. doesn't include subs (short for submarine sandwiches), or I can say that poptarts are sandwiches.
The problem is that reality is blurry and clear definitions are fundamentally incapable of capturing the nuance there.