People love talking about intelligence but I'm yet to see a measurable definition. The best anyone can manage is "you know it when you see it" (like porn). Am I missing something or is this all just a dark road to an unknown destination (possibly just a dead end?)
The value of definability is moot at best imho. "Mathematics" is also not easy to define, there are volumes philosophers of mathematics discussing this, some even say "mathematics is what mathematicians find interesting" (similar to your porn example) but this doesn't stop us from studying mathematics. Same goes for science e.g.. People like Popper or Kuhn spent a lot of mental cycles arguing what is and what is not…
I'm quite fond of a terrible mathematical joke which this reminded me of.
"I'm worried about my nephew, I was trying to teach him to add numbers, but he can't even pronounce zermelo fraenkel set theory, how's he ever going to learn it?!"