If something can't be measured, it becomes just a feel-good label for oneself. Something like the ability to live the "most artistic" life.
What's established is that there's G-factor (unrelated to g-spot), generalized intelligence greatly explaining the random person's capability to do any mental stuff. No, I'm not talking about asylum here.
Now, what kind of metrics and methods of measurement we have? Let's start with the metrics.
Pattern recognition, mathematics, logic, crystallized intelligence (What's the capital of France?), verbal intelligence, spatial intelligence, etc. All of these have a nice G-factor built in, i.e. they're strongly associated with a person being intelligent in general.
What are the methods to do those? We know how the men and women of the world tend to form structures, hierarchies, with other people lifting other to the top, and other people climbing to the top using others as ladders.
Speaking of any intelligence metric, we have the lowly people, barely able to recognize the existence of the thing. Then we have people more adept in it - the people above collectively pick themselves as the ones more able, and the others are left behind. Often the group A below the group B in ability X recognize their inferior ability in the thing too, and recognizes the group B as more able. This is how metrics are formed.
This is how people invent that some logic is better, some mathematics is better, etc. It works. People can actually agree on it to a great degree, except for the points in theory they're unable to handle due to insufficient knowledge or intelligence. But, more intelligent people have put those things in order, too.
Then there's subjects that fail to exhibit much order. Who's got funkiest outfit? Who's style of living is funniest? What's the right way to live? What's good for society? What kinds of dreams should one dream when traveling in a bus?
The society fails to put any kind of good ranking, order if you will, to these kinds of activities. One is not much more better than the other, and doing something a certain way doesn't make one much better in anything, compared to doing it the other way. This is why the said issues fail to be a factor in intelligence, which is adaptive capability to survive, and to make informed decisions in light of new evidence.
I'd like to be told tho, why running 100 meters under 10 seconds is "Physical intelligence", and just not running 100 meters fast.
Then there's the measurement I mentioned. Perhaps I'll save that for another time.