> But they'll often be close enough or even equivalent mathematically

Who is babbling? The number of concepts in human language that have no mathematical formalization far outnumber the ones that do, lol.

Yes, we can, obviously, come up with shared, mathematically precise definitions for certain concepts. Keep in mind that:

A. These formal or scientific definitions are not the full exhaustion of the concept. Linguistic usage is varied and wide. Anyone who has bothered to open an introductory linguistics textbook understands this.

B. The scientific and mathematical definitions still change over time and can also change across cultures and contexts.

I can assure you that someone who has scored very high on an IQ test would not be considered "intelligent" in a group of film snobs if they were not aware of the history of film, up to date on the latest greats, etc. etc. These people would probably use the word intelligent to describe what they mean (knowledge of film) and not the precise technical definition we've come up with, if any, whether you like it or not.

My point is not that it is impossible to come up with definitions, my point is that for socially fluid concepts like intelligence, which are highly dependent on the needs and circumstances of the people employing the word, we will likely never pin it down. There is an asterisk on every use of the word. This is the case with basically every word to more or lesser degree, that's why language and ideas evolve in the first place.

My whole point is that people that don't realize this and put faith in IQ as though it is some absolute, or final, indicator of intelligence are dumb and probably just egotists who are uncomfortable with uncertainty and want reassurance that they are smart so that they can tell other people they are "babbling" and feel good about themselves and their intellectual superiority complex (read: self justified pride in being an asshole).

My claim is that this high variability and contextual sensitivity is a core part of this word and the way we use it. That's what I mean when I say I don't think we'll ever have a good definition.

EDIT: Or, to make it a little easier to understand. We will never have a universal definition of "moral good" because it is dependent on value claims, people will argue morality forever. My position is that "intelligence" is equally dependent on value claims which I think anyone who has spent more than five minutes with people not like themselves or trained in different forms of knowledge intuitively understands this.