Psychometric intelligence ("g") is defined correlationally viz. cognitive tasks; that is, the definition is itself a correlation. But it's robust in the sense that it correlates beyond the correlations used in its definition, e.g.: https://www1.udel.edu/educ/gottfredson/reprints/1997whygmatt...
"g" is a measure of narrow set of skills and job performance outcomes that favor western developed society. It's not an observable, it's an inferred value. It makes sense that people good at math and reading are going to perform well in jobs that involve math and reading. And people without access to good schooling or even textbooks are going to have worse performance.
I don't think it's appropriate to measure intelligence as a correlation between the few things a statistician cares about, personally. It would be a naively meritocratic view to think performing well at the highest paying jobs is a decent measure for intelligence.
http://bactra.org/weblog/523.html
I am not sure if my 'g' is high enough that psychologist will allow me to express my opinions on the topic, but I have found the argument in the blog I linked to be quite interesting.
How does one find a definition of intelligence that allows us to correlate it to anything? My understanding is an IQ is defined and intelligence is not.