> Sorry, what exactly do you mean by "is representative of general intelligence"? This is a very abstract statement.

No need to apologize. Perhaps my g is too low to describe my thoughts properly.

> "is representative of general intelligence"?

This factor that is derived from the positive correlations, g, is called general intelligence. So, g is nominally general intelligence, but is g actually what the name implies? One can take n number of positively correlated but independent things, and there will always be a some factor that can be derived from it. However, that does not mean the underlying factor is necessarily causal.

> This is a very abstract statement.

We are discussing abstract concepts.

> What does this mean in scientific, empirical terms?

That causality would be scientifically and empirically verifiable.

> What kind of facts we would observe in the world where this is true? What empirical observations we'd make in the world where it's false?

Alas, that is precisely the point I was trying to paraphrase from Shalizi. Whether g be true or false -- the result wouldn't look any different. The methodology being used cannot determine what is true nor false, and that is the crux of this entire problem.