A good test of whether someone understands g is if they characterise it as a general factor in intelligence test scores and not as general intelligence (i.e., a substantive rather than statistical construct). But it’s interesting to see what Spearman originally said in his 1904 “General Intelligence,” Objectively Determined and Measured. On p. 272:
“… we reach the profoundly important conclusion that there really exists a something that we may provisionally term “General Sensory Discrimination” and similarly a “General Intelligence,” and further that the functional correspondence between these two is not appreciably less than absolute.”
He goes on to describe this as a “general theorem”, refining it to (p. 273):
“Whenever branches of intellectual activity are at all dissimilar, then their correlations with one another appear wholly due to their being all variously saturated with some common fundamental Function (or group of Functions).”
(Enthusiastic emphasis in original.)
There’s a recent argument against this (though perhaps not quite, given Spearman’s parenthetical “group of Functions”), by van der Maas, et al. (2006). The abstract:
“Scores on cognitive tasks used in intelligence tests correlate positively with each other, i.e., they display a positive manifold of correlations. The positive manifold is often explained by positing a dominant latent variable, the g-factor, associated with a single quantitative cognitive or biological process or capacity. In this paper we propose a new explanation of the positive manifold based on a dynamical model, in which reciprocal causation or mutualism plays a central role. It is shown that the positive manifold emerges purely by positive beneficial interactions between cognitive processes during development. A single underlying g-factor plays no role in the model. The model offers explanations of important findings in intelligence research, such as the hierarchical factor structure of intelligence, the low predictability of intelligence from early childhood performance, the integration/differentiation effect, the increase in heritability of g, the Jensen effect, and is consistent with current explanations of the Flynn effect.”