Proponents of g don't claim that it's an alternative to domain-specific abilities. They claim that it exists in addition to domain-specific abilities, and is w

Proponents of g don't claim that it's an alternative to domain-specific abilities. They claim that it exists in addition to domain-specific abilities, and is what explains the correlation between performance across domains. That is, people who do well on mathematical tests also tend do well on tests of verbal ability. The factor analytic model that yields g attempts to explain this by viewing mathematical ability as the combination of two factors: a domain-specific mathematical intelligence and a domain-agnostic general intelligence. A subject's performance on verbal tests would similarly be modeled as the product of their g and of a cognitive ability specific to verbal tasks. That a subject's performance on one type of test is partially predictive of their performance on the other type is then (according to this model) explained by the two cases sharing a single partial cause, g.