Nobody denies that psychometric 'g' exists, but there is contention about what it means. There's more than one theory here among psychometricians, including mutualism, or even (as Cosma Shalizi writes) that g is just a statistical artifact (he shows persuasively that any battery of tests you construct with the same structure as IQ tests are going to have some kind of g factor, even if the tests themselves are meaningless).