It is exactly that: think of it as the first principal component, of some group of tests. Obviously this always exists. The argument is really about how big th

It is exactly that: think of it as the first principal component, of some group of tests. Obviously this always exists. The argument is really about how big the 2nd component is -- if it were comparable, then talking about the 1st alone would be very misleading. And for a typical bundle of school-like topics (like math/english/biology exams) it's quite a long way down: IIRC a factor of 3 or 4? If the bundle of subjects is different, then the size and meaning of the components will vary. In the tests the army does to slot recruits into all sorts of roles, I think manual dexterity is one of the things they care about which is almost uncorrelated with g. Eyesight is I think one of the only things negatively correlated with g (and it's thought to be nurture: bookish kids spend too little time outdoors).