Either way, what you’re committed to is that there really isn’t any biological g. I think the comparison with immunity is quite apt: there isn’t a general factor of immunity, and I don’t think anyone believes such a notion is scientifically useful. That’s really the essence of the issue. Of course you’re free to talk about g as a shorthand for “all of the many and complicated factors that determine individual differences in intelligence”, but it’s not like it’s doing any scientific work for you, and in fact it’s going to mislead you if you think you’re going to find isomorphic neural correlates of g.

Incidentally, if you roll a die 1,000 times, it’s true you’ll end up with a mean of 3,500, but the distribution around that will be completely normal (by the central limit theorem). The thing to keep in mind is that, if the entire human race (or everyone but people with major deficits) falls between 3,300 and 3,700, someone who’s at 3700 is going to seem superhuman to you. You shouldn’t really expect anyone to be able to, say, run as fast as a cheetah; the distribution of abilities, and what defines high and low performance, is surely going to be relative to the norm. So I don’t really see this as as problem. Though I do agree that the you’re going to have a disproportionate number of people at the low end with very low performance (e.g., due to cerebellar damage), and possibly also at the high end due to interactions between different mechanisms.

Take the athleticism example, because it is more intuitive. You say that:

Imagine that instead of studying the relationship between different cognitive tasks, we decided to study the relation between performance at different sports. So we went out and rounded up 500 healthy young adults and had them engage in 16 different sports, including basketball, soccer, hockey, long-distance running, short-distance running, swimming, and so on. We then took performance scores for all 16 tasks and submitted them to a PCA. What do you think would happen? I’d be willing to bet good money that you’d get a strong first factor, just like with cognitive tasks.

I agree. But surely that tells us something about the structure of the “dozens if not hundreds of factors that should contribute a small amount of the variance to performance on multiple sports”. Because if there really were hundreds of different factors, which were not correlated with each other, and which contribute to athleticism in an additive way, everyone would be average at sports. If you roll a thousand 6 sided dice, you will almost always get a total of 3,500+- not much.

Yet in fact there are people who are just crap at sports and often there is a clear reason why. For example, if someone suffers a major cerebellar lesion, they will lose all coordination; you could be really strong and fast and have great eyesight but if you have a cerebellar lesion you will be crap at sports.

Now of course cerebellar integrity is not the only determinant of athletic ability, but it is a necessary component of it. So instead of hundreds of uncorrelated factors acting in an additive way, what we actually have are (say) hundreds of uncorrelated factors acting in a more complex way. Like a conveyor belt that makes a product: if one stage is broken, the final product will be broken even if the rest of the factory is working fine. So a simple but workable model would be to say that your overall athleticism is given by the single worst component of your “athleticism pathway”.

But if that’s the case, athleticism is a “real thing”; at least, it is as real as say “immune function”. People can have poor immune function for numerous reasons e.g. HIV, radiation exposure, genetic illnesses, but all of the causes impact the same pathway which is biologically real thing, not just a collection of hundreds of non-interacting bits. Now this doesn’t mean it would necessarily be useful to talk about i the general factor of immunity, but I think it would be more useful than Cosmo’s analysis (which relies on things being simply additive) would suggest… maybe.