One can take n number of positively correlated but independent things, and there will always be a some factor that can be derived from it.

I hope you understand that your vague question cannot be seen as equivalent to this rather more concrete statement. That’s why I asked for clarification, and your patronizing comments were really not called for.

In any case, Shalizi is very wrong, probably because he is entirely unfamiliar with the literature. He is wrong on multiple accounts.

First, yes, any number positively correlated measurements will yield a common factor. However, when talking about g, this is not an artifact of how we constructed IQ tests. Shalizi says:

What psychologists sometimes call the “positive manifold” condition is enough, in and of itself, to guarantee that there will appear to be a general factor. Since intelligence tests are made to correlate with each other, it follows trivially that there must appear to be a general factor of intelligence.

But this is just not true. Tests are not made to correlated with each other. Any time anyone attempts to construct a test of general mental ability, we always find the same g factor, even if they explicitly attempt to make a battery that tries to measure distinct, uncorrelated mental aptitudes. Observe how Shalizi fails to provide a single example of a test that does not exhibit the positive manifold with other tests.

Second, unlike Shalizi, we know that g is the predictive component of the IQ tests. IQ predicts real world outcomes very well, but what is really interesting is that the predictive power of individual subtests of an IQ test is practically perfectly correlated with g-loadings of the subtest. This would be very surprising if g was just a statistical artifact.

Shalizi says

So far as I can tell, however, nobody has presented a case for g apart from thoroughly invalid arguments from factor analysis; that is, the myth.

But this is just baffling if you have any familiarity with the literature.

Whether g be true or false -- the result wouldn't look any different. The methodology being used cannot determine what is true nor false, and that is the crux of this entire problem.

That’s just not true. For example, if g was a statistical artifact, one of the hundreds of intelligence tests devised would have not exhibited the positive manifold with all the others. It would not be correlated with heritability. It would not be correlated with phenotype features like reaction time. The world where g is a statistical artifact looks much different than our world.