These quotes attack psychologists for failing to find such tests, which would be pointless if Shalizi confidently thought there weren't any:

Since intelligence tests are made to correlate with each other, it follows trivially that there must appear to be a general factor of intelligence. This is true whether or not there really is a single variable which explains test scores or not.

The psychologists start with some traits or phenomena, which seem somehow similar to them, to exhibit a common quality, be it "intelligence" or "neuroticism" or "authoritarianism" or what-have-you. The psychologists make up some tests where a high score seems, to intuition, to go with a high degree of the quality. They will even draw up several such tests, and show that they are all correlated, and extract a common factor from those correlations. So far, so good; or at least, so far, so non-circular. This test or battery of tests might be good for something. But now new tests are validated by showing that they are highly correlated with the common factor, and the validity of g is confirmed by pointing to how well intelligence tests correlate with one another and how much of the inter-test correlations g accounts for. (That is, to the extent construct validity is worried about at all, which, as Borsboom explains, is not as much as it should be. There are better ideas about validity, but they drive us back to problems of causal inference.) By this point, I'd guess it's impossible for something to become accepted as an "intelligence test" if it doesn't correlate well with the Weschler and its kin, no matter how much intelligence, in the ordinary sense, it requires, but, as we saw with the first simulated factor analysis example, that makes it inevitable that the leading factor fits well. [13] This is circular and self-confirming, and the real surprise is that it doesn't work better.