It's an interesting and very common form of an entirely irrational argument. (Hypothetical) absence of a better test in no way implies that it is a good enough test for a select purpose. Especially when no one really tried to quantify the error you might get.
I prefer quantitative arguments to qualitative arguments; relatedly, I prefer certainty as a number to certainty as a word. I think it's better to make the most of mediocre data (and figure out which additional data is highest EV) than to throw out the best data available.
It is not true that people haven't tried to quantify the error they might get; this is actually a major concern of psychometricians. They've figured out several ways that a test can go wrong, and have come up with quantitative measures on how much those seem to have happened. For example, a problem with WWI-era IQ tests was that the modal number of correct questions was 0, which suggests that a large number of test-takers did not understand the instructions, which dropped the uncorrected mean significantly. Now they look for this problem.
For example, here's a paper about Raven's in Africa, which goes through the various ways that Raven's could underestimate African intelligence. It's full of quantative statements like "the correlation with other intellectual tests is generally about .6 in Western studies, but is .33 in African studies, suggesting it is less g-loaded for Africans."*
If you wanted, you could figure out what an individual Raven's score of 80 implies for any other cognitive test in Westerners and Africans respectively. Like any Bayesian exercise, this relies pretty heavily on the priors you choose: if you assume the score is accurate but not precise, then you have a mean centered on 80 but a difference variance for the two groups, with a larger African variance because your test is less precise. If you assume both groups have the Western mean, then the regression to the mean (i.e. upwards) is higher for the African than the Westerner, again because the test was less precise.
*I should point out that there are other, competing interpretations of this finding, and it seems that the correlation is lower for the more rural and less educated, suggesting the left half of Fig 4 is due to culture. But from the studies on the right half of Fig 4, we would end up with an estimate for African intelligence given Western culture that's about 80-85, which is a bit lower than African American intelligence.
I said, "doesn't do much arithmetic". You can look at the whites 1000 or 2000 years ago and vast majority don't do much arithmetic. "Haven't invented arithmetic" is your invention.
I was thinking of anumeric tribes, which are rare enough that we're not quite sure whether or not they exist. But many tribes seem at least partially anumeric, and I would be surprised if that were not predictive of the mean IQ of people currently in the tribe (setting aside the question of 'genetic IQ capability').
That most Romans did not do much arithmetic over the course of their lives doesn't say all that much about their ability to do arithmetic or their general intellectual capability; most modern Americans don't do much arithmetic (and, actually, they probably do less because they have more machines to do it for them).
Idang Alibi of Abuja, Nigeria writes on the James Watson affair:
An intriguing opening. Is Idang Alibi about to take a position on the real heart of the uproar?
Darn, it's just a lecture on personal and national responsibility. Of course, for African nationals, taking responsibility for their country's problems is the most productive attitude regardless. But it doesn't engage with the controversies that got Watson fired.
Later in the article came this:
This intrigued me for two reasons: First, I'm always on the lookout for yet another case of theology making a falsifiable experimental prediction. And second, the prediction follows obviously if God is just, but what does skin colour have to do with it at all?
A great deal has already been said about the Watson affair, and I suspect that in most respects I have little to contribute that has not been said before.
But why is it that the rest of the world seems to think that individual genetic differences are okay, whereas racial genetic differences in intelligence are not? Am I the only one who's every bit as horrified by the proposition that there's any way whatsoever to be screwed before you even start, whether it's genes or lead-based paint or Down's Syndrome? What difference does skin colour make? At all?
This is only half a rhetorical question. Race adds extra controversy to anything; in that sense, it's obvious what difference skin colour makes politically. However, just because this attitude is common, should not cause us to overlook its insanity. Some kind of different psychological processing is taking place around individually-unfair intelligence distributions, and group-unfair intelligence distributions.
So, in defiance of this psychological difference, and in defiance of politics, let me point out that a group injustice has no existence apart from injustice to individuals. It's individuals who have brains to experience suffering. It's individuals who deserve, and often don't get, a fair chance at life. If God has not given intelligence in equal measure to all his children, God stands convicted of a crime against humanity, period. Skin colour has nothing to do with it, nothing at all.
And I don't think there's any serious scholar of intelligence who disputes that God has been definitively shown to be most terribly unfair. Never mind the airtight case that intelligence has a hereditary genetic component among individuals; if you think that being born with Down's Syndrome doesn't impact life outcomes, then you are on crack. What about lead-based paint? Does it not count, because parents theoretically could have prevented it but didn't? In the beginning no one knew that it was damaging. How is it just for such a tiny mistake to have such huge, irrevocable consequences? And regardless, would not a just God damn us for only our own choices? Kids don't choose to live in apartments with lead-based paint.
So much for God being "just", unless you count the people whom God has just screwed over. Maybe that's part of the fuel in the burning controversy - that people do realize, on some level, the implications for religion. They can rationalize away the implications of a child born with no legs, but not a child born with no possibility of ever understanding calculus. But then this doesn't help explain the original observation, which is that people, for some odd reason, think that adding race makes it worse somehow.
And why is my own perspective, apparently, unusual? Perhaps because I also think that intelligence deficits will be fixable given sufficiently advanced technology, biotech or nanotech. When truly huge horrors are believed unfixable, the mind's eye tends to just skip over the hideous unfairness - for much the same reason you don't deliberately rest your hand on a hot stoveburner; it hurts.