Boris Johnson says (pdf):

It is surely relevant to a conversation about equality that as many as 16% of our species have an IQ below 85, while about 2% have an IQ above 130.

It might be relevant, but not in the way he intends.

The fact that 16% have IQs below 85 tells us not about people, but about the way standard IQ tests are constructed. They are designed so that it's always the case that 16% have a sub-85 IQ. This doesn't mean that IQ is fixed; the Flynn effect tells us it isn't.

However, whilst the distribution of IQs is fixed, the distribution of income isn't. The share going to top incomes - which I think is the relevant one in this context given Mr Johnson's talk of the 2% with IQs above 130 - shows a big U-shape over the last century.

This simple juxtaposition tell us that IQ alone doesn't much influence inequality; something that doesn't change can't explain something that does.

Of course, it could be that what's changed is the payoffs to IQ. The collapse in demand for unskilled workers in the west since the 1970s and rise in "winner-take-all" markets might mean that low-IQ is now penalized more than it was in the 60s and 70s, whilst a high IQ reaps bigger rewards.

Whilst these trends are undoubtedly important, I'm not sure they are strongly related to IQ. The correlation between IQ and incomes is low; many bosses, remember, fail basic maths. And insofar as there is a correlation, it is due in part to poverty causing low mental functioning and IQ tests favouring richer people's minds rather than to IQ causing income. In implying otherwise, Mr Johnson seems to be making that common error of the rich, of confusing success and merit.

But let's assume all this is false, and there were a link between IQ and inequality. Would this then mean inequality is tolerable? Not at all, for two reasons.

First, a link between IQ and income does not - in itself - tell us anything about the justice of a social system. If a dictator allocated jobs according to IQ, or if high-IQ people were better at stealing from others, there'd be a strong link between IQ and income. But this wouldn't mean the systems were just.

Secondly, a person's IQ is (largely) beyond their control. And one common principle of justice is that people should not suffer because of things they cannot control. If you think low IQ causes poverty, therefore, you might well reasonably think there's a strong case for redistribution. As John Rawls said, the distribution of talent is "arbitrary from a moral point of view":

There is no more reason to permit the distribution of income and wealth to be settled by the distribution of natural assets than by historical and social fortune. (A Theory of Justice, p74).

Sure, Rawls might be wrong. But this should be argued for - and Mr Johnson doesn't do this.

In claiming that IQ is relevant to a conversation about equality, then, Mr Johnson is wrong empirically. And even if he were right, IQ would be relevant in the opposite way from which he intends - because inequality of IQ might actually justify more egalitarian policies, and not an acceptance of inequality.