What Blair means by "unthinkable" is unthinkable to the Labour party. The thoughts are actually all too familiar, mainly from the publications of right-wing think-tanks. Unthinkable left-wing thoughts - the sort that could enthuse social-democratic egalitarians like myself - do not usually get a hearing.
But there are exceptions. One is the idea, about which I have written before, that every school or tertiary college in the country should be allocated a quota of places, awarded to its highest-performing pupils, at the Russell group of universities. This has been given an airing in the consultation report, published last month, of a taskforce on university entrance under Professor Steven Schwartz, vice-chancellor of Brunel University.
Where does this idea come from? From America, you will probably be amazed to hear. You may be even more amazed to learn that those heartland states of the Bush family, Texas and Florida, are in the forefront. In Texas, for example, students in the top 10 per cent of their high school are entitled to a place at one of the state's elite universities.
Researchers at Harvard have found that, far from lowering standards, these students do better on their courses. They are also less likely to drop out from university than students who are admitted conventionally on high scores in the scholastic aptitude test.
What the scheme has not done is to increase ethnic and social diversity in the universities. And commenting on the Schwartz report, the heads of some inner-city comprehensives here have suggested that the main beneficiaries could be children from well-heeled backgrounds who attend schools where most of their classmates are poor.
This does not worry me at all. I think it is nearly impossible to design any university admissions system that the middle-classes will not manage to exploit to their advantage.
Universities could design a points system that gave as much weight to low socio-economic background as it did to high A-level scores, reasoning that somebody from a deprived home has to run harder to reach the same standard.
But socio-economic status, though a useful tool for analysing large groups, is unreliable when applied to individuals. I would not put it past some middle-class professionals to take a year's sabbatical and find temporary employment as road-sweepers while their offspring were applying to university.
To my mind, the main point of the "top X per cent" plan, as Schwartz calls it, would be not to broaden the class basis of university entry (though it should certainly have some effect) but to remove any incentive for parents to pay enormous fees for private education. Why send your child to Eton when that school can get only the same number of places at Oxford, Cambridge or Bristol as a comprehensive of the same size?
Instead of falling over themselves to get their children into posh schools, or into state grammars and high-performing comprehensives, middle-class parents would clamour for places at schools on the local council estate.
They would calculate that, in such schools, their children would have a better chance of making the top X per cent. The fee-charging sector would collapse overnight. We would have a chance of getting schools with the kind of social mix which, research tells us, would raise standards across the board.
As well as getting rid of educational segregation we might get rid of housing segregation and find the middle-classes buying up council tower blocks.
I do not think that any of this is in Schwartz's mind. But it is good to see that, in one area, the truly unthinkable thought can at least be mentioned.
Peter Wilby is editor of the New Statesman