Do we really want more social mobility?
What would it take to give every child in the UK a fair chance to succeed? What does that kind of equality of opportunity even look like?
I debated that question on Start the Week with four people who had plenty to say on the subject. What struck me, most, was how little the debate has changed in the past 60 years.
David Kynaston's latest volume of postwar social history, "Modernity Britain" covers the last few years of the 1950s, when the word "meritocracy" was first being heard - along with CND, the Today programme and Bruce Forsyth.
As he reminded us, people were ambivalent about the move to a "meritocracy" even then; an ambivalence flagged up very clearly in Michael Young's classic book on the subject, published in 1958.
But everyone did claim to want greater social mobility, and the confident post-war planners thought they had the answer in the form of tower blocks and the 11-plus.
Disadvantaged families would be turfed out of the slums and put into high-rise flats (as Kynaston writes, usually over the loud objections of the families themselves).
And, those who did well on the day of that crucial exam would get the chance to improve their lot in life with a grammar school education.
Of course, things were not so simple, and by the 1960s, both the tower block and the grammar school were in retreat. But progress on social mobility continued, at least until the 1970s.
After that, the evidence suggests that social mobility stalled; a child from a poor background was no more likely to move up the social ladder than in the previous generation. In fact, some of the (mixed) evidence on this suggests that social mobility actually fell.
When you talk about the reasons for that lack of progress, the debate always seems to gravitate to the loss of grammar schools in many parts of the country, and the advent of comprehensives.
But neither Kynaston nor the others on the programme thought the evidence for that was clear-cut. In fact, we had a spirited defence of comprehensives from the Independent columnist Owen Jones and the novelist Zadie Smith.
Smith writes vividly about the way school, background and postcode combine to shape people's life chances in the corner of London she grew up in, in her latest novel NW.
Neither she nor Owen Jones liked the assumption hidden in all the talk about "social mobility" and providing "ladders out" - that the working class was always and everywhere something people should want to escape from.
In NW, the character who has "escaped" her background to become a barrister is pretty miserable. She missed the communal experience on offer in the community in which she grew up.
This gets us to a larger point, which is that when we talk about wanting more social mobility, we are often not really talking about making it easier for some to go up and others to fall. We are talking about what I mentioned at the start: Giving every child a fair chance to realise their potential (whatever that means).
As David Willetts reminded us on the programme, it's not just a problem for society if people are getting trapped at the bottom, it's bad for the economy as well. We need all the talents we can get.
But, it strikes me there is a very good reason we are still talking about this problem so many years after those optimistic social engineers of the post-war era thought they had it cracked.
The problem is most people - and certainly, most middle class people - only want "equal chances" for everyone else's children. Deep down, they'd rather like their own children to get a leg-up.
As Willetts spelled out in his book, "The Pinch", the baby boomers have been especially good at carving out the best opportunities for themselves and their children. They also had an added, structural advantage, that they came of age in an era when the economy was losing low skilled, blue collar work and growing the middle class.
Put simply, there were more people going up than going down.
That is no longer true. In fact, in Britain and many other advanced economies the change is often going the other way. In that sense, it is almost a matter of arithmetic that upward social mobility - narrowly defined as the capacity to move up from one social class to another - should have declined since the 1970s.
There are simply fewer "good" jobs for working class people to move into.
So, there may be structural reasons why social mobility has not progressed as far as people might have hoped, back in the late 1950s.
But one conclusion you might also draw from our post-war history is that British voters and policy makers may care about advancing social mobility, but they care about other things more - particularly the freedom for parents to help their children.
The freedom to send your child to a private school has always been protected. You can also give them a deposit to get onto the housing ladder, and leave them a tidy sum when you die.
Neither Labour nor Conservative governments have messed with those things - for very good reasons. But, as long as families can do all of these things, it's pretty difficult for the government or anyone else to level the playing field.
Successive governments have also encouraged the empowerment of women in this period. Yet, as David Willetts has pointed out, this has probably inadvertently raised income inequality and cut social mobility, because well educated women marry other well educated men and take jobs that might otherwise have gone to upwardly mobile working class men.
That doesn't mean that feminism was a mistake (!) It does suggest that empowering them has had consequences that have partly come through in reduced social mobility.
It's a matter of judgment whether successive governments could or should have done more to increase life chances at the bottom, or improve social mobility.
Clearly there are uncontroversial ways to approach that goal, like investing in early years education, which are supported by all parties and do not get in the way of every parents' desire to help their kids.
But when push comes to shove, in a world of hard choices and competing priorities, the lesson of the past 50 years would seem to be that British voters and policy makers do not have much desire to put social mobility first.