Not long ago I returned to my old university to give a talk as part of its careers programme. Perhaps inevitably, the question was asked: "What do you know now that you wish you had known before you embarked on your working life?" My answer was that you need to have the confidence to succeed.
I used to hold the unconscious assumption that people who write books, publish magazines or offer their opinions in newspapers like The TESS were a breed apart. It took me a long time to realise that they were no different from me and that with effort and application, I too could join their ranks.
After the talk one student came up to me and said that my words had struck a chord. He too felt as though there was a locked door separating him from some professional worlds. How, he asked, had I overcome that feeling? Before answering, I put a question to him: "What kind of school had he been to?"
I was not surprised to hear that it had been his local state comprehensive.
The reason I expected this answer is that I have come to believe the most valuable thing private education instils is social confidence: the belief that the world is full of opportunities and that you are able to take advantage of them. People educated in the state sector don't often leave school with this implicit self-belief.
This confidence gap seems to be one of the most important and unnoticed consequences of our two-tier education system. How do private schools do it ? In part, their success may be a product of their intake. Children from affluent, middle-class homes tend to be more sure that the world is their oyster than their working-class peers.
But that isn't the whole story. One important factor is the central role that clubs and societies play in independent schools. These are usually run by students, who elect presidents, treasurers and other officers.
Clubs are a secret ingredient in the independent sector's success. They foster the initiative of pupils. Working on a committee to organise events empowers the students and shows them that if they want something they can do it. In short, they build confidence that opportunities are there to be taken advantage of.
Of course, some state schools replicate this culture. But they are hindered by a lack of resources, teacher time and an absence of a tradition of this kind of club culture.
But, if having a thriving community of student societies which reflects the different interests of students is one of the major advantages of independent schools, then the opportunity is there for the state sector to follow their example.
To do this would not require large sums of money. The Government could choose to allocate a relatively small amount of money for each school to spend on student-run clubs and societies, whose theme could be on anything the students themselves wanted to pursue.
To give, say, pound;200 core funding, to societies which enrolled a minimum number of members, would enable the club to pay expenses of visiting speakers, subsidise trips or purchase equipment. Of course, that would not prevent the societies trying to raise more money or charge subs, if they needed it.
To encourage schools to build up this culture, uptake of the scheme should be one measure of school performance. That would go some way to correcting the current imbalance by which test results are credited with disproportionate importance.
We cannot expect teachers to pick up the extra burden of organising these clubs. They could be largely student-run, with teachers only required to approve key decisions. And schools should draft in local expertise. Parents and members of the community would be prepared to help a club centred on their skills or interests.
I am perhaps optimistic that this modest innovation could make a real difference not only to students' experience of school but to their future prospects. It could bring about a shift in mindset, so students stop seeing school as being all about onerous burdens and start seeing it as a place of opportunity. It can also plant that all-important mental seed: the realisation that with effort, we all have the ability to make things happen. It is not just other people who succeed.
Dr Julian Baggini is editor of The Philosophers'