I don’t know if Charles Clarke offered any sage advice to Ruth Kelly when she took over his old job, but if he did I somehow doubt he would have quoted Plato’s line: “The object of education is to teach us to love what is beautiful.” Yet in several ways, today’s educational orthodoxies owe a great unacknowledged debt not just to Plato, but to many other great thinkers of the past.

Plato’s most revolutionary idea was that education was the business of the state. When you consider that it was only in the last century that widely available (let alone compulsory and universal) state-provided education became the norm, you can begin to see how startling Plato’s proposition must have seemed to the ancient Athenians.

What is perhaps equally remarkable is how uncontroversial the idea is now.

We remain deeply sceptical and cynical about the motives and competencies of governments, yet Ivan Illich’s plea to “deschool” society in the 1970s found its only popular echo in a Pink Floyd song, in which a choir of unpaid children sang “we don’t need no thought control” with a disregard of good grammar that either supported or undermined their point, depending on how you look at it.

State-run education has not always been so blithely accepted as a good. The women’s rights pioneer Mary Wollstonecraft wasn’t a mad conspiracy theorist, but she recognised that education would reflect the cultural norms of the day. If these norms were defective, the education system itself would help perpetuate injustice.

“Till society be differently constituted,” she wrote, “much cannot be expected from education.”

Similar fears persist in modern times, from left-wing outrage in the later 20th century about schools that made girls study home economics while less able boys took maths and sciences, to more recent right-wing complaints about a left-wing teaching profession indoctrinating children with “politically correct propaganda”.

Education has also been attacked for being intellectually harmful. “Men are born ignorant, not stupid,” said Bertrand Russell. “They are made stupid by education.”

He went so far as to say that “education has become one of the chief obstacles to intelligence and freedom of thought.” Whether his complaint still holds today is made more doubtful by his observations of what actually happens in schools. Is there a teacher in the country who would now agree with Russell that “passive acceptance of the teacher’s wisdom is easy to most boys and girls”? Russell thought this “disastrous”; we might think it laughably implausible.

Perhaps the most difficult philosophical question about education is what can and should be taught. For Plato, teaching people to “love the beautiful” meant helping them to recognise what is both good and true. This is a moral as well as an intellectual matter.

His intellectual heir, Aristotle, disagreed. “Intellectual virtue owes both its birth and its growth to teaching,” he said, “while moral growth comes about as a result of habit.” In other words, you can’t teach people to be good. Rather, they have to become good by acting well, so that goodness infuses their character. Again, the debate between Plato and Aristotle still rages today, for example, in arguments about the scope and ambitions of the personal, social and health education (PSHE ) and citizenship curricula.

Oscar Wilde said that “Nothing that is worth knowing can be taught” and, in a very real sense, Plato agreed. It was his view that everything we know we know from birth, and what we call learning is really a process of recollection. It’s an extreme version of the more familiar idea that learning has to come from within and knowledge cannot simply be inserted into the learner’s brain from without. So Lessing, two millennia after Plato, wrote, that education gives a man “that which he could get from within himself, only quicker and more easily”.

The most influential expression of this broad idea came in Rousseau’s ‘Emile’, in which he developed the idea that education - in keeping with the meaning of its Latin root ‘educere’ - is a process of drawing out from the learner. Rousseau is often called the father of child-centred learning. But the kind of education he recommended was far removed from the soft, mollycoddling image of its alleged ancestor.

For Rousseau, education needs to toughen us up. “Thetis, to make her son invulnerable, plunged him, according to the fable, in the water of the Styx,” he wrote. The point of the allegory is that our duty to our children is to “open their pores to ills of every sort to which they will not fail to be prey when grown.”

Alfred North Whitehead once wrote that “The safest generalisation that can be made about the history of western philosophy is that it is all a series of footnotes to Plato.” That certainly seems to be the case in the philosophy of education. For once, at least, the footnotes are as interesting as the main text.

Julian Baggini is the author of What’s It All About? Philosophy and the meaning of Life (Granta)