'Universities, first and foremost, promote the "free pursuit of rational inquiry" as the route to understanding'

At a recent seminar I got into an argument with the chief executive of an organisation that awards vocational qualifications. It was about which certificates had value in today's labour market, and why.

Afterwards, half jokingly, I remarked that anyone listening should remember that we both had form - in the sense that we were both in the business of selling qualifications.

A mildly shocked politician in the group asked if that was all I thought universities were for. Of course it is not, but in a world of mass education it is hard to know quite what else they are for. All universities award qualifications (paid for from different sources - but paid for nonetheless). They enrol students who are above a certain age. Attendance is non-compulsory. What else?

Gordon Graham, regius professor of moral philosophy at Aberdeen University, has written the best recent discussion I know of on this question. In The Institution of Intellectual Values (which elaborates on his earlier monograph, Universities: the Recovery of an Idea ), Graham notes that "the word university does not mean what it did, hence the need for redefinition". He points out that the Humboldtian ideal of scholars devoted to intellectual inquiry for its own sake was different from, for example, the medieval ideal of a university. He goes on to argue that there never was a golden age when either of these existed in a fully formed and stable state. Yet ideals are important, because they allow us to evaluate trends and changes.

Today, governments increasingly emphasise one particular justification for university education - its contribution to economic growth. The funding of scientific research is discussed in terms of its immediate (for applied) and longer term (for pure) contributions to the economy. In the UK, we add a preoccupation with business links or direct collaborations with local companies.

However, the world's first great universities, as they emerged in 11th and 12th century Europe, had quite different aims. They were highly practical, training professionals who went out into society. But the subject with the highest status was theology and while universities produced lawyers and diplomats, their primary concern was with souls. If you find it self-evident that people have souls that can be lost or saved and that graduate Christian priests offer an effective means to salvation, then a university's most valuable purpose is to help save souls.

As this shows, what determines the nature of higher education institutions is less the trade-off between practical training and the pursuit of pure knowledge than between competing ideas of what is valuable. Graham's book discusses the inadequacy of appeals to "knowledge for its own sake" to justify universities' existence or to fund courses on their supposed relevance to the job market. As he points out, plenty of knowledge is quite valueless and is agreed to be such by most. Equally, "any piece of valueless knowledge... may become valuable" given the appropriate context and purpose. If you do not believe in God, revealed truths or the human soul, a great deal of knowledge - which to others is beyond price - will appear to you valueless. If you believe the only legitimate purpose for societies is to amass consumer goods and fight disease, then the role you envisage for university education will be circumscribed accordingly.

Graham sees the promotion of understanding as an important end in itself.

Just as we are concerned to ameliorate human suffering and physical hardship, so too we should wish to "ameliorate the human condition from the point of view of ignorance and misunderstanding". This is not, he emphasises, a novel or dramatic conclusion; on the contrary, it echoes the ideals of the very first higher education institutions, even though we mostly have very different ideas about the knowledge and principles of inquiry involved. It does, however, provide a basis for arguing that universities, first and foremost, promote the "free pursuit of rational inquiry" as the route to understanding.

This will not be the only thing universities do or the only criterion for deciding what - and how - we should teach. Nonetheless, it is an essential and defining characteristic. A society that does not accept this as important will not have universities in Graham's sense of the word.

Moreover, because autonomy is a necessary condition for such inquiry to be institutionalised, it is, Graham argues, central to the idea of a university.

All this seems to me to underline why it was lunacy to become totally dependent on the state. It brings us back to qualifications and degrees.

These must come into the definition somewhere, since without them, and without students paying towards them, how could we preserve any autonomy at all?

Alison Wolf is Sir Roy Griffiths professor of public sector management at King's College London.