However the coins are counted in the public spending cuts now facing the country, higher education is going to be one of the most affected sectors. Cuts in public subsidy - only partly compensated for by rises in student fees - will change the shape of universities and their purpose accordingly. For example, we can expect to see some, perhaps many, humanities departments being closed as part of the effort to keep science and vocational studies funded, even though these latter, unlike the humanities, will retain some public subsidy because of their importance to the economy.

Add to this how increases in tuition fees will not only fail to compensate fully for the cuts but will act as a brake on student recruitment, too, and the net impending effect will be a shrinkage in higher education, with the greatest shrinkage in the humanities.

Some will say that too many have been going to university anyway, with a concomitant lowering of standards and the introduction of too many "Disneyland degrees". This is true. They will add that many of these students should have gone into practical training, such as was provided by the polytechnics before they were misguidedly changed into universities. This is also true. Yet the ambition to educate more people to a high level, to meet not just the economy's needs but those of a complex society by enriching the lives of its individual members, was always a good one. What we see in the cuts is an abandonment of that ambition in favour of economic imperatives alone.

As change is now inevitable, let us take this opportunity to review the question of what higher education is for. Universities are hybrid entities that, since the adoption of the Humboldtian model of combined teaching-and-research institutions, have served a number of different purposes, many of them extremely important. But at least two kinds of confusion have got in the way of a clear grasp of some of those purposes. One is the mistake of trying to model the academic life of the humanities on that of the sciences. The other is a distorted view of what society stands to gain from advanced study.

First, note that everything that goes by the name of education is a mixture of training and education proper, the latter being the cultivation of intellectual power and sensitivity in conjunction with widened horizons of ideas about life and the world. Training is just what it implies: the acquisition (and practice) of skills and bodies of knowledge pertinent to their exercise.

One can construct a rough grid in which, in the vertical dimension, training progressively yields to education as pupils mature, while in the horizontal dimension, the balance of training over education is greater at the applied-science end of the spectrum, the opposite being the case at the other, literary and philosophical, end.

The key word there, however, is "balance". Engineers and biochemists can benefit from thinking about ethics and politics (they might find themselves working in the oil industry in developing countries where already vulnerable lives might be adversely affected by what they do). In the other direction, literary scholars can benefit from training in logic and the social sciences. Accordingly, at each vertical and horizontal limit of the grid, both training and education are necessary. To fail to explain to someone the point of being trained in a skill is to halve its value, while to invite people to reflect and discuss if they know little and cannot reason is futile.

But are engineers taught ethics? Are students of literature schooled in logic? This is not a question of C P Snow's "two cultures" - the abyss separating science from the humanities - though it goes without saying that this is a vast problem all on its own. It is instead the more modest and fundamental question of the proper mixture of training and education that advanced study should deliver.

One reason why the two sides of universities barely speak to each other is that there is no time for it: degree courses are too short. Three years is not enough for an advanced education; neither does it suffice for professional or scientific training, which mostly requires postgraduate study or post-university professional qualifications. We are now contemplating two-year degrees as a cheap option. Almost all universities elsewhere in Europe (including Scotland) - engaged in the Bologna Process, which makes it possible for students to travel between universities, as they did in medieval times - have courses that last at least four years and see the English model as inadequate.

The second reason is that the humanities have fallen into the ghastly trap of mimicking the sciences in trying to be research disciplines in the same way. Science is fundamentally about research. University science is both about that and about equipping future researchers by ensuring that they have the knowledge and skills to do it. For instance, postgraduate students work in teams in laboratories under the supervision of established scientists and publish their work alongside them. Publishing papers in journals is the principal means of communicating results and, correlatively, is the main measure of career progress for scientists. No emerging scientist would wish to be taught by, or even work with, another scientist who does no research.

Literary theorists and philosophers (I do not include historians in the coming strictures) likewise do research and publish in journals. But the similarity is superficial. Alas, what I am now about to write will be unpopular with colleagues, even though I know that many of them will secretly agree. Most of what is published is inconsequential trivia: jargon-laden, narrow and speaking to a handful of other specialists. The problem is not that it is remote from practical utility - that is not an argument against it - but that it has scarcely any impact on enlarging and enriching the public mind and, too often, scarcely any more impact on the minds of students (save for the relatively few with scholarly or intellectual instincts).

In the humanities, it is not the research published in journals but the teaching and learning of the subjects at an advanced level that are the truly valuable enterprise. These are the things that help deliver to society the enlarged, informed and reflective minds it needs and provide individual students of the humanities with the potential for lives lived accordingly.

I do not mean that literature academics and philosophers should not be thinking and writing - far from it. By their own studies and thought, they have become gatekeepers of magnificent estates, into which they should usher as many people as possible, adding as they do so their own insights and reflections.

In the university setting, they have the opportunity and responsibility to make young minds feel free with the treasures of these estates, to encourage them to help themselves to as much as they can consume. But the tendency to lock the gates behind polysyllabic obscurities in imitation of scientific research is one reason why we have lost sight of the importance to society of a higher education in the humanities.

Society certainly needs engineers, physicists, doctors, computer specialists, biochemists and geologists. But it also needs its lawyers, journalists, politicians, civil servants, writers, artists and teachers - and it needs everyone on both sides of the science-humanities divide to be a thoughtful voter, good neighbour, loving parent, responsible citizen. In short, society needs to have a civilised conversation with itself about its values and about what is to be learned from the experience of mankind. Informed and reflective minds, educated by contact with the great traditions of thought and literature in civilisation, are a priceless asset: and this is what the humanities are about. To diminish this aspect of our social self-education is to do ourselves a great injury.

A C Grayling is professor of philosophy at Birkbeck, University of London. He will be taking part in the opening debate of this year's Inside Out festival at 7.30pm on 25 October at Senate House, Malet Street, London WC1.For more details, visit: insideoutfestival.org.uk/2010