It is said that the University of Bristol once asked all its departments to come up with a mission statement. One member of the philosophy department, so I am told, suggested "Analysing concepts in the Somerset and Avon region". I don't think it was adopted, but it does bring out an important aspect of philosophy: one thing we do is analyse concepts.

As a political philosopher, I am sometimes asked to help analyse concepts that are fundamental to our practical political life. Social justice used to be the thing. Once I was asked to join in a two-day workshop on welfare state reform: on the first day we would analyse what social justice meant; on the second we would apply it to real life to work out how to make our society just. And on the third day, presumably, we would rest.

These days, social justice has taken a backseat to the rather more bloodless notion of fairness. This government, to its credit, wants to be fair. Firm, but fair. Whether it succeeds on either count is a topic for other pages of this newspaper.

My first request to deliver a talk on fairness came from a committee struggling with a government brief on social care for the elderly. "We wanted to come up with a fair scheme, so we had first to decide what fairness meant," the committee chair told me. "We thought that would be the easy bit, but we got into a bit of a tangle."

Is it odd that a committee of highly intelligent and accomplished grownups got confused about the notion of fairness, when young children can handle the concept with ease? Or rather, should we say children have little trouble with the concept of unfairness? Much in life is unfair: almost none of it is fair. Except, apparently, recent government policy.

Having accepted the invitation to come and talk about fairness, I then had a few anxious weeks trying to work out what to say: what is fairness? The problem is well illustrated by the philosopher and Nobel prize-winning economist Amartya Sen. He sets out the example of three children who are squabbling about a flute. One made the flute, a second is by far the best at playing it, and the third has no other toys. What is the fair answer to the question of who should have it?

Our difficulty is that there are several different plausible conceptions of fairness, and they can point in different directions. To take just two: one prominent idea is that fairness needs some sort of reciprocity; getting back out what you have put in. This is related to ideas of desert. A second idea is that fairness has to be responsive to need: those in greatest need should have first claim. However, as the 19th-century Austrian theorist Anton Menger observed, these highly intuitive ideas can conflict. As long as we have a society where some are not able to work, then in order to meet need, the productive can't keep all they have produced.

In consequence, many schemes can be justified as being fair according to one view of fairness. But from another, they can be unfair. As a result, we cannot settle the debate about whether something is the right thing to do simply by insisting it is fair. The chances are, it can also be described as unfair.

What can we do? The best solution I know comes from the work of the American philosopher John Rawls, who proposed the idea of the "veil of ignorance". Where there is a dispute about fairness or justice, Rawls asks you to consider how you would want the situation resolved if you didn't know your role in it.

For example, in considering welfare reform, you need to ask what system you would want in place if you didn't know whether you were taxpayer or claimant. This may not lead to universal agreement, but it at least requires each of us to consider carefully how everyone would be affected.

And this is why, for example, it is perfectly reasonable to ask a politician whether he or she could live on the lowest level of benefits.

Jonathan Wolff is professor of philosophy at University College London and dean of arts and humanities

Guardian