The subject of inequality has come back to nag at our consciences and baffle our political energies. Of course, it never really went away. Ever since the Second World War, in the guise of equality of opportunity, it has been the guiding motive of successive British governments. The general sense of a shared mission led to something dangerously close to complacency. We were slowly moving in the right direction and the only argument was about the average speed and right time to change gear. Now we are not so sure of ourselves. The statistics tell us that social mobility has more or less ground to a halt. Incomes seem to be polarising and our society is divided into what I call ‘uppers’ and ‘downers’: the former full of confidence and looking to the future, the latter desperately trying to cling on to what little they have got. Behind the statistics we glimpse the formation of a demoralised underclass, deprived in both cultural and material terms, and a good deal larger than we hoped.

Inequality is tricky terrain, rather like parts of a First World War battlefield: a swamp sown with unexploded bombs and crossed by ancient trenches; some now crumbling and unoccupied, others still fiercely defended. Arguments about equality have gone on so long, and aroused such fierce feelings, that anyone venturing into this particular no-man's land needs to tiptoe. Much of the confusion is due to the assumption shared by many of the combatants that equality and inequality are simple and easily defined concepts. To begin to untangle the muddle, I suggest that we divide inequality into five rough types:

• • political equality, in which I include civic equality and equality before the law;

• • equality of outcome or result, by which I mean primarily equality of income and wealth;

• • equality of opportunity, these days often called equality of access or of life chances;

• • a less examined idea, equality of treatment, which can be taken to include or at least help to generate equality of agency and responsibility; and

• • something that is not often recognised as a kind of equality at all, equality of membership in society.