Apologising today for Britain's involvement in the slave trade two centuries ago would be a futile cosmetic act more about contemporary PC gesture-politics than the real lessons of history. And these have profound lessons to teach.

For one thing, every one of us is descended from both slaves and slave owners, as we would find by looking far enough back into history. With few exceptions all societies have employed slavery in some form, from the classic galley slave chained to his oar to the bonded serf tied to the land, involving majorities of the populations then existing. So accepted was slavery in the ancient world that even Aristotle claimed it as part of the natural order of things. Defeat in war meant inevitable enslavement for everyone, women and children included, who was not killed; no one was exempt.

Who then should apologise to whom? History emphatically says: all of us to everyone else, and all of us to ourselves. That empties the very idea of meaning. But it should not distract us from a far more important, indeed shocking, fact, which is that today's slavery problem is vastly greater than at any time in history.

The United Nations calculates that there are at least 12.3 million slaves today, comprising those in forced labour, bonded labour, child labour, trafficked prostitutes and sweated pittance-wage labour. Most of them are in Africa, south Asia and China, and many of them are in slavery because of the developed world's insatiable demand for the cheapest possible manufactured goods.

The UN figurenearly equals the number of Africans sold by their own fellow-Africans and Arab slavers to Europeans in the four centuries of the colonial slave trade, begun by the Portuguese in the 15th century, and participated in by Britain for two centuries, until Parliament in London abolished the trade in 1807. In these facts lie further reasons for not engaging in the empty gesture of historical apology.

One is that Africans enslaved Africans, and the worst (the most extensive and brutal) slavers were Arabs. Who then should be apologising most? Another is that we British ended the slave trade, and by that means helped eventually to end American slavery too. If there are to be rites of apology, how about rites of thanks too?

Apology is an important thing when made by actual perpetrators of wrongs to their actual sufferers. Europeans and Americans alive today are not slave traders or slaves. Some descendants of slaves blame their present difficulties on the past, and sometimes can be right to do so. If the mere word "sorry" really could solve problems that are long-term effects of history, how quick and easy that would be. But it is only real actions that can do this, just as with today's massive slavery problem: and that is why we should be focusing seriously on the latter, and not distracting ourselves with cosmetic gestures.

A C Grayling is professor of philosophy at Birkbeck College, University of London. He was due to chair the debate last night at the British Empire and Commonwealth Museum in Bristol about whether the city should apologise for its involvement in the slave trade